..:;-3 .;:,::J ,~~::Itt. ,~ ~ ~ FLO OF FLUIDS ~ THROUGH ~ ~ VALVES, FITTINGS, AND PIPE ~ ~ By the Engineering Division ~ :z::::t .:::=:t ..~ --:.:=) Copyright, 1969-Crane Co; .~" All rights reserved: This publication is fully protected ~ by copyright and nothing that appears in it may be reprinted, either wholly or in part. without special permission . ;::::) . ~:::::) .=:,) :::::) :::::::) .=::.:) CRANE CO. :::::l Direct inquiries to 4100 S. Kechi. Aven'ue Chicago, Illinois 60632 Executive Office 300 Park Avenue New York, N.Y. 10022 ::::::l ~ ::::') Technical Paper No. 410 Price $2.50 PR1~TED (rw~lfth IN U. S. A. Print.ing-1972) ~"" TablE~ of Contents CHAPTER 2 •_ .....- -_ _. - - - - - CHAPTER Theory of Flow in Pipe page flow of fluid:$ Through Valves and Fittings Introduction ............... _.. _................................. _.... _....... _.. 1-1 Physical Properties of Fluids_....... _..._... __ .... __ ..... _. __ ..... Viscosity .. '" ...... _.............................. _. __ .. _._ ... _.. _.......... VV' eigh t density ....................................._........ _......... Specific volume .................. _..................................... Sped fic gra \' ity ......................... _.............__ ............... 1-3 1-3 Nature of Flow in PipeLaminar and TurbulenL ................. _.... _.... _... ___ ._ ..... _.. _. IIIean velocity of flow ..................... _.. _......... _........... Reynolds number ............. _.......... _........ ___ ....._........ _... Hydraulic radius ................................ _..................... 1-4 1-4 1-4 1-4 1-2 1-2 1-3 General Energy EquationBernoulli's Theorem ......................................... _._ ........ 1-5 Measurement of Pressure.......... _................................... 1-5 Darcy's FormulaGeneral Equation for Flow of Fluids..................... _.. 1-6 Friction factor _............... _......................................... 1-6 Effect of age and use on pipe friction .................. 1-7 Principles of Co:npressible Flow in Pipe.._............... Complete isothermal equation .. _............................. Simplifiedcornpressible flowgas pipe line formula .. _._ ..................... _....._......... Other commonly used formulas for compressib:.e flow in long pipe lines ........ _....... Comparison of formulas for compressible flow in pipe lines ............ _... _._ ....... Limiting flow of gases and vapors ....... _................ Introduction ...........__ .............................. _........................ Types of Valves and Fittings Used in Pipe Systems ........._..._.........__...................._...... 2-2 Pressure Drop Chargeable to Val ves and Fittings........... _...................................'" 2-2 Crane Flow Tests ............................ _.................. _........ ; 2-3 Relationship of Pressure Drop to Velocity of Flow.. _.... _............. _............................_... 2-7 Resistance Coefficient K, EquivalentLength LID, and Flow.Coefficient Cv ••••••-••••••••••••••••••••••••••••••• 2-8 Relationship of Equivalent Length LID and Resistance Coefficient K to the . Inside Diameter of Connecting Pipe ............. _............ Z-lC Valves with Gradually Increased Ports ....._..:........ _.. 2.:..iD Effect of End Connections ......._.... _..................... _... _... 2-1C Laminar Flow Conditions.. __........_.... _... _........._............ 2'-11 1-7 1-8 Basis for Design of Charts for Determining Equivalent Length, Resistance CoeffiCient, and Flow Coefficient_............................ _.. _........_............ 2_11 1-8 Resistance of Bends ............ _... _..... _............................,., 2-12 1-8 1-8 1-9 Steam-General Discussion ._.......................... _...... _.... 1-10 Other Resistances to Flow...._..............~ ......:_................ 2-13 Flow Through Nozzles and Orifices_...........____.......... 2..lJ Liquids, gases, and vapors ........................... _......... _Z-1:l Maximum flow of compressible:, fluids in a nozzle......................... _..... _... _.............. 22..15 Flow through short tubes .............._............_._ ......... 2-15 Discharge of Fluids Through Valves, Fittings, and Pipe Liquid flow ..._....._.......... _........... _._._ ....._.... _... _... _...... 2-15' Compressible' flow ._ ................_............. __...... _~ ........ _. 2~15 - - - - - - CHAPTER 3 Formulas cmd Nomographs for Flow Through Valves, Fittings, and Pipe 1 - - - - - - - CHAPTER 4 Examples of Flow Problems page Introduction ........... _............ _.............._................. _....... _ 3-1 Summary of Formulas.. _...................... _............ 3-2 to 3-5 Formulas and Nomographs for Liquid Flow V e10ci ty ...................................................... _......... _.....3-6 Reynolds number; friction factor for clean steel and wrought iron pipe.................... 3-8 Pressure drop for turbulent flow ..... _.: .................... 3-10 Pressure drop for laminar flow .......... _................... 3-12 Flow through nozzles and orifices................ _....... 3-14 ;f"~". 10 . -" '-~""-:l I . Formulas and Nomographs for Compressible Flow Velocity ............................................. _....................... Reynolds number; friction factor for clean steel and wrought iron pipe .................... Pressure drop .......................................................... _. Simplified flow f.ormula ............................................ Flow through nozzles and orifices ........................ I9';ge Introduction ._ .................................._........... _.................. _ 4'-1 Reynolds Number. and' Friction Factor for Pipe Other than Steel or Wrought Iron .................... 4-1 Determination of Valve Resistance in L, . LID, K, and Flow Coefficient C•........ _....................... 4-:2 Check Valves-Determination of'Size...................... 4--3 Laminar Flow in' Valves, Fittings, and Pipe, ......... _.. 4-4 Pressure Drop and Velocity in Piping Systems .............. __......................................... ~ Pipe Line Flow Problems ..... _...................................... 4-10 3-16 3-18 3-20 3-22 3-24 Discharge of Fluids from Piping Systems................ 4-:1'2 Flow Through Orifice MeterL .. _............................... 4-15 Application of Hydraulic'Radius to Flow Problems .......................................................... 4-:11 Determination of Boiler ~.apacity ..... - ... -... -............··· 4-:18 APPENDIX A ------------~----------- APPENDIX B Engineering Data Physical Properties of Fluids and Flow Characteri'stics of Valves, Fitfings, and Pipe page E-I Introduction page Introduction ............................................... ~.................. A-I Physical Properties of Fluids Viscosity of steam .................................. A-2 Viscosity of \vater ................................................ A-3 Viscosity of liquid petroleum products .............. A-3 Viscosity of various liquids ............................... A-4 Viscosity of gases and hydrocarbon vapors ...... A-5 Viscosity of refrigerant vapors .......................... A-5 Physical properties of water.. .................................. A-6 Specific gravity-temperature relationship for petroleum oils ....................... A-7 Weight density and specific gravity of various liquids ................................. A-7 Physical properties of gases ................................... A-8 Volumetric composition and specific gravity of gaseous fuels ........................ A-8 Steam-values of k .................................................. A-9 Weight density and specific volume of gases and vapors ............................... A-lO Equivalent Volume and 'Weight Flow Rates of Compressible Fluids.......................... B.,..2 Equivalents of Viscosity Absolute ............................................................ ;....... B-3 Kinematic ................................................;................ B-3 Kinematic and Saybolt UniversaL ......... :............ B-4 Kinematic and' Saybolt FuroL. ............................. B'-4 Kinematic, Saybolt Universal, . Saybolt Furol, and Absolute ............................ B-5 Saybolt Universal Viscosity CharL ......................... B-6 ! Equivalents of Degrees API, Degrees Baume, Specific Gravity, Weight Density, and Pounds per Gallon ................ B-1 ,I Steam Data Boiler capacity .....................................................:... B-8 Horsepower of an engine.......................................... B-8 Ranges in steam consumption by prime movers ................................................. B-8 Properties; saturated steam, saturated water _________ A-12 Properties; superheated steam ............................... A-16 Properties; superheated steam, compre,osed water ..... A-19 Vlow Characteristics of )zzles and Orifices Flow coefficient C for nozzles ................................. Flow coefficient C for square edged orifices ........................................ Net expansion factor Y for compressible flow ........................................ Critical pressure ratio, rc for compressible flow ........................................ A-20' A-20 A-21 A-21 Flow Characteristics of Pipe, Valves, and Fittings Net expansion factor Y for compressible flow through pipe to a larger flow area ........ A-22 Relative roughness of pipe materials and friction factor for complete turbulence ............A-23 Friction factors for any type of commercial pipe ............................ A-24 Friction factors for clean commercial steel and wrought iron pipe ........ A-25 Resistance in pipe due to sudden enlargements and contractions............ A-26 Resistance in pipe due to pipe entrance and exit.. ........................ A-26 Resistance of 90 degree bends .............................. A-27 Resistance of miter bends ....................:................. A-27 Types of valves (sectional ilJustrations) ............ A-28 Schedule (thickness) of steel pipe used in obtaining resistance of valves and tittings of various pressure classes ................ A-30 Representative equivalent length ( LID) in pipe diameters of valves and tittings .............. A-30 Equivalent lengths L and LID and resistance coefficient K .............................. A-31 Equivalents of resistance coefficient K and flow coefficient C,...................................... A-32 Power Required for Pumping..................................... B-9 Equivalents (General) Measure ...........................................................:........... vVeight ...............................................................:....... Velocity ...................................................................... Density ........................................................................ B-J 0 B::..! () B-IO B-IO Physical constants ................................................... 13-10 Temperature ............................................................... B-IO Pretixes ........................................................................ B-IO Liquid measures and weigh t3................................... B-11 Pressure and head ....................................................... B-II Four-Place Logarithms to Base 10............................ B-12 Flow Through Schedule 40 Steel Pipe Water .......................................................................... B-14 Air ................................................................................. B-15 Commercial Wrought Steel Pipe. Data Schedules 10 to 160 ................................................. B-16 Standard, extra strong, and double extra strong...................................... B-18 Stainless Steel Pipe Data Schedules 55, lOS, 40S, and 80S ............................ B-19 APPENDIX C page Bibliography C-l Nomenclature ........................................... 5ee next page 1 I 1 \ Nomendature---------·--~---Unless otherwise stated, all symbols used in this book are defined os follows: A a B C Cd Cv cross sectional area of pipe or orifice, in square feet cross sectional area of pipe or orifice, in square inches rate of flow in barrels (42 gallons) per hour flow coefficient for orifices and nozzles = discharge coefficient corrected for velocity of approach = Cd / " I-(do/d.)' discharge coefficient for orifices and nozzles flow coefficient for valves: expresses flow rate in gallons per minute of 60 F water with 1.0 psi pressure drop across valve = D d ,t !,, , t e / g H h f f r h, hL h", K k Lm M MR n P P' length of pipe, in feet equ;\'a:ent length of a resistance to flow, in pipe diameters length of pipe, in miles molecular weight univer~al gas constant = 1;44 exponent in equation for polytropic change .(p' \! ~ = constant) pressure. in pounds per square inch gauge pressure, pounds per square inch absolute (see page 1-5 for diagram showing relationship betu:een gauge and absolute pressure) p' Q q q' q'. q' • q .. , q .. individual gas constant I s s. T Q v pi (6q!:::.P) internal diameter of pipe, in feet internal diameter of pipe, in inches base of natural logarithm = 2.718 frictio:::! factor in formula hL =/Lv'/D2g acceleration of gravity = 32.2 feet per second per second total head, in feet of fluid static pressure head existing at a point, in feet of fluid total heat of steam, in Btu per pound loss of static pressure head due to fluid flow, in feet of fluid static pressure head, in inches of water resista:.'lce coefficient or velocity head loss in the formula, hL = KV'/2g' ratio of specific heat at constant pressure to specific heat at constant volume = cJ)/c~ L L/D R pressure, in pounds per square foot absolute rate of flow. in gallons per minute rate of flow, in cubic feet per second at flowing conditions rate of flow. in cubic feet per second at standard conditions (14.7 psia and 60F) rate of flow. in millions of standard cubic feet per day, MMsefd rate of flow. in cubic feet per hour at standard conditions ('4.7 psia and oaF), scfh rate of flo\\', in cubic feet per minute at flowing conditions rate of flow, in cubic feet per minute at std. conditions (14.7 pSia and 6oF), sefm v Va v v, Wi W Wa x Y Z AfR.'1 544/M Reynolds number hydraulic radius, in feet critical pressure ra[;o for compressible flo'.' specific gravity of liquids relative to wate:both at standard temperature (60 F) specific gravity of a gas relative to air = the ratio of the molecular weight of ct." gas to that of air absolute temperature. in degrees Rankine (460 + t) temperature, in degrees Fahrenheit specific volume of fluid, in cubic feet pc:-. pound mean velocity of flow, in feet per minute volume. in cubic feet mean velocity of flow, in feet per second sonic (or critical) velOCity of flow of a gas. in feet per second rate of flow, in pounds per hour rate of !low, in pounds per second weight, in pounds percent quality of steam = 100 minus pe, cent of moisture net expansion factor for compressible flow through orifices, nozzles, or pipe potential head or elevation above reference level, in feet Subscripts indicates orifice or nozzle conditions unless otherwise specified (I) indicates inlet or upstream conditions unless otherwise specified (2) . indicates outlet or downstream conditions unless otherwise specified (100) . refers to 100 feet of pipe (0) Greek LeHers L.lta f:" differential between two points Epsilon • absol ute roughness or effective height ot pipe wall irregularities, in feet Rho P p' weight density of fluid, pounds per cubic ft. density of fluid, grams per cubic centimeter Mu , J1. , v , v absolute (dynamic) viscosity, in centipoise absolute viscosity in pound mass per foot second or pou~dal seconds per sq foot absolute viscosity. in slugs per foot sec~mc: or pound force seconds per square 100! kinematic viscosity, in centistokes kinematic visc9sity, square feet per secon<.i 1 .1 Thec,ry of Flow ~ =» lin Pipe :;::;t ~ CHAPTER 1 .~ .::1 :::t =:I :::::t =:t '=3 The most commonly employed method of transporting fluid from one point to another is to force the fluid to flow through a piping system. Pipe of circular section is most frequently used because that shape offers not only greater structural strength, but also greater cross sectional area per unit of wall surface than any other shape. Unless otherwise stated, the word "pipe" in this book will always refer to a closed conduit of circular section and constant internal diameter. Only a few special problems in fluid mechanics .... laminar flow in pipe, for example .... can be entirely solved by rational mathematical means; all other problems require methods of solution which rest, at least in part, on experimentally determined coefficients. },,1any empirical formulas have been proposed for the problem of flow in pipe, but these are often extremely limited and can be applied only when the conditions of the problem closely approach the conditions of the experiments from which the formulas were derived. .=:3 :::.'.) =» ==i '=::) Because of the great variety of fluids being handled in modern industrial processes, a single equation which can be used for the flow of any fluid in pipe offers obvious advantages. Such an equation is the Darcy* formula. The Darcy formula can be derived 'rationally by means of dimensional analysis; howevrer, one variable in the formula . . . . the friction factor .... must be determined experimentally. This foimula has a wide application in the field of fluid mechanics and is used extensively throughout this paper. ·Thc Darcy formula is also known as the \Veisbach formula or the DarcyWcisbach formula; also, as the Fanning formula, sometimes modified so thal~ the friction factor is one-fourth the Darcy friction factor. 1-2 CHAPTER 1 - THEORY OF flOW IN PIPE CRANE Physical Properties of Fluids The solution of any flow problem requires a knowl- second and is equivalent to 100 centistokes. edge of the physical properties of the fluid being • • _ J.< (centipoise) handled. Accurate values for the properties affecting v (centlstokes) - '( ') p grams per cu b IC cm the flow of fluids ... namely, viscosity and weight density ... have been established by many authori- By definition, the specific gravity, S, in the foreties for all commonly used fluids and many of these going formula is based upon water at a temperature data are presented in the various tables and charts .of 4 C (39.2. F), whereas specific gravity used in Appendix A. throughout this paper is based upon water at 60 F. In the English system, kinematic viscosity has Viscosity: Viscosity expresses the readiness with dimensions of square feet per second. which a fluid flows when it is acted upon by an external force. The coefficient of absolute viscosity Factors for conversion between metric and English or, simply, the absolute viscosity of a fluid, is a system units of absolute and kinematic viscosity are measure of its resistance to internal deformation or given on page B-3 of Appendix B. shear. Molasses is a highly viscous fluid; water is comparatively much less viscous; and the viscosity The measurement of the absolute viscosity of fluids of gases is quite slY.all compared to that of water. (especially gases and vapors) requires elaborate equipment and considerable experimental skill. On Although most fluids are predictable in their vis- the other hand, a rather simple instrument can be cosity, in some, the viscosity depends upon the used for measuring the kinematic viscosity of oils previous working of the fluid. Printer's ink, wood and other viscous liquids. The instrument adopted pulp slurries, and catsup are examples of fluids as a standard in this country is the Saybolt Universal possessing such thixotropic properties of viscosity. Viscosimeter. In measuring kinematic viscosity with this instrument, the time required for a small Considerable confusion exists concerning the units volume of liquid to flow through an orifice is deterused to express viscosity; therefore, proper units mined; consequently, the "Saybolt viscosity" of the must be employed whenever substituting values of liquid is given in seconds. For very viscous liqUids, viscosity into formulas. In the e.G.S. (centimeter, the Saybolt Furol instrument is used. gram, second) or metric system, the unit of absolute viscosity is the poise which is equal to 100 centi- Other viscosimeters, somewhat similar to the Saybolt poise. The poise has the dimensions of dyne seconds but not used to any extent in this country, are the per square centimeter or of grams per centimeter Engler, the Redwood Admiralty, and the Redwood. second. I t is believed that less confusion concerning The relationship between Saybolt viscosity and units will prevail if the centipoise is used exclUSively kinematic viscosity is shown on page B-4; equivaas the unit of viscosity. For this reason, and since lents of kinematic, Saybolt Universal, Saybolt Furol, most handbooks and tables follow the same pro- and absolute viscosity can be obtained from the cedure, all viscosity data in this paper are expressed chart on page B-5. in centipoise. The ASTM standard viscosity temperature chart for The English units commonly employed are "slugs per liquid petroleum products, reproduced on page B-6, foot second" or "pound force seconds per square is used to determine the Saybolt Universal viscosity foot"; however, "pound mass per foot second" or of a petroleum product at any temperature when the "poundal seconds per square foot" may also be en- viscosities at two different temperatures are kno\\TI. countered. The viscosity of water at a temperature The viscosities of some of the most common fluids are given on pages A-2 to A-5. It will be noted that. of 68 F is: with a rise in temperature, the viscosity of liquids o.ol poise' decreases, whereas the viscosity of gases increases. I centipoise* = 0.01 gram per cm second lo.ol dyne second per sq cm The effect of pressure on the viscosity of liquids and perfect gases is so small that it is of no practical (0.000 672 pound mass per foot second interest in most flow problems. Conversely, the lO.OOO 6j2 poundal second per square foot viscosity of saturated, or only slightly superheated. I _ {o.ooo 0209 slug per foot second vapors is appreciably altered by pressure changes, as p., 0.000 0209 pound force second per square ft indicated on page A-2 showing the viscosity of steam. Unfortunately, the data on vapors are incomplete Kinematic viscosity is the ratio of the absolute vis- and, in some cases, contradictory. Therefore, it is cosity to the mass density. In the metric system, expedient when dealing with vapors other than the unit of kinematic viscosity is the stoke. The steam to neglect the effect of pressure because of [he stoke has dimensions of square centimeters per lack of adequate data. f , 1 1 .~ \ • Actually the viscosity of water at 68 F is 1.005 centipoise. ..:;;='3 "'J~ CRANE CHAPTER I - THEORY Of flOW IN PIPE ,;;:::3 Physical Properties of Fluids - .:::::J ..~ ":::=3 ~ ~ .~ ~ :==»~ '=::.t ::;:::::) =:3 Weight density, specific volume, and specific gravity: The weight density or specific weight of a substance is its weight per unit volume. In the English system of units, this is expressed in pounds per cubic foot and the symbol designation used in this paper is p (Rho). In the metric system, the unit is grams per cubic centimeter and the symbol designation used is p' (Rho prime). The specific volume V, being the reciprocal of the weight density, is expressed in the English system as the number of cubic feet of space occupied by one pound of the substance, thus; V = ::::;) :::::» ~::::) ":::::.') I p' ::.:::::) .::::) .::::) :.::::» ,~ "~ The variations in weight density as well as other properties of water with changes in temperature are shown on page A-6. The weight densities of other common liquids are shown on page A-i. Unless very high pressures are being considered, the effect of pressure on the weight of liquids is of no practical importance in flow problems. The weight densities of gases and vapors, however, are greatly altered by pressure changes. For the socalled "perfect" gases, the weight density can be computed from the formula; p = 144 P' f[T' The individual gas constant R is equal to the universal gas constant, AiR = 1544, divided by the molecular weight of the gas, R = In steam flow computations. the reciprocal of the weight density, which is the speCific volume, is commonly used; these values are listed in the steam tables shown on pages A-12 to A-19. A chart for de~ termining the weight density and specific volume of gases is given on page A-II. Specific gravity is a relative measure of weight density. Since pressure has an insignificant effect upon the weight density of liquids, temperature is the only condition that must be considered in designating the basis for specific gravity. The specific gravity of a liquid is its weight density at 60 F (unless otherwise specified) to that of water at standard temperature, 60 F. p Computations in the metric system are not commonly referred to in terms of specific volume; however, the number of cubic centimeters per gram of a substance can readily be expressed as the reciprocal of the weight density, that is; =:) ~ .~ 1544 M Values of R, as well as other useful gas constants, are given on page A-8. The weight density of air for various conditions of temperature and pressure can be found on page A-ID. continued S = p p any liquid at 60 F, l {unless otherwise specified! (water at 60 F) , ! I"! A hydrometer can be used to measure the specific gravity of liquids directly. Three hydrometer scales are common in this country .... the API scale which is used for oils .... and the two Baume scales, one for liquids heavier than water and one for liquids lighter than water. The relationship between the hydrometer scales and specific gravity are: For oils. S(60F/60F) I)!.; +deg.API For liquids lighter than water, S (60 F/60 F) 140 1)0 + deg. Baume For liquids heavier than water. S (60 F/60 F) 145 145 - deg. Baume For convenience in converting hydrometer readings to more useful units, refer to the table shown on page B-7 . The specific gravity of gases is defined as the ratio of the molecular weight of the gas to that of air, and as the ratio of the individual gas constant of air to that of the gas. S = R (air) _ M (gas) • R (gas) - M (air) :=} i j 1·4 CHAPTER 1 - THEORY Of flOW IN PIPE Nature of Flow in Pipe - CRANE Laminar and Turbulent. -.--"'-'-.-~---~------ '... Flgu .... 1~11 Figure 1 ~2 Laminor Flclw Actual photograph of colored Alamenfs being carried along undisturbed by a !.treom of water. Flow in Critical Zone, 8otw •• n Laminar and Transition Zones. At the critical velocity, the filaments begin to break up, indicating flow is becoming turbulent. A simple experiment (illustrated above) will readily show there are two entirely different types of flow in pipe. The experiment consists of injecting small streams of a colored fluid into a liquid flowing in a glass pipe and obsel-ving the behavior of these colored streams at different sections downstream from their points of injection. If the discharge or average velocity is small, the streaks of colored fluid flow in straight lines, as shown in Figure 1··1. As the flow rate is gradually increased, these streaks will continue to flow in straight lines until a velocity is reached when the streaks will waver and suddenly break into diffused patterns, as shown in Figure 1-2. The velocity at which this occurs is called the "critical velocity". At velocities higher than "critical"' , the filaments are dispersed at random throughout the main body of the fluid, as shown in Figure 1-3. i I , i ,1 1 I " The type of flow which exists at velocities lower than "critical"' is known as laminar flow and, sometimes, as viscous or streamline flow. Flow of this nature is characterized by the gliding of concentric cylindrical layers past one another in orderly fashion. Velocity of the fluid is at its maximum at the pipe axis and decreases sharply to zero at the walL At velocities greater than "critical", the flow is turbulent. In turbulent flow, there is an .irregular random motion of fluid particies in directions transverse to the direction of the main flow. The \'elocity distribution in turbulent flow is more uniform across the pipe diameter than in laminar flow. Even though a turbulent motion exists throughout the greater portion of the pipe diameter, there is always a thin layer of fluid at the pipe wall .... known as the "boundary layer" or "laminar sub-layer" which is moving in laminar flow. Mean velocity of flow: The term "velocity", unless otherwise stated, refers to the mean, or average, velocity at a given cross section, as determined by the continuity eq~;ation for steady state Row: v =3.. A =~ Ap ,= wV A Eq Clation J.. ' (For nomenclature, sec page preceding Chapter i) "Reasonable" veiocities for use in design work are given on pages 3-6 and 3-16. ....., ..... ,--" .~./ -~ '\~- . ,--..; ;-'< -:. ....:... . - Figur. 1.3 Turbulent Flow This illustrotion shows the turbulence in th" stream completely dispersing the, colored filaments 0 short distance downstream fro", the point of injection. Reynolds number: The work of Osborne Reynolds has shown that the nature of Row in pipe .... that is, whether it is laminar or turbulent .... depends on the pipe diameter. the density and viscosity of the flowing fluid, and the velocity of flow. The numerical value of a dimensionless combination of these four variables, known as the Reynolds number, may be considered to be the ratio of the dynamic forces of mass flow to the shear stress due to Viscosity. Reynolds number is: Re = Dvp Equation 1.. 2 (other forms of this equation; page 3-2.) For engineering purposes, flow in pipes is usually considered to be laminar if the Reynolds number is less than 2000, and turbulent if the Reynolds number is greater than 4000. Between these two values lies the "critical zone" where the flow .... being laminar, turbulent, or in the process of change, depending upon many possible varying conditions . . . . is unpredictable. Careful experimentation has shown that the lammar zone may be made to terminate at a Reynolds number as low as 1200 or extended as high ~s 40.000, but these conditions are not expected to be realized in ordinary practice. Hydraulic radius: Occasionally a conduit of non· circular cross section is encountered. In calculating the Reynolds number for this condition, the equivalent diameter (four times the hydraulic radius) is sub· stituted for the circular diameter. Use friction factors given on pages A-24 and A-25. RH = cross sectional flow area wctted perimeter This applies to any ordinary conduit (circular conduit not flowing full, oval, square or rectangular) but not to extremely narrow shapes such as annular or elongated openings, where width is small relatlvc to length. In such cases, the hydraulic radius IS approximately equal to one-half the width of the passage. To determine quantity of flow in following forll1ui,L q /hLD = o.o.n 8d'\j-jL the value of d' is based upon an equivalent ,li.Hl1<·:" of actual flow area and 4RI/ is substitute,! lor I) -:t:I CRANE :::a General Energy Equation Bernoulli's Theorem :::3 .:=:1 .=- The Bernoulli theorem is a means of expressing the application of the law of conservation of energy to the flow of fluids in a conduit. The total energy at any particular point, above some arbitrary horizontal :3 -:::8 - - - - l l -,- Energy Gfade Line hL r~ :::J -=3 2g --11--1- ~ ~ .:::1 :::::2' •.:::3 datum plane, is equal to the sum of the elevation head, the pressure head, and the velocity head, as follows: Z + 144 P P +~ =H 2g If friction losses are neglected and no energy is added to, or taken from, a piping system (i.e., pumps or turbines), the total head, H, in the above equation will be a constant for any point in the fluid. However, in actual practice, losses or energy increases or decreases are encountered and must be included in the Bernoulli equation. Thus, an energy balance may be written for two points in a fluid, as shown in the example in Figure 1-4. Note the pipe friction loss from point 1 to point 2 is hL foot pounds per pound of flowing fluid; this is sometimes referred to as the head loss in feet of fluid. The equation may be written as foHows: z, .::::1 :::I '·5 CHAPTER 1 - THEORY OF FLOW IN PIPE Arbitrary Horizontal Datum Place Equation ' ..3 ZI Figure 1 ~4 Energy Balance for TWI) Points ~n . a Fluid + 144 P , PI + 2i = 2 g Zz + I 44P, + 2~g + hL P, All practical formulas for the flow of fluids are derived from Bernoulli's theorem, with modifications to account for losses due to friction . By permission. from Fll1id Mechanics'> by R. A. Dodge and M.). Thompson. Copyright 1937; McGraw-Hili Book Company, Inc. ::::I ;:::]I Measurement of Pressure -=:I Any Pressure Above Atmospheric Figure 1-5 graphically illustrates the relationship between gauge and absolute pressures. Perfect vacuum cannot exist on the surface of the earth, but it nevertheless makes a convenient datum for the measurement of pressure. -::;3 ::::3 -:.::I ::::» :E v E At Atmospheric Pressure Level-Variable ~------~~--~~~~~~~~~~~~----"OJ + ,. ~ ::::::I ""II e tl .::.:3 -~ ~ E aro > Any Pressure Below Atmospheric ~ ct ~ ~ ::::a ~ "'" Absolute Zero of Pressure-Perfect Vacuum figure 1 ~5 Relationship B,atween Gauge and Absolul'e Pressures I~ I Barometric pressure is the level of the atmospheric pressure above perfect vacuum. "Standard" atmospheric pressure is 14.696 pounds per square inch, or 760 millimeters of mercury. Gauge pressure is measured above atmospheric pressure, while absolute pressure always refers to perfect vacuum as a base. Vacuum, usually expressed in inches of mercury, is the depression of pressure below the atmospheric level. Reference to vacuum conditions is often made by expressing the absolute pressure in inches of mercury; also millimeters of mercury and microns of mercury. *Ail sl/perlor ligures used as reference morle, reler to 'he Bibliography; see page C-f. CRANE 1 ·5 CHAPTER I - THEORY OF FLOW IN PIPE -- General Energy Equation Bernoulli's Theorem .~. The Bernoulli theorem is a means of expressing the application of the law of conservation of energy to the flow of fluids in a conduit. The total energy at any particular point, above some arbitrary horizontal ~ .---il-'"=~-- - - - - - ---11 -,- EC~Line HYdraulic Graoe L· Ine hL ----~~-+, 1."'2 2g -_!f.--J- >;~ ..~ + 144 P P +~ = ;zg H If friction losses are neglected and no energy is added to, or taken from, a piping system (Le., pumps or turbines), the total head, H, in the above equation will be a constant for any point in the fluid. However, in actual practice, losses or energy increases or decreases are encountered and must be included in the Bernoulli equation. Thus, an energy balance may be written for two points in a fluid, as shown in the example in Figure 1-4. Arbitrary Horizontal Datum Plane 4 Equation 1-3 Z, Figure 1 ..4 Energy Balance for Two Points in a Fluid - Z Note the pipe friction loss from point to point 2 is hL foot pounds per pound of flowing fluid; this is sometimes referred to as the head loss in feet of fluid. The equation may be written as follows: z, By permission, from Fluid Nfecnanics 1* by R. A. Dodge and M. J. Thompson. Copyright 1937; McGraw-Hili B:)()k Company, Inc . .- datum plane, is equal to the sum of the elevation head, the pressure head, and the velocity head, as follows: + 144P, + .EL = z. + 144P. + vi + hL P, 2 g p. 2 g All practical formulas for the flow of fluids are derived from Bernoulli's theorem, with modifications to account for losses due to friction. ~easurement of Pressure Any Pressure Above Atmospheric ~ .,.g _______ §r-__~At~Aft~mo~s~Dh~e~ric~P~r~es~su~r~e~Le~ve~I-~va~r~iab~le~____~ ~ co + ~ ~ ~ ~ '"II E B- ~ Any Pressure Below Atmospheric Figure 1-5 graphically illustrates the relationship between gauge and absolute pressures. Perfect vacuum cannot exist on the surface of the earth, but it nevertheless makes a convenient datum for the measurement of pressure . Barometric pressure is the level of the atmospheric pressure above perfect vacuum. "Standard'· atmospheric pressure is 14.696 pounds per square inch, or 760 millimeters of mercury. Gauge pressure is measured above atmospheric pressure, while absolute pressure always refers to perfect vacuum as a base. Absolute Zero of Pressure-Perfed Vacuum Figure 11-5 Relationship Berween Gauge and Absolute Pressures Vacuum, usually expressed in inches of mercury, is the depression of pressure below the atmospheric level. Reference to vacuum conditions is often made by expressing the absolute pressure in inches of mercury; also millimeters of mercury and microns of mercury. , I - I "'All supElrior figu,'es used as reference maries refer'o the Bibliography; see page C.J. II ~~ C~H~A~PT~E~R~l T~H~E~O~RY~O~F~Fl~O~W~IN~P~IP~E __________________________ ___ ________________________ ~C~R~A~N~E Darcy's Formula General Equation for Flow of Fluids Flow in pipe is always accompanied by friction of fluid particles rubbing against one another, and consequently, by loss of energy available for work; in other words, there must be a pressure drop in the direction of flow. If ordinary Bourdon tube pressure gauges were connected to a pipe containing a flowing fluid, as shown in Figure 1-6, gauge PI L would indicate a higher static pressure Figure 1 .. 6 than gauge p •. The general equlltion for pressure drop, known as , Darcy's formula and expressed in feet of fluid, is hL = fLv 2 /D 2g. This equation may be written to express pressure drop in pounds per square inch, by substitution of proper units, as follows: pf L ;~. l::.P = - - - 144 D 2g Equation 1-4 has lower limits based on laminar Rowand upper limits based on turbulent flow conditions. . At Reynolds numbers above approximately 4000, flow conditions again become more stable and definite friction factors can be established. This is imPortant because it enables the engineer to determine the flow characteristics of any fluid Rowing in a pipe, providing the viscosity and weight density at flowing conditions are known. For this reason, Equation 1-4 is recommended in preference to some of the commonly known empirical equations for the flow of water, oil, and other liquids, as well as for the flow of compl'essible fluids when restrictions previously mentioned are observed. If the flow is laminar (R, < 2000), the friction factor may be determined from the equation: f = (For other forms of this equation, see page 3-2.) The Darcy equation is valid for laminar or turbulent flow of any liquid in a pipe. However, when extreme velocities occurring in a pipe cause the downstream pressure to fall to the vapor pressure of the liquid, cavitation occurs and calculated flow rates will be inaccurate. With suitable restrictions, the Darcy equation may be used when gases and vapors (compressible fluids) are being handled. These restrictions are defined on page 1-7. Equation 1-4 gives the loss in pressure due to friction and applies to pipe of constant diameter carrying fluids of reasonably constant weight density in straight pipe, whether horizontal, vertical, or sloping. For inclined pipe, vertical pipe, or pipe of varying diameter, the change in pressure due to changes in elevation, velocity, and weight density of the fluid must be made in accordance with Bernoulli's theorem (page 1-5). For an example using this theorem, see page 4-8. , '1 Friction factor: The Darcy formula can be ration'ally derived by dimensional analysis, with the exception of the friction factor, f, which must be determined experimentally. The friction factor for laminar flow conditions (R, < 2000) is a function of Reynolds number only; whereas, for turbulent flow CR, > 4000), it is also a function of the character of the pipe wall. 64 R, = 64 Il, D vp = 64 Il d vp 124 If this quantity is substituted into Equation 1-4, the pressure drop in pounds per square inch is: . IlLv l::.P = 0.000668 ( j ' l Equation 1-5 which is Poiseuille's law for laminar flow. When the flow is turbulent (R, > 4000), the friction factor depends not only upon the Reynolds number but also upon the relative roughness, E/D .... the roughness of the pipe walls (E), as compared to the diameter of the pipe (D). For very smooth pipes such as drawn brass tubing and glass, the friction factor decreases more rapidly with increasing Reynolds number than for pipe with comparatively rough walls. Sinc€' the character of the internal surface of commercial pipe is practicai!y independent of the diameter, the roughness of the walls has a greater effect on the friction factor in the small sizes. Consequently, pipe of smail diameter will approach the very rough condition and, in general, will have higher friction factors than large pipe of the same material. The most useful and widely accepted data of friction factors for use with the Darcy formula have been presented by L. F. Moody" and are reproduced on pages A-23 to A-25. Professor Moody improved upon the well-established Pigott and Kemler", 26 friction factor diagram, incorporating more recent investigations and developments of many outstanding scientists. A region known as the "critical zone" occurs between Reynolds number of approximately 2000 and 4000. In this region, the flow may be either laminar or turbulent depending upon several factors; these include changes in section or direction of flow and obstruc-. The friction factor, j, is plotted on page A-24 on tions, such as valves, in the upstream piping. The the basis of relative roughness obtained from the friction factor in this region is indeterminate and chart on page A-23 and the Reynolds number. The CRANE ~~ :::::; ::3 =:) ,:::,) -;:) ~ .~ ~ CHAPTER I - THEORY OF flOW IN PIPE Darcy's Formula General Equation for Flow of Fluids value of f is determined by horizonta I projection from the intersection of the d D curve under consideration with the calculated Reynolds number to the left hand vertical scale of the chart on page A-23. Since most calculations involve commercial steel or wrought iron pipe, the chart on page A-25 is furnished for a more direct solution. I t should be kept in mind that these figures apply to clean new pipe. continued causes a 10o/c increase in pressure drop; a 59c reduction of diameter increases pressure drop 23 S~. In many services. the interior of pipe becomes encrusted with scale. dirt, tubercules or other foreign matter; thus, it is often prudent to make allowance for expected diameter changes. Authorities' point out that roughness may be expected to increase with use (due to corrosion or Effect of age and use on pipe friction: Friction incrustation) at a rate determined by the pipe loss in pipe is sensitive to changes in diameter and material and nature of the fluid. Ippen'B, in discussroughness of pipe. For a given rate of flow and a ing the effect of aging, cites a 4-inch galvanized fixed friction factor, the pressur.e drop per foot of. steel pipe which had its roughness doubled and its pipe varies inversely with the fifth po\\-er of the friction factor increased 20'70 after three years of diameter. Therefore, a 2% reduction of diameter moderate use. Principles of Compressible Flow in Pipe .~ ':) -:) -::) ,~:j An accurate determination of the pressure drop of a compressible fluid flowing through a pipe reqUires a knowledge of the relationship between pressure and specific volume; this is not easily determined in each particular problem. The usual extremes considered are adiabatic flow (p'V:~ = constant) and isothermal flow (p'Va = constant). Adiabatic flow is usually assumed in short, perfectly insulated pipe. This would be consistent since no heat is transferred to or from the pipe, except for the fact that the minute amount of heat generated by friction is .added to the flow. Isothermal flow or flow at constant temperature is often assumed, partly for convenience but more often because it is closer to fact in piping practice. The most outstanding case of isothermal flow occurs in natural gas pipe lines. Dodge and Thompson! show that gas flow in insulated pipe is closely approximated by isothermal flow for reasonably high pressures. Since the relationship bet\\'een pressure and volume may follow some other relationship (p'V: = constant) called polytropic flow, specific information in each individual case is almost a::1 impossibility. The density of gases and vapors changes considerably with changes in pressure; therefore, if the pressure drop between PI and p, in Figure 1-6 is great, the density and velocity will change appreciably. When dealing with compressible fluids, such as air, steam, etc., the following restrictions should be observed in applying the Darcy formula: 1. If the calculated pressure drop (PI - P,) is less than about 10% of the inlet pressure PI, reasonable accuracy will be obtained if the specific volume used in the formula is based upon either the upstream or downstream conditions, whichever are known. 2. If the calculated pressure drop (PI - P,) is greater than about 10%, but less than about 40% of inlet pressure PI, the Darcy equation may be used with reasonable accuracy by using a specific volume based upon the average of upstream and dO\\'nstream conditions: otherwise, the method given on page l-q may be used. 3. For greater pressure drops, such as are often encountered in long pipe lines. the methods given on the next two pages should be used. ' (cont;nued on the next page) 1-8 CRANE CHAPTER I - THEORY OF flOW IN PIPE Principles of Compressible Flow in Pipe (continued) Complete isothermal equation: The flow of gases in long pipe lines closely approximates isothermal conditions. The pressure drop in such lines is often large relative to the inlet pressure, and solution of this problem falls outside the limitations of the Darcy equation. An accurate determination of the flow characteristics falling within this category can be made by using the complete isothermal equation: Equation J·6 ] [(P;)' ;;; (P~)'] The formula is developed on the basis of these assumptions: I. Isothermal flow. 2. No mechanical work is done on or by the system. 3. Steady flow or discharge unchanged with time. 4. Tne gas obeys the perfect gas laws. 5. The velocity may be represented by the average velocity at a c.ross section. 6. l1t1e friction fa.ctor is constant along the pipe. 7. The pipe line is straight and horizontal between end points. Simplified Compressible Flow-Gas Pipe Line Formula: In the practice of gas pipe line engineering, another assumption is added to the foregoing: 8. w2 = [ hfl. Equation 1-1 Pi This is equivalent to the complete isothermal equation if the pipe line is long and also for shorter lines if the ratio of pressure drop to initial pressure is small. Since gas flow problems are usualiy expressed in terms of cubic feet per hour at standard conditions, it is convenient to rewrite Equation 1-7 as follows: , , q' h = 1 14.2 ~ i[(p't)' - (P")'] d.' . f l.m T S, Equafion J-7a Other commonly used formulas for compressible flow in long pipe lines: Weymouth formula": I _ q• - d,.m 8 2 .0 " Equation '[(PII)' - (PI,),] 520 S. l... T q'. ,'O, The flow efficiency factor E is defined as an experience factor and is usually assumed to be 0.92 or 92% for average operating conditions. Suggested values for E for other operating conditions are given on page 3-3. Comparison of formulas for compressible flow in pipe lines: Equations 1-7, 1-8, and 1-9 are derived from the same basic formula, but differ in the selection of data used for the determination of the friction factors. Friction factors in accordance with the t-..loodv" diagram are normally used with the Simplified Compressible Flow formula (Equation 1-7). However, if the same friction factors employed in the IVeymouth or Panhandle formulas are used in the Simplified formula, identical answers will be obtained. f = Then, the formula for discharge in a horizontal pipe may be written: DN] [(P')' - (P')'] 1 2 Equation (P\l' - (PI,),] 0.5394 = ,6.8 E ,p."" [ l.rn- The Weymouth friction factor" is defined as: Acceleration can be neglected because the pipe line is long. 144 g Panhandle formula' for natural gas pipe lines 6 to 2-!-inch diameter, Reynolds numbers 5 x 10' to 14 x 10', and S, = 0.6: l-a 0.03 2 d1 /' This is identical to the Moody friction factor in the fully turbulent flow range for 20-inch 1.D. pipe only. Weymouth friction factors are greater than Moody factors for sizes less than 20-inch, and smaller for sizes larger than 20-inch. The Panhandle friction factor' is defined as: f= d 0.1225 ----s (q h )0.,451 9 In the flowTange to which the Panhandle formula is limited, this results in friction factors that are lower than those obtained from either the Moody data or the Weymouth friction formula. As a result, flow rates obtained bv solution of the Panhandle formula are usuaily great~r than those obtained by employing either the Simplified Compressible Flow formula with Moody friction factors, or the Weymouth formula. An example of the variation in flow rates which may be obtained for a specific condition by employing these formulas is given on page 4-11 .. CRANE 1-9 CHAPTER 1 - THEORY OF flOW IN PIPE Principles of Compressible Flow ill Pipe (continued) ·.~ .•::;:::::J ~ .,:t .=t .=3 ~ ::=J ::J .::::J .:=J =:.1 ==» .=.::t .::::) ::::!) :::::::::» :::"J ~ .:=2 .-. -, Limiting flow of gases and vapors: The feature not evident in the preceding formulas (Equations 1-4 and 1-6 to 1-9 inclusive) is that the weight rate of flow (e.g., Ibs/sec) of a compressible fluid in a pipe, with a given upstream pressure, will approach a certain maximum rate which it cannot exceed, no matter how much the dowmtream pressure is further reduced. The maximum velocity of a compressible fluid in pipe is limited by the velocity of propagation of a pressure wave which travels at the speed of sound in the fluid. Since pressure falls off and velocity increases as fluid proceeds downstream in pipe of uniform cross section, the mc:ximum velocity occurs in the downstream end of the pipe. If the pressure drop is sufficiently high, the exit velocity will reach the velocity of sound. Further decrease in the outlet pressure will not be fdt upstream because the pressure wave can only travel at sonic velocity, and the "signal" will never translate upstream. The "surplus" pressure drop obtained by lowering the outlet pressure after the maximum discharge has already been reached takes place beyond the end of the pipe. This pressure is lost in shock waves and turbulence of the jetting fluid. The maximum possible velDcity in the pipe is sonic velocity, which is expressed as: Equation r-1 0 v, = .,JkgRT = .,Jkgl44P'V The value of k, the ratio of specific heats at constant pressure to constant volume, is 1.4 for most diatomic gases; see pages A-8 and A-9 for values of k for gases and steam respectively. This velocity will occur at the outlet end or in a constricted area, when the pressure drop is sufficiently high. The pressure, temperature, and ;;pecific volume are those occurring at the point in question. When compressible fluids discharge from the end of a reasonably short pipe of uniform cross section into an area of larger cross section, the flow is usually considered to be adiabatic. This assumption is supported by experimental data on pipe having lengths of 220 and 130 pipe diameters discharging air to atmosphere. Investigation of the complete theoretical analysis of adiabatic flow!' has led to a basis for establishing correction factors, which may be applied to the Darcy equiltion for this condition of flow. Since these correction factors compensate for the changes in fluid properties due to expansion of the fluid, they are identified as Y net expansion factors; see page A-22. The Darcy formula, including the Y factor, is: Equation l .. JJ (Resistance coefficient K is defined on page 2·8) It should be noted that the value of K in this equation is the total resistance coefficient of the pipe line, including entrance and exit losses when they exist, and losses due to valves and fittings. The pressure drop, i'c,p. in the ratio i'c,P/P', which is used for the determination of Y from the charts on page A-22, is the measured difference between the inlet pressure and the pressure in the area of larger cross section. In a system discharging compressible fluids to atmosphere, this i'c,P is equal to the inlet gauge pressure, or the difference between absolute' inlet pressure and atmospheric pressure. This value of i'c,P is also used in Equation I -11, whenever the Y factor falls within the limits defined by the resistance factor K curves in the charts on page A-n. When the ratio of i'c,P/ P' 1, using i'c,P as defined above, falls beyond the limits of the K curves in the charts, sonic velocity occurs at the point of discharge Of at some restriction within the pipe, and the limiting values for Y and i'c,P, as determined from the tabulations to the right of the charts on page A-22, must be used in Equation 1-1 I. -1 Application of Equation 1-11 and the determination of values for K, Y, and i'c,P in the formula is demonstrated in examples on pages 4-13 and 4-14. The charts on page A-22 are based upon the general gas laws for perfect gases and, at sonic velocity conditions at the outlet end, will yield accurate results for all gases which approximately follow the perfect gas laws. Steam and vapors deviate from the perfect gas laws, and application of the Y factor obtained from the charts to these flows, will therefore yield flow rates slightly greater (up to about 5%) than those calculated on the basis of sonic velocity at the outlet. However, greater accuracy will be obtained if the charts are used to establish the downstream pressure when sonic velocity occurs, and the fluid properties at this pressure condition are used in the sonic velocity and continuity equations (Equations 3 -8 and 3-2 respectively) to determine the flow rate. An example of this type of {Jow problem is presented on page 4-13. This condition of flow is comparable to the flow through nozzles and venturi tubes, covered on page 2-15, and the solutions of such problems are similar. . , 1 • 10 CHAPTER 1 - THEORY OF FlOW IN PIPE CRANE Steam General Discussion Substances exist in anyone of three phases .... solid, liquid, or gas. \Vhen outside conditions are varied, they may change from one phase to another. Water under normal atmospheric conditions exists in the form of a liquid. When a body of water is heated by means of some external medium, the temperature 'of the water rises and soon small bubbles, which break and form continuously, are noted on the surface. Th:s phenomenon is described as "boiling". I, !i The amount of heat necessary to cause the temperature of the water to rise is expressed in British Thermal Units (Btu), where, I Btu is the quantity of heat required to raise the temperature of one pound of water from 60 to 61 F. The amount of heat necessary to raise the temperature of a pound of water from 32 F (freezing point) to 212 F (boiling point) is ISO.I Btu. When the pressure does not exceed 50 pounds per square inch absolute, it is usually permissible to assurr.e that each temperature increase of 1 F represents a heat content increase of one Btu per pound, regardless of the temperature of the water. II I ~ ~: ~ Assuming the generally accepted reference plane for zero heat content at 32 F, one pound of water at 212 F contains ISO.17 Btu. This quantity of heat is called heat of the liquid or sensible heat. In order to ~ ! ~. 1 1 ! 1 - 1 ! change the liquid into a \'apor at atmospheric pressure (14.7 psia), 970.3 Btu must be added to each pound of \\'ater after the temperature of 212 F is reached. During this transition period. the temperature remains constant. The added quantity of heat is called the latent heat of erapuralioll. Consequently, the total heat of the \'apor, formed when water boils at atmospheric pressure, is the sum of the two quantities .... ISO. I Btu and 970.3 Btu, or, 1150.5 Btu per pound. If water is heated in a closed vessel not completely filled, the pressure will rise after steam begins to form accompanied by an increase in temperature. Saturated steam is steam in contact with liquid water from which it was generated, at a temperature which is the boiling point of the water and the condensing point of the steam. It may be either "dry" or "wet", depending on the generating can· ditions. "Dry" saturated steam is steam free from mechanically mixed water particles. "Wet" saturated steam, on the other hand, contains \\'ater Darticles in suspension. Saturated steam at any pressure has a definite temperature. Superheated steam is steam at any given pressure which is heated to a temperature higher than the temperature of saturated steam at that pressure. 2·1 rr-3 C=:J -=3 tr-:3 ~~~ //"'~"-------~ // Flow of Fluids (Through Valves and Fittings) '~--------- .d ~ 8:::J ~ a:::) ~ -=::J ~~-~ .::::') ~ i 1 It.."":l t:::) .:::;) L-:;) II:::::.:) e=:,) a::::) e::=l ~ The preceding chapter has been devoted to the theory and formulas used in the study of fluid flow in pipes. Since industrial installations usually contain a considerable number of valves and fittings, a knowledge of their resistance to the flow of fluids is necessary to determine the flow characteristics of a complete piping system. Many texts on hydraulics contain no information on the resistance of valves and fittings to flow, while others present only a limited discussion of the subject. In realization of the need for more complete detailed information on the resistance of valves and fittings to flow, Crane Co. has conducted extensive tests in their Engineering Laboratories and has also sponsored investigations in other laboratories. These tests have been supplemented by a thorough study of all published data on this subject. Appendix A contains data from these many separate tests and the findings have been combined to furnish a basis for calculating the pressure drop through valves and fittings. Representative resistances to flow of various types of piping components are given on pages A-26. A-27, and A-30. For conversion of "equivalent length in pipe diameters", as obtained from page A-27 or A-30, to "equivalent length in feet of pipe" for any size of valve or fitting, see page A-31. The chart on page A-31 also illustrates the correlation of equivalent length, resistance coefficient K, and pipe size. A chart is presented on page A-32 which may be used to readily determine the C" flow coefficient of any valve for which the resistance coeffIcient is known or can be determined from page A-30 and page A-31. I!'.~ .~ A discussion of the eqUivalent length and resistance coefficient K, as well as the flow coefficient Cv methods of calculating pressure drop through valves and fittings is presented on pages 2-8 and 2-9. CHAPTER 2 2-2 CHAPTER 2 - FLOW OF flUIDS THROUGH VALVES AND FITTINGS CRANE Types of Valves and Fittings Used in Pipe Systems Valves: Although the great variety of valve designs precludes any t'lorough classification, most of the designs may be considered as modifications of the two basic types: I. the gate type 2. the globe type If valves were classified according to the resistance which they offer to flow, the gate type valves would be put in the low resistance class and the globe type valves in the high resistance class. The classifIcation is not all-inclusive, however, because a large number of modified valve types fall between the two extremes. :lome of the most commonly used valve designs are illustrated on pages A-28 and A-29. Fittings: Fittings may be classified as branching, reducing, eXf'anding, or deflect ing. Such litt in.!.;, as tees, crosses, side outlet elbows, etc., may be called branching fittings. Reducing or expanding fittings are those which change the area of the fluid passageway. In this class are reducers and bushings. Deflecting fittings ..... bends, elbo\\'s, return bends, etc ... , . are those which change the direction of flow. Some fittings, of course, may be combinations of any of the foregoing general ~lassifications. In addition, there are types such as couplings and unions which offer no appreciable resistance to flow and, therefore, need not be considered here. Pressure Drop Chargeable To Valves and Fittings When a fluid is flowing steadily in a long straight pipe of uniform diameter, the flow pattern, as indicated by the velocity distribution across the pipe diameter, will assume a certain characteristic form. Any impediment in the pipe which changes the direction of the whole stream, or even part of it, will alter the characteristic flow pattern and create turbulence, causing an energy loss greater than that normally accomp;mying flow in straight pipe. Because valves and fir:tings in a pipe line disturb the flow pattern, they produce an additional pressure drop. The loss of pressure produced by a val ve (or fitting) consists of: I. The pressure drop within the valve itself. 2. The pressure drop in the upstream piping in excess of that which would normally occur if there were no valve in the line. This effect is small. 3. The pressure drop in the downstream piping in excess of tha'~ which would normally occur if there were no valve in the line. This effect may be comparatively large. From the experimental point of view it is difficult to measure the three il:ems separately. Their combined effect is thc desired quantity, howe vcr, and this can be accurateiy measured by well known methods. 4---------C--------~ Figure 2-1 shows two sections of a pipe line of the same diameter and length. The upper section contains a globe valve. If the pressure drops, D.P. and D.P" were measured between the points indicated. it would be found that D.P, is greater than D.P,. Actually, the loss chargeable to a valve of length "d" is D.P. minus the loss in a section of pipe of length "a + b". The losses, expressed in terms of equi\'a lent length in pipe diameters, of various val\'es and fittings as given on page A-30, include the loss due to the iength of the valve or fitting. i •. t::J CRANE 2-3 CHAPTER 2 - flOW QF flUIDS THROUGH VALVES AND FITIINGS Crane Flow Tests ..~ ±::) b ~I I ,:::;) i ,:=) , ,~ ;~ Crane Engineering Laboratories have facilities for conducting water, steam, and air flow tests for many sizes and types of valves and fittings. Although a detailed discussion of all the various tests performed is beyond the scope of this paper, a brief description of some of the apparatus will be of interest. -'-~,~"'"C"'''-' The test piping shown in Figure 2-3 is unique in that 6-inch gate. globe. and angle valves or 90 degree ells and tees can be tested with either water or steam. The vertical leg of the angle test section permits testing of angle lift check and stop check valves. r } F Figure 2-2 Saturated steam at 150 psi is available at flow rates up to 100,000 pounds pe~ rour. The steam is throttled to the desired pressure and its state is determined at the meter as well as upstream and downstream from the test specimen. For tests on water, a steam turbine driven pump supplies water at rates up to 1200 gallons per minute through the test piping. :r ::::.1 Static pressure differential is measured by means of a manometer connected to piezometer rings upstream and downstream from test position 1 in the angle test section, or test position 2 in the straight test section. The downstream piezometer for the angle test section serves as the upstream piezometer for angle valve f; r ;;" r: E Results of some of the flow tests conducted in the Crane Engineering Laboratories are plotted in Figures 2-4 to 2-7 shown on the two pages following. -II> iiti' ..g ~-) Exhaust to Atmosphele ~ \ Water Header (Meteled Supply flam tumine dliven pump) !i' ) .~ ~ ~:) Figura 2-3 Test piping apparatus for measuring the pressure drop thrQugh valves and nnlngs on sfoam or water lines. Elbow Can Be Rotated to ________" " Admit Water Of Steam " I , i Flow test piping for 12-inch cast steel the straight test section. Measured pressure drop for the pipe alone between piezometer stations is subtracted from the pressure drop through the valve plus pipe to ascertain the pressure drop chargeable to the valve alone. ~ ~~ .;;. 2-4 CRANE CHAPTER 2 - flOW OF flUIDS THROUGH VALVES AND FITTINGS Crane Water Flow Tests 1~ r:~:=ll::::~:rI:;"=l1::If==l::;:=l=;:::::7.I'MIrL~-:;~ 8~4-~~4-+-~ji+--r-r+-r+--~/~//'~~~ I ; I I II//!/illl ! IIII VIJLJ, I I ~ ! IJIL /1/1111 i NIl 1///111 I I 3~~-+i+l+i+-~~H&VW,~~~~~-; IXII V;{riv/ 3 "I' I '" 1 'II I 1/ II II I 1/ I I I V VI 2 I II I V fhVl 1 (;) 2 4 3 20 5678910 2 3 Water Velocity, in Feet per Second Figure 2 ...4 Figure 2 .. 5 Woter Flow Tests Fluid FigurE' No. Curve No. Size, Inches I 2 Figure 2-4 Water I figure 2··5 I Curves 1 to 18 Valve Tl:'pe* % 2 4 6 3 4 S 6 7 8 9 10 11 12 13 14 15 16 17 18 678910 Water Velocity, in Feet per Second ISO-Pound Cast Iron Y-Pattern Globe Valve, Flat Seat 111. 2 2% 3 Ill. I 2 2% 3 ISO-Pound Brass Angle Valve with Composition Disc, Flat Seat I I ISO-Pound Brass Conventional Globe Valve With Composition Disc-Flat Seat % II. 3,4 11,4 II 2 6 2oo-Pound Brass Swing Check Valve ! US-Pound Iron Body Swing Check Valve *Exccpt for check valves at lower velocities where curves (l4 to 17) bend, all valves were .tested with disc fully lifted. CRANE - Crane Steam Flow Tests LO , 9 8 7 6 ~ :::::t I / , 4 i /, 3 V tJ ",f = :.:3 i/~ .2 !J ~ .1 V '" o "- .: I ~ .09 c .08 ~ .0 7 a:~ .06 .==.) 1"24 -==:.::) -=:) 4 I !" " '" V 3 -:::::;) .. 4 6 7 8 S 10 20 .0I 3 30 Fluid No. CUrvl~ 19 .:':::, 29 .L V / "', "- '" 30 ~ 1....... 31 L il .L I 45678910 30 20 Figure 2-7 Size, Inches No. t-2sl Steam Velocity, ifl Thousands of Feet per Minute Stearn Flow Tesfs Figure .. 1/ V 1/1/ Figurn 2 .. 6 .. :=) 1 Vv Steam Velocity, in·ThoLisands of Feet per Minute ::::) ~ 1L':::::::' V 1/ V V l.'f-L~V- LI~~,L.-"-i--:'::--'---:: L ' 27 I. j I .02 ::::::l) V II IL .03 -;:::) k' L i/ L .04 =::) .L .L L / .L If .05 !Ii /1 V I il II. ~ v Ii " ~ •..:::J 'I .L .L .L ~ ~ I 1. L .:; 2! .1 .1 -5 gl I / 3 ~ ,.:.::::) .1.1 I 5 ·~I .=:11 2-5 CHAPTER 2 - flOW OF FLUIDS THROUGH VALVES AND FITTINGS :::::) 20 .~ 21 2 6 6 21 6 Curves 19 to 31 Valve' or Fitting Type I' loo-Pound 300-Pound lOO-Pound [ lOO-Pound Brass Conventional Globe Valve ............. Plug Steel Conventional Globe Valve ............. Plug Steel Angle Valve ........................... Plug Steel Angle Valve ......................... Ball to Type Seat Type Seat Type Seat Cone Seat Figure 2-6 ::::.) ~ -~ 23 Saturated Steam 24 25 50 psi gauge 26 ::::::) Figure 2-7 I I 6 G G I) 27 2 18 (; 29 30 31 I) 6 6 GOO-Pound GOO-Pound GOO-Pound 600-Pound Steel Steel Steel Steel Angle Stop-Check Valve Y-Pattern Globe Stop-Check Valve Angle Valve Y-Pattern Globe Valve 90° Short Radius Elbow for Use with Schedule 40 Pipe 250-Pound Cast Iron Flanged Conventional 90° Elbow GOO-Pound Steel Gate Valve 125-Pound Cast Iron Gate Valve ISO-Pound Steel Gate Valve 'Except for check valves at lower velocities where curves (23 and 24) bend, all valves were tested with disc fully lifted. 2-6 CHAPTER 2 - flOW OF flUIDS THROUGH VALVES AND FITTINGS CRANE Figure 2.8 Flow test piping for 2 V:z -inch corl steel ongle valve. Figure 2 ...9 Steam capacity feft of a V:z-inch bra" relief yalve. J I 1j j i Figure 2-10 Flow fest piping lor 2-inch fabricaled steel y-pattern globe valve. CRANE CHAPTER 2 -- flOW OF flUIDS THROUGH VALVES AND FlTIlNGS 2-7 Relatiionship of Pressure Drop to Velocity of Flow ...•» ,. ,. ;;:::j '~ ::::::) . .~ .~ :=3 ==:3 "":::) '=::t .=:) :.=) .=) .:::::;) .=:) Many experiments have shown that the head loss due to valves and fittings is proportional to a constant power of the velocity. When pressure drop or head loss is plotted against velocity on logarithmic coordinates, the resulting curve is therefore a straight line. In the turbulent flow range, the value of the exponent of v has been fm;nd to vary from about 1.8 to 2.1 for different designs of valves and fittings. However, for all practical purposes, it can be assumed that the pressure drop or head loss due to the flow of fluids in the turbulent range through valves and fittings varies as the square of the velocity . This relationship of pressure drop to velocity of flow is valid for check valves, only if there is sufficient flow to hold the disc in a wide open position . The point of deviation of the test curves from a straight line, as illustrated in Figures 2-5 and 2-6, defines the flow conditions necessary to support a check valve disc in the wide open position. Most of the difficulties encountered with check valves, both lift and swing types, have been found to be due to oversizing which results in noisy operation and premature wear of the moving parts. Referring again to Figure 2-6, it will be noted :hat the pressure drop, at the point where the two curves representing check valves deviate from a straight line, is about 1Yz to 2 pounds per square inch. This value will vary somewhat for different valve designs depending upon the relative weight and size of the disc; however, it has been found to be a good "rule of thumb" to size check valves so that the pressure drop in the fully open position is about 2 psi in lift checks and about Yz psi in swing checks. This rule applies only to check valves designed on the basis of established fundamental considerations which assure a full disc lift at low flow rates. On some poorly designed lift check valves, tests have shown that the disc will not lift fully even at extremely high flow rates. In many cases, application of this rule will result in check valves smaller in size than the pipe line; however, the actual pressure drop will be little, if any, higher than that of a full size valve which is used in other than a wide open position. The losses due to sudden contraction and enlargement which will occur in such an installation with bushings or reducing flanges can be readily calculated from the data given on page A-26. if tapered reducers are used, the loss due to gradual contraction at the inlet to the smaller size valve is partially compensated for by the corresponding gradual enlargement on the outlet side, so that the added pressure drop due to these effects is minor. In-line ball check valves of the design shown in Figure 2-11 should be installed in a horizontal position wherever possible. In this position, the flow required to move the disc to the fully open position is very low and the valves Figure 2.11 can be full size to match In· line ball check valve the pipe line; this will in horizontal position result in low pressure drop at all flow rates. If it is necessary to install this type of valve in a vertical line, due to piping arrangement or for other reasons, it should be sized so that the flow rate will be sufficient to cause a pressure drop of about 2Yz psi across the valve. This will provide full disc lift and prevent noisy operation and premature wear of parts. ==» :::::'» ::::3 :::::::) -:::::) ~ ,' - Figure 2-12 Both woter and steam fests ore conducted on this set-up. 2-8 CRANE CHAPTER 2 - FLOW OF FLUIDS THROUGH VALVES AND FITTINGS Resistance Coefficient K, Equivalent length L/D, And Flow Coefficient Cv The numerous types of valves and fittings and the great variety of service conditions make it virtually impossible to obtain test data on every size and type of valve and fitting used today. For this reason, it is desirable to find a means for utilizing the limited test data which are available. Several methods of accomplishing this have been devised; the most commonly used are the "equivalent length", .. resistance coefficient", and' 'flow coefficient". Velocity in a pipe is obtained at the expense of static head, and decrease in static head due to velocity is: h = v' -, 2g which is defined as the "velocity head". Flow through a valve or fitting in a pipe line also causes a reduction in stati.C head which may be expressed in terms of velocity head. The resistance coefficient K in the equation hL = K -2gv' , Equation 2-2 therefore, is defined as the number of velocity heads lost due to the valve or fitting. Also, the same head loss in straight pipe is expressed by the Darcy equation hL=(ii;)~ Equation 2 ..3 I t follows that, K = (it) Equation 2-4 The ratio LID is the equivalent length in pipe diameters of straight pipe which will cause the same pressure drop as the valve under the same flow conditions. The resistance coefficient K would theoretically be a constant for all sizes of a given design or line of valves and fittings if all sizes were geometrically similar. However, geometric simiiarity is seldom, if ever, achieved because Figure 2-13 the design of valves Geometrical dis.similarity between 2 and and fittings is dic12-inch standard cast iror:, flanged elbows tated by manufacturing economies, standards. structural strength, and other considerations. An example of geometric dis12-IHCH SIZE 1/6 SCALE (>' similarity is shown in Figure 2-13 where a 12-inch standard elbow has been drawn to 1/6 scale of a 2-inch standard elbow. so that their port diameters are identical. The flow paths through the two fittings drawn to these scales would also have to be identical to have geometric similarity; in addition. the relative roughness of the surfaces would have to be similar. Figure 2-14 on the opposite page is based on the analysis of extensive test data from various sources. The K coefficients for a number of lines of valves and fittings have been plotted against size. It will be noted that the slopes of the K curves show a definite tendency to follow the same slope as the I(LID) curve for straight pipe. It is probably coincidence that the effect of geometric dissimilarity between different sizes of the same line of valves or fittings upon the resistance coefficient K is similar to that of relative roughness, or size of pipe, upon friction factor. Based on the evidence presented in Figure 2-14, it can be said that the resistance coefficient K, for a given line of valves or fittings, tends to vary with size as does the friction factor I for straight pipe, and that the equivalent length LID tends toward a constant for the various sizes of a given line of valves or fittings. In the flow range of complete turbulence as defined by the Friction Factor Charts, pages A-24 and A-25, the K coefficient for a given size and the LID value are, of course, constant. In the transition zone, where I for pipe increases with decreasing Reynolds numbers, it is assumed that the value of LID is constant and that K varies in the same manner as the friction factor. Limited tests have shown that this is not an exact relationship and that it may vary for different types of valves and fittings: however, since the tendency is in this direction, it is believed to provide more accurate solutions than would the assumption that K is constant for all Reynolds numbers. It has been found convenient in some branches of the valve industry, particularly in connection with control valves, to express the valve capacity and the valve flow characteristics in terms of the flow coefficient Cy . The Cy coefficient of a valve is defined as the flow of water at 60 F, in gallons per minute, at a pressure drop of one pound per square inch across the valve. By the substitution of appropriate equivalent units in the Darcy equation, it can be shown that, C _ y - ~ 29·9cl' _ It - 29·9cl' -vI< Equallo. 2-5 CRANE 2·9 CHAPTER 2 - fLOW OF fLUIDS THROUGH VALVES AND FITTINGS Resistance Coefficient f{, Equivalent length l./D, And Flow Coefficient Cy - continued ' .. ~ .:=J~ .~. ;;::) ';:dI ::::::) -- K - Resistance Coefficient Figure 2-14, Variation of Resistance Coefficient K (=f L{D) with Size Product Tested Symbol o 0- 9 -0 6 -0- 9 -¢cf Q. )::( Authority Schedule 40 Pipe, 30 Diameters Long (K = 30 f) .... : . . Moody AS.M.E. Trans., Nov.-1944' 125-Pound Iron Body Wedge Gate Valves .............. Univ. of Wise. Exp. Sta. Bull., Vol. 9, No. I, 1922" 600-Pound Steel Wedge Gate Valves ................... Crane Tests 90 Degree Pipe Bends, RID = 2 ....................... Pigott AS.M.E. Trans., 1950' 90 Degree Pipe Bends, R/D = 3 ....................... Pigott AS.M.E. Trans., 1950' 90 Degree Pipe Bends, R/D = 1 ....................... Pigott A.S.ME. Trans., 1950' 600-Pound Steel Wedge Gate Valves, Seat Reduced .... Crane Tests JOO-Pound Steel Venturi Ball-Cage Gate Valves ....... Crane-Armour Tests 125-Pound Iron Body Y-Pattern Globe Valves ......... Crane-Armour Tests 125-Pound Brass Angle V a1 yes, Composition Disc ...... Crane Tests 125-Pound Bras!: Globe Valves, Composition Disc .... .. Crane Tests (toflfinued from the preceding page) Also, the quantity in gallons per minute of any liquid having a viscosity close to that of water at 60 F that will flow through the valve can be determined from: Equation 2-6 and the pressure drop can be computed from the same formula arranged as follows: /::,.p=P 62-4 (Q)' C - v Equatjon 2-6 Since Equations 2-2, 2-3, and 2-6 are simply other forms of the Darcy equation, the limitations regarding their use for compressible flow (explained in Chapter I, Page 1-7) apply. Other convenient forms of Equations 2-2, 2-3, and 2-6 in terms of commonly used units are presented on page 3-4. 2 - 10 - - - - -CHAPTER 2 - CRANE flOW OF flUIDS THROUGH VALVES AND fITTINGS Relath)t1Ship of Equivalent length 1./D and Resistance Coefficient K To Inside Diameter of Connecting Pipe Tests have shown that the pressure drop due to a given va!\'e or titting does not change when the product is installed with pipe of the same nominal size but of differem thickness, Small variations in entrance and exit losses caused by mating the valve ends to \'ariable pipe thicknesses, within reasonable limits, are insignitlcant. Since the pressure drop is a function of the square of the velocity, and velocity is a function of the square of the internal diameter, it follows that the equivalent length of a given valve or fItting, expressed in terms of the pipe to which it is connected, varies as the fourth power of the internal diameter (If the pipe, For example, if the equivalent length of a ! i-inch valve is determined by test to be 100 pipe diameters of Schedule 80 pipe, its equi\'alent length will be 169 diameters of Schedule 40 pipe, since the ratio of the inside diameters of the twO pipes to the fourth power is 1.69, This ratio, of course, varies with the different sizes and thicknesses of pipes. In vie\\' of this condition, the Crane Engineering Laboratories have established the practice of making all flow tests with pipe having internal diameters normally used with the particular valve or fitting. For this purpose, pipe normally used with the various pressure classes of valves and fittings has been arbitrarily established in accordance with the table shown at the top of page A-30. Computation of pressure drop using equivalent length data established on the ba;;is of this tai'k should be made USing pipe dimensions specified on pages B-IO to B-19; for installation conditions not in agreement with the table. the eLJui"aknt length In pipe diameters. should be multiplied by the ratIo of diameters to the fourth power. L) a D ( L) • (d (D ,db - - - a )' Equatiolt 2..7 Subscript "a" dcfmes the eLJuivalcnt lengths \\'ith reference to the internal diameter of the plpC in which the \'alve \\'i11 be installed. Subscript "b" defines the known equi\'alent fengths and internal diameters of the pipe for which these equivalent lengths were established. This procedure of obtaining equl\'alent length data with respect to pipe of various internal diameters corrects a signifIcant variable that has often been neglected in translating tcst data and makes pos~ible a more accurate prediction of the 110w characteristics of untested valves and fittings by comparison of detail dimensions and shapes with tested items. Resistance coefficient K can be calculated for the pipe in \\'hich the valve will be installed byemploying the formula Ka = fa (~ ) .. or expressed in termS of . resistance coefficients, the formula may be written: Ka= K. (X) (~:)' Valves with Gradually Increased Ports Various types of valves are often made with reduced seats and have uniformly tapered ports, Straightthrough \'alves such as gate, ball, plug, and conduit types when so designed are sometimes referred to as venturi or reduced seat valves, The added resistance in these valves, due to the tapered sections from port size to seat size to port size, exceeds that of the straight-through port" valve with correction for flow resistance based on Equation 2-7, for included venturi angles of 20 degrees or less with seat to port ratio of diameters less than 0.8, Equation 2-7 yields reasonably accurate results for included venturi angles of 7 degrees or less and \\'ith a ratio of seat to port diameters greater than 0.8, In globe and angle type valves where the loss through the seat section is high with respeer to the loss through the venturi ends, Equation 2-7 may be used with reasonable accuracy for included venturi angles up to 20 degrees and for seat to port ratios of diameters greater than 0.7. Effect of End Connections Before the advent of full port straight-through ball, plug, and conduit type \'alves, the losses due to end connections \\'ere inSignificant with respect to the over-all loss through the valve, This is still true for higher resistance val Yes, Where the flo\\' resistance of a valve in pipe diameters is equal to its end-to-end dimension, small additional losses should be computed since they may add Significantly to the over-all valve's loss, I n screwed end val ves, the losses due to sudden enlargements and contractions (page A-26) may be a signifIcant part of the total loss, especially in the small er sizes. CRANE 2 - 11 CHAPTER 2 - FLOW OF flUIDS THROUGH VALVES AND FITTINGS Laminar Flow Conditions One of the problems in flow of fluids confronting engineers from time to time . for which there is very meager information, is the resistance of valves and fittings under laminar flow conditions. Flow through straight pipe is adequately c~vered by the basic flow equation, L v' hL = I D zg' :::::::3 .==:) ::::) .. .:= .-. .::=.:) ':::::) .~ ..=:::) =:) :::::II ':: :II =1 ::::) ~I Subscript "s" refers to the equivalent length in pipe diameters under laminar flow conditions where the Reynolds number is less than 1000. which is identical to Poiseuille's law for laminar Row when the equation for I in this flow range, I = 64/R" is included in the formula. Subscript ..t'. refers to the equivalent length in pipe diameters determined from tests in the turbulent flow range. Representative values of equivalent length are given in the table on page A-30. For solution of these problems, we have developed on the basis of data presented in "Principles of Chemical Engineering" by Walker, Lewis, McAdams and Gilliland", the empirical relationship between equivalent length in the laminar flo\\' region (for R, < 1000) to that in the turbulent region. namely: The minimum equivalent length is the length in pipe diameters of the centerline of the actual flow path through the valve or fitting. \Vhile laboratory test data supporting this method is meager, reports of field experience indicate that the results obtained agree closely with observed conditions. Basis for Design of Charts for Determining Equivalent Length, Resistance Coefficient, and Flow Coefficient The table on page A-30 lists average equivalent length data expressed in pipe diameters abstracted from all available tests. It is not practical to identify all valve and fitting types with the many variations in design which may affect the flow charactenstlCS. The data given for globe and angle valves represent actual tests on the variation of designs indicated. By using the data given in this table along with the principles presented from page 2-8 to this point as a basis, reasonable equivalent length values can be estimated for any valve or fitting upon consideration of design features, such as, the relative area of sea.t or restricted sections to pipe diameter and the shape of the flow passage. The chart on page A-3! provides a convenient means of translating equivalent length in pipe diameters as given in the table on page A-30, to equivalent length in feet of pipe for any given size of valve or fitting. Also, the resistar:.ce coefficient K for fully turbulent flow range can be readily determined from this chart for any size, if the resistance coefficient or equivalent length for any other size of the same item has been established, eit~er by experiment or estimate. The chart on page A-32 givi:s a graphical solution of Equation 2-5 and permits a readv determination of Cy if K is known. An example i-i1ustrating the use of this chart is given on page 4-2. Limitations of charts: As explained on page 2-8 and at the top of this page, the value of L;D for a given type of valve or fitting is considered to be constant for flow conditions resulting in Reynolds numbers of 1000 or greater. Equivalent lengths either in pipe diameters or feet of pipe, <;is determined from pages A-30 or A-3J, are therefore legitimate for all flow conditions except in the laminar flow range where the Reynolds number is less than 1000. For Reynolds numbers .Jess than 1000, values of L/ D must be determined in accordance with Equation 2-8 . [t should be pointed out that the equivalent length data given on pages A-30 and A-31 are based upon clean commercial steel pipe. On the other hand, values of K, as determined from pages A-31 and A-32, are legitimate only for flow conditions resulting in Reynolds numbers falling in the completely turbulent flow range, as defined by the friction factor on pages A-24 and A-25. At lower flow rates, values of K vary in approximately the same manner as does tlo;, value of friction factor with Reynolds number. At the lower flow rates, the value of K as determined from pages A-31 and A-32 should be multiplied by the raja: I f (at calculated Rcynoks number) (in range of complete turbulence, where f is constant) ---------------- When K has been corre~t.ed for flow in the transition or laminar flow range, Cv can be obtained directly from page A-32 by employing the corrected K factor. However, if the Cv factor is furnished for the completely turbulent flow range, as defined by the friction factor charts on pages A-24 and A-25, it must be corrected by multiplying it by the ratio, If (in range of complct~ turbulence. where f is constant) '\J I (at calculated Rc\'nG'~ls number) since Cv varies inverse1:; with the square root of the friction factor. 2" 12 CHAPTER 2 - flOW OF FlUIDS THROUGH VALVES AND FITTINGS CRANE Resistance of Bends Figure 2-15 5Qcondory Flow In Bands Secondary flow: The nature of the flow of liquids in bends has been thoroughly investigated and many interesting facts have been discovered. For example, when a fluid passes around a bend in either viscous or turbulent flow, there is established in the bend a condition known as ··secondary flow'·. This is rotating motion, at right angles to the pipe axis, which is superimposed upon the main motion in the direction of the axis. The frictional resistance of the pipe walls and the action of centrifugal force combine to produce this rotation. Figure 2-15 illustrates this phenomenon. Resistance of bends to flow: The resistance or head loss in a bend is conventionally assumed to consist of .... (I) the loss due to curvature .... (2) the excess loss in the downstream tangent .... and (3) the loss due to length, thus: h, = h. + h, + hL Equation 2-9 where: h, h. I! I total loss, in feet of fluid excess loss in downstream tangent, in feet of fluid loss due to curvature, in feet of fluid loss in bend due to length, in feet of fluid if: h. Equation 2-JO then: h, = h. + h" The chart on page A-27 shows the resistance of 90 degree bends in terms of equivalent length of straight pipe. These curves .... also based on the work of Beij .... are believed to represent a\·erage conditions for the flow of fluids in 90 degree bends. Tests have shown that the loss due to continuous· bends greater than 90 degrees. such as in pipe coils, is less than the summation of the losses in the 90 degree bends contained in the coil, considered separately. This is reasonable. since the loss h p in Equation 2-9 occurs only once in such a bend. Reasonably accurate results for pipe coils and expansion loops consisting of continuous bends can be obtained by the use of the chart on page A-27 .... if the number of 90 degree bends contained in the coil minus one, multiplied by the resistance due to length plus one-half of the bend resistance, is added to the total resistance of a 90 degree bend. For example, a pipe coil consisting of four complete turns .... sixteen 90 degree bends .... and having a relative radius of five pipe diameters, would have a total equivalent length, in pipe diameters, of: 15 (8 However, the quantity h. can be expressed as a function of velocity head in the formula: v' h. = K.2g The relationship between K, and rid (relative radius*) is not well defined, as can be observed by reference to Figure 2-16 (taken from the work of Beij2I). The curves in this chart indicate that K. has a minimum value when rid is between 3 and 5. Equation 2-J J + 4) + 16 = 196 I t will be noted that this assumes h p = he in Equation 2-9; this relationship has not been established by tests but is believed to represent the most accurate estimate that can be made until further experimental data are available. where: K. v g the bend coefficient velocity through pipe, feet per second 32.2 feet per second per second Resistance of miter bends: The equivalent length of miter bends, based on the work of H. Kirchbach', is also shown on page A-27. "The relative radius of a bend is the ·ratio of the radius of the bend axis to the intemal diameter of the pipe. Both dimensions must be in the same units .. CRANE CHAPTER 2 - FLOW OF flUIDS THROUGH VALVES AND FITTINGS Resistance of Bends - continued .6r----,----,-----r----,----.-----r----.--~---r----,----.----~ I /V - A ~ .b ~3 °O~--~2----~4-----6~--~8----~1~O----~12~--~14~--~1~6----~18~--~2~O--~22 Relative Radius, rjd Figure ~!-16, Bend Coefficients Found by Various Investigators (BeW') From "Pressu.re Losses for Fluid Flow in 90° Pipe Bends" by K. H. Ber;. Courtesy of Journal' of Research of National Bureau of Standards. t=:) Investigator c:=:;, Diameter Balch ... , ....................... 3-inch ............... . . Davis ........................... 2-inch ............... . Brightmore ..................... 3-inch ............... . Brightmore ..................... 4-inch ............... . Hofmann ................. 1.7-inch (rough pipe) ........ . Hofmann ............... , 1.7-inch (smooth pipe) ....... . VogeL ...................... 6, 8, and lO-inch .......... . Beij ............................ 4-inch ............... . t=:t Symbol •o II o it.. 6. T + Other Resistances to Flow c,:- ~I In addition to the resistance due to valves and fittings already discussed, losses due to sudden enlargement and sudden contraction are encountered whenever fittings such as reducing or increasing flanges, bushings, etc., are used. Also, when a fluid enters or leaves an open end pipe, entrance and exit losses occur. As in the case of VE:lves and fittings, these losses can be expressed by the formula: hL = K!!... 2g Unlike most other fittings. there is no length involved in losses due to these conditions; thus, relative roughness is not a factor in these resistances, and geometric similarity does exist. The resistance due to sudden enlargement and sudden contraction, as well as entrance and exit losses expressed in terms of velocity head or K factor, are therefore independent of pipe size. Resistance coefficient K for such conditions are given on page A-26. EqUivalent lengths corresponding to these resistance coefficients for any size can be readily determined from the chart on page A-31. For example, the equivalent lengths of sharp edged entrances (K = 0.5) to 2 and 6-inch pipes can be read from the nomograph on page A-3J as 26 diameters of 2-inch pipe and 33 diameters of 6-inch pipe, respectively. 2 -14 CHAPTER: 2 - FLOW OF flUIDS THROUGH VALVES AND FITIINGS CRANE Flow Through Nozzles and Orifices The discharge of fluids through nozzles and orifices has been subject to continued investigation and, as a result, well-established data are still being supplemented. A portion of the subject is co\'ered on these faCing pages but more complete references will be found in the Bibliography" " lO, or from the data supplied by meter manufacturers. The rate of flow of any fluid through an orifice or nozzle, neglecting the velocity of approach, may be expressed by: Equation 2-J2 Velocity of approach may have considerable effect on the quantity discharged through a nozzle or orifice. The factor correcting for velocity of approach, ing a low viscosity, i.e., water, gasoline. etc., the Reynolds number need not be calculated since it will fall in the range of the values on page A-20, where the flow coefficient C is a constant. Flow of gases and vapors: The flow of compressible fluids through nozzles and orifices can be expressed by the same equation used for liquids except the net expansion factor Y must be included. Equa/;on 2-15 may be incorporated in Equation 2-12 as follows: q CdA = -;====; ~I-(~:y .,-'V 2g hL Equation 2.13 The expansion factor Y is a function of: I. The specific heat ratio, k. 2. The ratio of orifice ot throat diameter to inlet diameter. 3. Ratio of downstream to upstr.eam absolute pressures. The quantity is defined as the flow coefficient C. Values of C for nozzles and orifices are shown on page A-20. Use of the flow coefficient C eliminates the necessity for calculating the velocity of approach, and Equation 2-13 may now be written: Orifices and nozzles are normally used in piping systems as metering devices and are installed with flange taps or pipe taps in accordance with ASME specifications. The values of hL and D.P in Equation 2-14 are the measured differential static head or pressure across flange taps when values of Care taken from page A-20. The flow coefficient C is plotted for Reynolds numbers based on the internal diameter of the upstream pipe. Flow of liquids: For nozzles and orifIces discharging incompressible fluids to atmosphere, C values may be taken from page A-20 if hL or !';P in Equation 2- I 4 is taken as the upstream head or gauge pressure. f'or most conditions of flow of fluids hav- This factor"lO has been experimentally determined on the basis of air, which has a specific heat ratio of 1.4, and steam having specific heat ratios of approximately 1.3. The data is plotted on page A-21 and values of other specific heat ratios have been included to extend the use of the data. Values of k for some of the common vapors and gases are given on pages A-8 and A-9. The specific heat ratio, k, may vary slightly for different pressures and temperatures, but for most practical problems the values given will provide reasonably accurate results. Equation 2-15 may be used for orifices discharging com;xessible fluids to atmosphere by using: I. Flow coefficient C given on page A-20 in the Reynolds number range where C is a constant for the given diameter ratio. 2. Expansion factor Y per page A-21. 3 . Differential pressure !,;P, equal to the inlet gauge pressure. This also applies to nozzles discharging compressible fluids to atmosphere only if the absolute inlet pressure is less than the absolute atmospheric pressure divided by the critical pressure ratio r,; this is discussed on the next page. When the absolute inlet pressure is greater than this amount, flow through nozzles should be calculated as outlined on the following page. CRANE --c:='lll ":;::3 .~ :.:=:11 ~. .~ .::::J =::3 2 -15 CHAPTER 2 - flOW OF flUiDS THROUGH VALVES AND FITIINGS Flow Through Nozzles and Orifices Maximum flow of compressible fluids in a nozzle: A smoothly convergent nozzle has the property of being able to deliver a compressible fluid up to the velocity of sound in its minimum cross section or throat, providing the available pressure drop is sufficiently high. Sonic velocity is the maximum velocity that may be attained in the throat of a nozzle (supersonic vel.ocity is attained in a gradually , divergent section fo.llowin,c; the convergent nozzle, when sonic velocity exists In the throat), continued Equation 2-15 may be used for discharge of compressible fluids through a nozzle to atmosphere, or to a downstream pressure lower than indicated by the critical pressure ratio r" by using vaiues of: Y .. , . minimum per page A-21 C .. , , page A-20 ;::,p , , , . P', (l - r,); T, per page A-21 p , .. , weight density at upstream condition The critical pressure ratio is the largest ratio of downstream pressure to upstream pressure capable of producing sonic velOCity. Values of critical pressure ratio r" which depend upon the ratio of nozzle diameter to upstream diameter as well as the specific heat ratio k, are given on page A-21 . Flow through short tubes: Since complete experimental data for the discharge of fluids to atmosphere through short tubes (LID is less than, or equal to, 2.5 pipe diameters)' are not available, it is suggested that reasonably accurate approximations may be obtained by using Equations 2-14 and 2-15, with values of C somewhere between those for orifices and nozzles, depending upon entrance conditions. Flow through nozzles and venturi meters is limited by critical pressure ratio, aCId minimum values of Y to be used in Equation 2-15 for this condition, are indicated on page A-21 by the termination of the curves ar p'.IP', = f,. If the entrance is weil rounded, C values would tend to approach those for nozzles, whereas short tubes with square entrance would have characteristics similar to those for square edged orifices. ::=::J =:t -:::::'J :::::) ::::::) Dischar!3e of Fluids Through Valves, Fittings, and Pipe Liquid flow: To determine the flow of liquid through pipe, the Darcy formula is used. Equation 1-4 (page 1-6) has been converted to more convenient terms in Chapter 3 and has been rewritten as Equation 3-14. The form of Equation 3-14 which is most applicable to liquid flow is written in terms of flow rate in gallons per minute. h _ =.t =:a ::::=) =l .'=:) ~'~ :::) L - 0. 002 59 d' Loss of head in terms of resistance coefficient K has been selected sin(;e entrance and exit losses are usually given in terms of velocity head loss, K (see page A-26). Solving for Q, the equation can be rewritten, Q ' . i'"il; 19· 6 5d"'J K KQ2 Q Equation :2.76 Equation 2-16 can be employed for valves, fittings, and pipe where K would be the sum of all the resistances in the piping system, including entrance and exit losses when they exist. Examples of problems of this type are shown on page 4-12 . Compressible flow: When a compressible fluid flows from a piping system into an area of larger cross section than that of the pipe, as in the case of discharge to atmosphere, a modified form of the Darcy formula, Equation I-II developed on page 1-9, is used. The determination of values of K, Y, and 6.P in this equation is described on page 1-9 and is illustrated in the examples on pages 4-13 and 4-14, , .~ -1110 ~" 3·1 formulas ~ond Nomographs For Flow Through .-.~. .... ,!!l Valves, F:ittings, and Pipe CHAPTER 3 ~i ~ :t::::D Only basic formulas needed for the presentation of I:he theory of fluid flow through valves, fittings, and pipe were presented in the first two chapters of this paper. In the summary of formulas given in this chapter, the basic formulas are rewritten in terms of units which are most commonly used in this country. This summary provides the user with an equation which will enable him to arrive at a solution to his problem with a minimum conversion of units. Nomographs presented in this chapter are graphical solutions of the flow formulas applying to pipe. Valve and fitting flow problems may also be solved by means of these nomographs by determining their equivalent length in terms of feet of straight pipe. Due to the wide variety of terms and the variation in the physical properties of liquids and gases, it was necessary to divide the nomographs into two parts: the first part (pages 3-6 to }-15) pertains to liquid flow, and the second part (pages }-16 to }-25), pertains to (;ompressible flow. All nomographs for the solution of pressure drop problems are based upon Darcy's formula, since it is a general formula which is applicable to all fluids and Clan be applied to all types of pipe through the use of the Moody Friction Factor Diagram. Darcy's formula also provides a means of solving problems of flow through valves and fittings on the basis of equivalent length or resistance coefficient. Nomographs proVide simple, rapid, practical, and reasonably accurate solutions to flow formulas and the decimal point is accurately located. ~ ~ ! <:~::j. I Accuracy of a nomograph is limited by the available page space, length of scales, number of units provided on each scale, and the angle at which the connecting liine crosses the scale. Whenever the solution of a problem falls beyond the range of a nomograph, the slide rule or arithmetical solution of the formula must be employed. 3-2 CRANE CHAPTER 3 - FORMULAS AND NOMOGRAPHS fOR flOW THROUGH VALVES, FITTINGS, AND PIPE Summary of Formulas To eliminate needLess duplication, formulas ha\'e been written in terns of either srecific \olume '\ or \\'elf:!ht density p. but not in terms of both. since one is the reciprocal of the other. I P = ~ \. These equations may be substituted in any of the formulas shown in this rarer whene\'er necessary. , Z + I P + ...:=.... 144 p I CD Mean velocity of flow in pipe: (Continuity Equolionj V \ ! ] I -rrz 0.286 0.001 l' 1 I =A = lI'V = 18n q'.T 4. P'd'- T V A V 0. 086 5 2·40 -a- q'.T 3. 06 fL \\",V' d' fLpl" fLp'v" d- 6.P 0.001 294 ~d 6.P 43·; 6.P 0.000 1 0 ; 8 - - r = 0.000001 16-~ 6.P 0.000 000 007 26 6.P 0.000 000 01959 jLpq' --cJ.5 = 0.000 000 J 59 fLpQ' 0.000 11b ~ jL \PV fLpR' IL T(q'.)'S, d'P' jUq'.)'S; d'p ----;;F For simplified compressible fluid formvJa, see page 3-22. 'X'V d' ---;;J.2 G Reynold. number of flow in pip,!: CD Head loss and pressure drop with laminar flow in straight pipe: Equation 3-3 R, = i jLB' -r q'.S, 0.233 P'Ql q'.S, 0.003 8 9 \YlV qm fUr ~~ 0.0311 Equation 3 . . 2 q B Equol;olt 3-5 ' 0.01;24 1 t' Darcy', formula: H 2g 1 1 Pressure loss due to tlow is t he same In a ,jorlng, \'ertical, or horizontal rir£. Ilo\\C\'el', the ,lif· ference in pressure due to the ,1I((crence In head must be considered in rressure ,irop calculations: see rage I';: Equation 3 ... 1 • Bernoulli's Iheo,<!m: -! • Head lOiS and pressure drop in straight pipe: For laminar flo\\' conditions (R- < lOcal. the friction factor is a direct mathematical function of the Reynolds number only, and can he exrressed h~ the formula:/ = b4R,. Substituting this \'alueof r i.1 the Darcy formula, it can be rewritten: Equation 3-6 R, = 1 I ~ R, = j 04 82 ~d;- 6·31 dJl' R, Dr dl' -.~ -~, " 12v I 4 I 9 000 -!cr i !, o Viscosity equh,alents: v = I" , P Bp q'.S, \X' R, I 1 22 774 0 35·4 dp, dl' 00393 0. 02 75 - IlU3 -.~,- d P V 3lbOv~ p,LQ hr. W'V 394 vd Equation 3-4 ilL!' 6.P 0.000 668 6.P 0.000 273 6.P --;]2 dOP 0.00 .. 9 0 J1.L \\" d' p' CRANE - -< Summary of Formulas • 9 Limitations of Darcy formlu!a Non_compressible fh,w; liquids: The Darcy formula may be used without restriction for the flow of water. oil, and other liquids in pipe. However, when extreme \-elclCities occurring in pipe cause the downstream pressure to fail to the vapor pressure of the liquid, cavitation occurs and calculated flow rates are inaccurate. CompreuibJe flow; gellse!: end vapors: When pressure drop is less than 10'/C of PI. use p or V based on either inlet or outlet conditions. When pressure drop is greater than 10% of p, but less than 40% of P" use the average of p or \7based on inlet and outlet conditions, or use Equation 3-20_ When pressure drop is greater than 40% of P" use the rational or empirical formulas given on this page for compressible flow, or use Equation 3-20 (for theory, see page I-g)_ 9 Isothermal flow of gas = 0.371 JV = Empirical formulas for the flow of water, steam, and gas Although the rational method (using Darcy's formula) for solving flow problems has been recommended in this paper, some engineers prefer to use empirical formulas. Hazen and Williams formultl far flow of water: - Q = 0.442 d'.6' C F";) , _ q. - n 14-2 140 for new steel pipe 130 for new cast iron pipe c ! 10 for riveted pipe Equation 3-10 Spifzglass formula for low pressure gas: (pressure less than one pound gouge) Equation 3-ll I(~ d' ') V,/L, (P,,)2 P,~ (P'2)') The maximum possible velocity of a compressible fluid in a pipe is equi,-alent to the speed of sound in the fluid; this is expressed as: v, ,I k g 144P' V, 68_1 -.j k P' V Equation 3-8 V 3 "'6 + -j- + 0.03 d) Flowing temperature is 60 F. • Maximum (sonic) velocifY of compressible fluids in pip.! "jkgRT JS. L l:.h d' Equation 3-7 a - (P' ,)2) 5 'If'( (P',)2 f Lm T So d v, 355 0 (I J( ~,4/;) (P',)2;, (P'2)2) '\l C Babcock formula for steam flow: q'. = - . L P', V, D + log, 0.1072 (P, -L P2)O-" where: c Weymouth formula for high pressure gas: q w Eqllof;on 3-9 d' • Simplifled compressible fl,)w for long pipe lines w continued Equation 3-1 in pipe lines W 3·3 CHAPTER 3 - fORMULAS AND NOMOGRAPHS fOR flOW THROUGH VALVES, FITTINGS, AND PIPE ,_8 h - 2 -"_667 .0 U- Equation 3-12 ,(P,,)2S.-Lm(P' 2)') (52T0) \j Panhandle formula' for natural gas pipe lines 6 to 24-inch diameter and R, = (5 x 10') to (14 x 10'): q' h = 36.8E U"'·6'82 ( (P',)' Equation 3-13 Zm (P' 2)2 Y_5'94 where: gas temperature = 60 F 0.6 flow efficiency 1.00 (100%) for brand new pipe without any bends, elbows, valves. and change of pipe diameter or elevation E 0-95 for \'cry good operating conditions E 0-92 for 8\'erage operating conditions E 0.85 for unusually unfavorable operating conditions S, E E 3-4 continued Summary of Formulcs • CRANE CHAPTER 3 - FORMULAS AND NOMOGRAPHS FOR flOW THROUGH VALVES. FITTINGS. AND PIPE Head 1055 and pressure drop through valves and flttings .. Head loss and pressure drop with laminar flow (R,< 2000) through valves; Darcy's formult! Head loss through vah'es and fittings is generally given in terms of resistance coefficient K which indicates static head loss through a vah'e in terms of "\'elocity head", or, equivalent length in pipe diameters Lj D that will cause the same head loss as the valve. From Darcy's formula, head loss through a pipe is: hL v' -2g = f -L D Equation 3·5 and head loss through a valve is: hL = K v' therefore: K L\ I'd'pQ ( D) (DL) d'p I'q hL 1-470 hL 0.0004 08 j.l::.. D = fJ,P 0.000 0557 (L) l5 dI'V tJ.P 0.0000228 (L) I5 d3 tJ.P 0.000 015 93 (L) 1'8 D (j3 tJ.P 0.000 002 84 (L) I'WV D ------cJ3 Equarion 3.15 To eliminate needless duplication of formulas, the following are all given in terms of K. Whenever necessary, substitute (f LID) for (K). 522 Kq' --d-'-- KQ' = 0.002 59 (II 0.001 270~ 0.010 21 Kpv' = 0.000 1078 fJ,P 3·62 tJ.P 0.000 008 82 ~ (L) I'~ D d' pQ .. Equivalent length correction for laminar flow with R, < 1000 Equation 3-18 1000 0.000 0403 tJ.P Kpq' = R, KB' -F = Equation 3·14 (fJ) dp JJ'I} 0.008 02 ( DL) ~ I' \VV' Equation 3.14 2g Equotion 3·11 0003 28 0.000 000 0300 Kp V' KpQ' 0.000 017 99 ~ See pages 2-1 I and A-30. Minimum (LID), ,;, length of center line of actual ftow path through valve or fitting. Subscript s refers to equivalent length with R, < 1000. Subscript t refers to equivalent length with R, > 1000. .. Discharge of fluid through valves, fittings, and pipe; Darcy's formula KpB' Equation 3-:" tJ.P = 0.000 000280 KW'V d' tJ.P 0.000000000 60 5 tJ.P = 0.000000001 633 q K(q'h)' T S. d' P' Q K (q'.)' S; d' p W For compressible flow with hL or .6P greater than approximately 10% of inlet absolute pressure, the denominator should be multiplied by',". For values of Y, see page A-21 . • Pressure drop aMid flow of liquids, with viscosity similar to waler al 60 F, using flow coefficient tJ.P Q Cv K = (Q Cv Y1)2.4 p Cv ~ tJ.P Q 6:. 4 = ~ tJ.P ~62-4) Equation 3-1' 0.043 8pd' W = Cv /tJ.P -Y-p- 29.9 d' 29.9 d' oJ jLjD oJK 157.6Pd'~ ~ , q. 40700 , Yd' ~ tJ.P PI -S. K I 6P P'. 678 Yd' ~ KTI S. = , qm q' W L K D T =j 891 d' (Cv )' L 74.3 d' j (Cv )' / 6P PII Yd' \ KTIS, Equation 3-20 24700 - - 11.30 /6PP'1 Yd' \j KTI S, 0·525 Yd' '\jK'V; 891 d' (Cv )' !Jt Compressible flow: q. 7.9 0 ~ = ~ Yd' I 6P PI Yd' ItJ. ?PI 412 Tv -y--pc- = 6.87 Tv \ j - r W= 18 91 16P Yd' '\j KV Values of Yare shown on page A-21. For K, Y. and .6P determination, sec examples on pages 4-13 and 4-14. I .~ C R A.N E 3-5 CHAPTER J - fORMULAS AND NOMOGRAPHS FOR flOW THROUGH VALVES, FITTINGS, AND PIPE ----~-------------- .==t Summary of Formulas - ! • Flow through nozzles Clnd orifices (h L and [o.P measured acrass flange taps) Liquid: q • concluded Specific gravity of liquids Any liquid: Equation 3-21 s AC ..; 2g hL = p p Equo,ion 3·25 any liquid at 60 F, ) ( unless otherwise specified (water at 60 F) q Equation 3-26 S (60 F/60 F) Q w W' = 140 130 + Deg Baume S (60 F/60 F) = 1891 d'oC.,f[o.Pp Values of C are shown on page A-20 Cornprnsible Equa/ion 3-27 Liquids lighter than water: 0.0438d"oC"~:;Z = 0·P5d'oC;/[o.Pp 157.6d"oCYhLf~ 131.5 +DegAPl Equation 3-28 liquids heavier than water: ffuid~: 145 S (60 F /60 F) = Deg Baume 145 CD Speciflc gravity of gases q'm S, R (air) 53· 3 ---= R (gas) R (gas) S. M (gas) M (air) ~. q' Equation 3·29 q' • P'V. w p w R M (gas) 29 General gas laws for perfect gases w. RT w. V. Equation 3·30 p' 144 P' Efr RT Equation 3-37 1544 AT Equation 3-33 Values of C are shown on page A-20 Values of Yare shown on page A-21 n. M RT P'V. = n. 1544T w. = M 1544 T Eq:.raticn 3·34 • Equivalents of head lots and pressure drop 144 [o.P p p = w. p'M V. = 1544 T P'M 10.72 T 2.70 P'S, T where: [0.1'" number of mols of a gas • • Changes in equivalent le'ngth LID required 10 compensate for different pipe I. D. Equation 3·24 (see page A-3D) Subscript a refers to pipe in which valve will be installed. Subscript b refers to pipe for ,I,'hich the equival~nt length L/ D was established. Hydraulic radius' cross sectional flow area wetted perimeter Equivalent diameter relationship: D = 4RH d = 48R H 'See page 1-4 for limitations. Equation 3-35 3-6 CHAPTER 3-FORMUlAS AND NOMOGRAPHS FOR FLOW THROUGH VAlves, FITTINGS, AND PIPE CRANE Velocity of Liquids in Pipe The mean velocity of any flowing liquid can be calculated from the following formula, or, from the nomograph on the opposite page. The nomograph is a graphical solution of the formula. , l (For values of d', see pages B-16 to B-18) The pressure drop per 100 feet and the velocity in Schedule 40 pipe, for water at 60 F, have been calculated for commonly used flow rates for pipe sizes of Ys to 24-inch; these values are tabulated on page B-14. 1 w d p Qq v Example 1 Example 2 Given: No. J Fuel Oil at 60 F flows through a 2inch Schedule 40 pipe at the rate of 45,000 pounds per hour. Given: Maximum flow rate of a liquid will be )00 gallons per minute with maximum velocity limited to 12 feet per second through Schedule 40 pipe. Find: The rate of flow in gallons per minute and the mean velocity in the pipe. Find: The smallest suitable pipe size and the velocity through the pipe. Solution: Solution: 1 Connect I 2. 3· .............. page A-7 p 1. I W= 45 000 = 100 IQ L-- I Read I P = 56 .02 I Q = 100 I 2' Sched 40 V = 10 I Read Connect 1. Q I Q =3 00 Boiler Feed ....................... 8 Pump Suction and Drain Lines .... 4 General Service .................. 4 City.. . . . . . . . . . . . . . . . . . . . . . . . . .. = 12 I 372' Sched 40 Reasonable Velocities For the Flow of Water through Pipe Service Condition V d = 3.2 3 1/ 2' Schedule 40 pipe suitable 2. 3· 300 Reasonable Velocity to 15 to 7 to 10 to 7 feet feet feet feet per per per per second second second second I v = 10 CRANE 3·7 CHAPTER 3·- FORMULAS AND NOMOGRAPHS FOR FLOW THROUGH VALVES, FITIINGS, AND PIPE Velocity of Liquids in Pipe (continued) d Q tv 10000 ::::::I~ 3IlOO =~ :::::II q 40000 30000 GOoo 4000 3000 :::3' ;:::::::11 l :=::11 1000 1\4 :::='II L5 100 :; :.: c ~'600 '" ~ '" ~ :::J ,,400 '" "- ~3J0 ~ 100 0; '" "- ~ c 'iii'" 200 ~ :::3 0; a, ~ =c ==t ~ c =c ~ :::JI i v Q 4"::::.':31 ~ ~ <!J ~ ~ u c ~ c ='" >- ~. '" c ",' ~ 2"- ~ ~ or :.::::1 - ~ "~ ~ ~ ~ ==t 20 ~ '"I or 0- 40 I .08 "" .06 ;:,.. 10 .04 .~ .03 ~ .02 2 80 60 4J II Zl IS 10 8 6 4 3 2 ~ ='" ~ c '" '" ~ ~ :;; C. .4 .3 .2 c. "- "- '" '" :; c ." ~ '" > ., '" 2.S = ~ .= c ,; = 't5 ~ 2\2 c 0; Q; 1 .8 .6 .:: ",. 3 c. "- ~ 3.5 '"E co 0; ~ ~ N 5 c E .•01 .008 '::=JJ ~ .003 .8 .S r:<J '~I .8 .6 .S .3 F, '" ~ .0 ~ (.) :;; "~ =c = Q "- .= ,:: 8 .1 10 10 12 14 18 Zl 20 .002 0 c '" 0 :::; = I '" '" I Q, 16 .004 "- ~ c '":;l 6 ...~ 3 ~ D ~ ~ ~ z'" ~ ~ ='" '" '" 0; I 2 9 <~ ! 112 ::=1' =::::J !, P 24 25 ~. I I 1 I • ~"~"J,\::';::\ ::-;;"'!',i·7t~Y::'"i.:t". - ' - -.. ~ •• ,.~ .... -"~" ,-.,.:<:;.",,~ltWI'_J,.("""'-<';'''''':-' _ _-""..._ _ _ _ ~I.-~ •. , ",<._"","",,,",,,,,.,,-,",,~", ~"-'=""" ,--""", -~"~"'"~---'''-''""--~--- __ "''''.'''''''''-<'''' "",,"~_"'<J."""""''''''''''''''_~ ____ ' ___ '__ '_'f' ~~ Co) Reynolds number may be calculated from the formula below, or, from the nomograph on the opposite page. The nomograph is a graphical solution of the formula. R, = 22 700 ~: 50.6 -~ co ! = 6.31 (For values of d. see p"gcs B-16 to B-18) .." ... The friction factor for clean steel and wrought iron pipe can be obtained from the chart in the center of the nomograph. Friction factors for other types of pipe can be determined by using the calculated Reynolds number and referring to pages A-23 and A-24. I' q.Q !i> -. o-. '".. "Y1 0 ~ ... m n .... :J I Il ..,.., ... "'" - ('I) o -< d ":J \\7 0' 2... Q.. p (") '" ti" Q :J VI J -po z c 3 0'" to ('I).. C1i Example 1 ..... .a < c: <; -. Given: Water at 200 F flows through 4-inch Schedule 40 steel pipe at a rate of 415 gallons per minute. Given: Fuel Oil No. 3 at 60 F flows through 2-inch Schedule 40 steel pipe at a rate of 100 gallons per minute. Find: The /low rate in pounds per hour, the Reynolds number, and the friction factor. Find: The flow rate in pounds per hour, the Reynolds number, and the friction factor. CO Solution: Solution: o... p 60. 107 2. }.t 0.3 0 4· Q = 41 5 W = 200 000 Index 5· 6. R, = 1 000 I 1. p . page A-3 2. }.t I Cooo'" J. .. page A-6 = 60. 10 7 }.t 000 I ~or~~tally Ij 0, - 4.03 56 .02 .... page A-7 ........... page A-3 9·4 = 0.017 I Connect 3· Q = 100 4· W = 45 000 ). Index 6. ... o R, = I 4 Read IW I 2" Schcd 40 I I = 9·4 I R, I p = 5602 }.t 600 I tohorizontally I d = 2.07 f Q.. c: .." o::r ~ - R.;"~ I W' = 200 000 I 4" Schcd 40 I Index I = 0·30 IR, = 1 000 000 p o Cl'" :J r... _. Example 2 r. ...... <; ~ c e;~ > 6 Z g g ~ ~ '" 0 '" ~ 0 :::: ... :r 0 C Q :r < ~ < m !" ~ ::; ~ Z :J ~ "0 > Z "0 ('I) " :! ~ m = 45000 Index = 14600 n 0.03 > ". = Z m ( b n n 0 UII UII 'I r; II II UUtl U0 II UUnun n tl u uu u uHH 'I W 10 000 8000 6000 Internal Pipe Diameter, Inches Index _74 .21 1111r-- Re 800 600 3/8~.5 ID Co '"<= "C ;;; ~ 0 Co a.. ';; .,., "- '"<= "C .0 '" ~ OJ> '-' ~ 0 = f- o "- .1 ';; ., .08 ;;; .06 -- '" .04 I ~. 0 "- ';; 2 '" ~ '" o <= .,>- ~ f-- .8 .9 1.0 .. P - ;:;. :::-. 0 1/2 -\1 \" A\·, .01 .02 ~ <= '-' ~" - 2 Co a: ., ';; ., ro V> 0 0;; n; '"<= ~ ...ca.. 0 a.. - ,<= 50 .::';;; .,<= 0 <= ~ I ';;; z 7 ~ '< (D C ::J !I) CI) 0 :J D.. 0 c: - to '" ::J" I ... Q. ~ 0 ::J 3! .01 .008 " CI) 12 14 .006 .004 .003 ~ c ); ::J ,.'" 0 0 D.. z Z en 0 Z Q C 3: 0 ~ .." 3 0> (D 0 0- ... ,.. -. 0 ..c c: -. :l: ~ '" ~ 5 ~ ~ :l: '" 0 c Q :l: D.. -n ,.< 0 .'" ~ < m ~ ~ Z Q ,.z !" c :!! .." m 18 20 300 .002 500-::1 600 .. -."... ~--.."",>"......,..,"""".,..."""'-..."..,.,".--.• '~--..•-",.. ~~-.-",-.•-.-.---.,...,~,. Co) • 24 -0 ..,"",~.,.,--"""!"",~,, ..• ~ (D - ..,VI :.E .... 0 bQ <= E .2 ::I :::'; ::I 'C n; .,EO n 0 Co E N Factor for Clean Steel and Vlrought I ron Pipe ;0 '" ., - u ;;; ';; f . Friction ~ Co a:: 0 (") .c 2.5 ':- =... .O~ ... c .:. 211 ::tI 0 2.c: ~ "C ,-.04 I c; n -.. a> ;; ,- "'t\. .03 "f" =~ .,<= '\'\\ a> '" 0 , -... 65 ., -. -n 0 1.5 - , I~... "1"1 ::J I 3/4 '-- .4 =- . f= c:::::,f- 2 .6 _ -<! f-" 10 6 4 ~ "" L .! "" .03 .02 _\ ~ "C ',-1 -~ .0(, '" 100 :--"0 ~ 60 ~ 40 -. ~ 200 <= 10 ., 60 ~ 40 -z 20 :: ~ z m ~~~P'~-i-=-= il$ 200 400 ;; 0 300 :: :3 ID '":Ii- .7 1 0110 V) W .6 2000 <= H-~~,. n d J.l 4000 3000 "C 'iia .. ... -.'" ~""--"'''''.'''''''''''"'.-"''''-.." , ~,"., - .....,··,~.....--...~ ........ ___ ~""~_,,~""··_"'-"" ..C"'""'~'~A~.~,~ ~_,,_,'"-'-',".(~""'_k'"".'_'_~""",' •.-. -<"~"'"'-'~~~.""'~."~·'-"'';''''''''''''''''_.''''''''''''-.C''''''-'''''''''''''''~_~'''''--''''''''''",b_,~ ..• ,,,,;,,,,,,.., .... ,~~_,,~ ... ~ ..... ,~ __ .........."".~~....-'.,.,_.,,-"'W._,.... ,~ ......,.,..~,.., ..........~, .,,~.'"~''''''''' , Co> The pressure drop of flowing liquids can be calculated from the Darcy formula that follows, or, from the nomograph on the opposite page. The nomograph is a graphical solution of the formula. 6. P 100 6.P100 0. 12 9"; f pv' -d 4350 fpq~ de, f W' fpQ' 0.0216 ~- 0.000 336 ~ (For values of d and d', see pages 8-16 to 8-18) q 12 Q I P c.P,O<l d - o Example 1 Given: Water at 200 F flows through 4-inch Schedule 40 new steel pipe at a rate of 200,000 pounds per hour. Find: The pressure drop per 100 feet of pipe. Solution: 1; p 60.1 0 7 · ............... , .. ,page A-6 2. P, 0.)0 · ................... page A-3 J. f 0.017 · ...... , .. Example I, page 3-8 4· Q 415 5· ... "til III · ...... , .. Exarnple I. page 3,8 - - - , _.._ - - Connect Read -T::-~-I-~--60.I07 6. Index 7· Index 2 I I Q = 4I 5 1 4" Sched 4~ Index Index 6.P 1oo I 2 3.6 = ..... .. _. w III I c: (5 III c C '"> 0 "tl !< ;: z 0 z ::J 0 V- ,.,0 -. a... r-. ::lI '"'" n" c: 3: 0 . ". .. ..CD Example 2 Given: No. 3 Fuel Oil at 60 F flows through a 2-inch Schedule 40 pipe at a velocity of 10 feet per second. When flow rate is given in pounds per hour (W), use the following equation to convert to gallons per minute (Q), or use the nomograph on the preceding page. W Q = 8,02;; For Reynolds number less than 2000, flow is considered laminar and the nomograph on page )-1) should be used. The pressure drop per 100 feet and the vc!ocity in Schedule 40 pipe, for water at 60 F, have been calculated for commonly use,J flow rates for pipc sizes of Ys to 24-inch; these values are tafJulated on page B-14. Find:· The pressure drop per 100 feet of pipe. P 2. Q J. f 4· ). 6. -I ...C- c: c: iD Solution: 1. 0 -::J 56 .02 100 0.0)0 - · ..... , ..... , .. , .... page A-7 <:onneet 1 f 1 0.030 Q = 100 Index 2 1 2" Sched 40 E 0 :Ii · ....... , . Example 2. page 3-H 56.02 Index I p = ." · . ,Example I. Step 3; page 3-6 R~Il~ 'I I ;;-(l:~ --Index- i 6.P:- o---: --:--10 1 .-- - - - - - - - - - - ----- - - - .. :l! I m I 2 ~ n :IV :to Z m n H nIt • ~If w. ft • ~'1 D U···· t n n n " rt ft U· nftJt-R--n-----u'---11ft ff~ U rt n r ~ U ~ v. u U • ~ u• u w U lU' n n" tt~1 U \ ! q n Q :>:I ~r" Index 2 Z 30 20 » p r" 10000 --a 000 d 6000 .06 .OB.1 ·"1 ---00 J ---\ 2000 ,+'' .05 S w 800 ~ 600 w .04 Q. 20 16 9 u.. '" 200 -:; 2f) 2 ~ 60 If) I '" ~ '" b e ~ roc c e'" ",. :;;; c B" "" '" ~ "'" I '- ~ " ~ .03 Q. .8 .7 .6 .5 .04~ 2O~ .01 .= 50 '" E '" 3/8 1" .01t 4 .;: ,,' _ '" .ooa .006 3_ 0."- r -= u w m 0 ...0 3: c:: ); .... ~ " 0- <n 'U :;; Q. ::lI ~ ..... ~ c "o ..... ..ac "0 a.. "- ~ w '" "" :=: Le- ::I ,.... tD :::I c .e:: :;; Q. III :; ~ ~ '" a. k I: II , > z 0 z 0 3: 0 C> f ,f I L ~ > "::I: V> 0 '" 0 ~ -0 :c m m '" ~ ! ." C> t 0 i: :E C> 0: < > < ~ z '>z" :!! " m t ! I i· f t. 1. t ~,~ ao 100 0 i~ I. e c 0 40 50 60 I IT - 8 !I '"0c: ::I (( <J V> f ... .., -I C w ~ l ~ m 0 Q. e e I ~40 I~'" 0 .4 118 en en C c "0 0- ~ 100 80 '-. C>~ -:; w:: .2 0 :;; Q. u.. 0 =u" a:: 5 :;:; u u 7 .:: 6 .,; ~ .4 ~•• 3 c .02 =" -'= u B .= 400 300 .03 ~ ;; 55 ~ 1O~ , ....fI) .:: 12 12 10 .." -I f- Index 1 m /:"[>10. i [' ! .004 -=!.• 003 1 I '" Co) I 1 0' "':<''-.1 •• _.~_.~ .".'. ..-".",..,~'" .• "a~~""_>r;:JI"-,...,.J<,~'"""...."..._.-.'_"',',"'_' :,.',,....,~ •• , • ,,"w,._~~.,*~ .• ,_.~ •.. ~~.~~, -~.,.'''''~.".~'.."_,,.,~¥ .. _.' __ ~,,_''''''~~,,~~ ! ~. i / 3-12 / CRANE CHAPTER 3-fORMUlAS AND NOMOGRAPHS fOR flOW THROUGH VALVES, FITTINGS, AND PIPE ~~-------~----------------------~~~~~--~~~ Pressure Drop in liquid lines for Laminar Flow Pressure drop can be calculated from the formula below, or, from the nomograph on the opposite page, only when the flow is laminar. The nomograph is a graphical solution of the formula_ Flow is considered to be laminar at Reynolds number of 2000 or less; therefore, before using the formula or nomograph, determine the Reynolds number from the formula on page 3-2 or the nomograph on page 3-9. _ 6.PIOO - )LV 0.0668 d 2 _ - )Lq 12.25 d' ~ _ )LQ - 0.02,3 d' (For values of d' and d" see pages 8-16 to 8-18) Q q d Example 1 Example 2 Given: SAE )0 Lube Oil at 60 F flows through a 6-inch Schedule 40 steel pipe at a rate of 500 gallons per minute. Given: SAE 10 Lube Oil at 60 F flows in a 3-inch Schedule 40 pipe at a velocity of 5 feet per second. Find: The pressure drop per 100 feet of pipe. Solution: Solution: 1. P 56.02 2. )L 45 0 ..... . page A-3 J. R, 55 0 .. ' . page 3-9 4· Since R,< 2000, the flow is laminar and the nomograph on the opposite page may be used. r= 5· 6. ! I Ii I Find: The flow rate in gallons per minute and the pressure drop per 100 feet of pipe. )L = ......... page A-7 Index 0 Q p 2. Q J. )L 4· R, 5· 54. 6 4 115 = 500 6' Sched 40 ... page 3-7 .... page A-3 1100 ............ page 3-9 Since R, < 2000, the flow is laminar and the nomograph on the opposite page may be used. Connect Index I 6.P100 = ............. page A-7 95 Read Connect 45 l. 6. 4.5 7· p. = 95 Index Q Read = 1 15 3' Sched 40 I Index ! 6.P100 = 3.41 ~ ... CRANE CHAPTER 3 - ~ORMULAS AND NOMOGRAPHS FO~ flOW THROUGH VALVES, FITTINGS. AND PIPE ,;::::3 Pressure Drop in Liquid lines for laminar Flow ~~ (continued) { 3·13 q Index 4 d 3 2 L:::.P,oo 1.5 1.0 .8 .6 .5 .4 .3 5 .2 . 4 .15 3ll 3 '""' c. '" '" '" c. '" 0- '" 0 u "' ::- ., ~ ::::::3 ·0 "' « ~ ::::=3 ::t :=:t ",' <.> :?: ::=:D ::::=1_ "' ='" '"' -= . '" ';; '" '"E 0'" 0; '" ~ .10 ~ '" = 2 -= .08 ~ u ,; ., I = .r: '" u 3/4 '" ';; ~ N '" 1/2 -'" ~ 3/8 z;; u '";;; c. ~ .03 -='" u ~ ~ c..:> .02 0 '" ",' "~ ., m a: .oJ '"'" .OOB '"c'";;; ~ c. '" -c c ~ 0 0- '" ., ~ u.. = ~ -= ;;; ';; e U- ~ '" '" ~ c. c. 0 ~ ~ "''" ~ I 1/4 g r:t; <J ==:B 2 .002 1.5 ~. ~. 0 0- =::::t :::::3 -c c -:;; .04 u.. Il1 c. 0III = ~ u ~ .06 .05 '" :; .r: -=~ 1.0 .B .7 .6 .5 . 1 .0015 .5.4 3. j:.. .0006 2!·000S • _ .0004 .4 .IS} .= .3 .1- J .2 001 .0008 .0003 "', ;-:' 3 -14 CRANE CHAPT€R 3 - fORMULAS AND NOMOGRAPHS fOR FLOW THROUGH VALVES, fITTINGS, AND PIPE Flow of Liquids Through Nozzles and Orifices Example 2 The flow of liquids through nozzles and orifices can be determined from the following formula, or, from the nomograph on the opposite page. The nomograph is a graphical solution of the formula. q '2 e .... d" e '\jp if':,p = 0.043 8 do Y} II. = 0.)25 '0 Q }-Icad loss or pressure drop is measured across the flange taps. CqQ Cil'cn,' The flow of water, at 60 F through a 6-inch Schedule 40 pipe. is to be restricted to 225 gpm by means of a square edged orillce, across which there will be a differential heaJ of 4 feet of water. Find: The size of the orifice opening. Solution: I. P 62·371 ... . page :\..:6 2. J.L 1.1 . . rage :\-3 J. Re 105000 (1.05 X 10') .. page J-C) 4· Assume a ratio of do/d" say 0.50 5· d, 6.06; rage B·16 6. do 0.50 d, (0.;0 X 6.065) ).033 7. e 0.624 ' ,page A·20 I do p Read Connect 8. 9· Index I I Q Index do = 22; = 3" An orifice diameter of 3 inches will be satisfactorv, since this is reasonably close to the assumed value used in Step 6~ 1 I. If the value of do determined from the nomograph is smaller than the assumed value used in Step 6, repeat Steps 6 to 10 inclusive, using reduced assumed values for do until it is in reasonable agreement with the value determined in Step 9. 10. Example 1 Example 3 Given' A differential pressure of 2.5 psi is measured across the flange taps of a 2.000-inch LO. nozzle assembled in a 3-inch Schedule 80 steel pipe carrying water at 60 F. Given,' A differential pressure of 0.; psi is meas· ured across flange taps of a I.ooo-inch 1.0. square edged orince assembled in I !:l'-inch Schedule 80 steel pipe carrying S:'\E 30 lubricating oil at 60 F. Find: The flow rate in cubic feet per second. Solution: ............. page 1\-7 I. 56 .02 P . I !,~' Sched 80 pipe; rage 8-16 2. d, 1.27 8 1.278) = 0.7 8 3 3· do/d, = (1.000 .... susrect fiow is laminar since 0 J.L 45 4· Find. The flow rate in gallons per minute. Solution: I. 2. 3· 4· ,, 1 l j I I ~ 5· 6. 7· 8, 2.900 .... 3" Sched 80 pipe; page B-17 = (2.000 -7- 2.900) = 0.69 1 .07 .. turbulent flow assumed; page A-20 ......... page 1\-6 onnect I Read = 62,371 g = 1.07 I, do = 2.000 I I I hL = 5. 8 5 I p Ie Index Q = 200 Calculate R" based on I.O. of pipe (2.900"). . ... page 1\-3 1.1 Jl 9· R, 10. 200000 ". page 3-9 I I. e 1.07 correct for R, = 200 000; page 1\-20 12. When the e factor assumed in Step 3 is not in agreement with page A-20, for the Reynolds number hased on the calculated flow, the factor must be adjusteJ until reasonable agreement is reached by repeating Steps 3 to 11 inclusive. 5· e \'iscosity is high; rage A-3 , ... assumed; page A·20 1.05 Connect 6. f':,P = 0·5 hL = 1.3 I, 7· Index 8. 9. 10. 1 I. ! I p e = 56 .02 I I = 1. 0 5 I do = 1.0 I, i Read hL = I.) Index q I !i , = 0.052' Calculate R, based on 1.0. of pipe (1.278") . R, = 115 ......... '" . page 3-9 = 1.0') .correct for R, = 110; page A-20 e When the e factor assumed in Step 5 is not in agreement with page A-20, for the Reyn· olds number based on the calculated flow, it must be adjusted until reasonable agreement is reachd by repeating Steps 5 to 11 inclusive. 12. CRANE 3-15 C:HAPTER 3 - fORMULAS AND NOMOGRAPHS FOR HOW THROUGH VALVES, fITTINGS, AND PIPE ------- Flow of liquids Through Nozzles and Orifices (continued) do hL b.P C Index q p 24 Q alOO LIl lOOO 800 600 400 300 200 10 ~ ~ "" u '" ~ .= N N :=ro ~ = '";;; ~ 200 ..... 150 -;; '" ~ "C 0= ~ 0 100 c 80 .,; c... ~ ~ Cl e.> ~ '" :::"' Ii $ "' 60 -' "C ro 50 e.> 40 :c "'" '" 0 0 Z '";;; '"ro 0= '"u -~ - 0 .E ::;; ~ u ~ 10 8 U ~ ~ '-' ~ '" 0 "- ~ 0 "" I- .ero 1.0 .8 .6 "" .4 0 I .3 .:.., 20 <J 15 .2 10 6 .1 .08 .06 4 .04 .03 3 .02 Co) "" .01 .008 .006 .5 .4 ~ '"ro ~ 0 ""u .= ~ .0 .004 .003 .002 .001 ~ ~ ro u ~ ~ = '" -;; ~ ,; .= ..... ;;:; 0 = a; ..... ~ 0= ~ '-' -, 8 .6 ~ 0 "- ~i a; ..... ~ .; -- '0 0 ..... u .0 ~ '-' u 0 -;; .e ~ '" ~ ~ 0 "~ ~ E ro ?:;- Cl == ,; .= ..... ro E ~ ~ -;; .ero "" 0> Cl ~ CD ~ 0 ~ '" Q, ><.,.."."k-'",-'·""'>'.' " ... 0. The mean velocity of compressible fluids in pipe can be computed by means of the following formula, or, by using the nomograph on the opposite page. The nomograph is a graphical solution of the formula. V = 3. 0 6.'!1 V a' j 1.:06 n'I~Ul W (For values of d', see pages 8-16, to 8-18) i I I 1 '1 1 I I I 1 Example 1 Given: Steam at 600 pounds per square inch gauge and 850 F is to flow through a Schedule 80 pipe at a rate of 30,000 pounds per hour with the velocity limited to 8,000 feet per minute. Find: The suitable pipe size and the velocity through the pipe. Solulion: Connect l I. I 2. ,j 1 I J. 4· 5· 6. , -~ II 1 4 Read F vertically to 600 psig horizontally to = I.2Z 850 V Index ---_ .. W V 4" Schedule ___Index 0_._. psig 600 V = = = 8000 80 pipe is suitable. I. 22 Index 30000 d = 14" Sched 80 pipe 1V = :1: ,....m (.> I < ,.0 - ,.'"z !2.. 0 !:!. Example 2 '< Given: Air at 400 pounds per square inch gauge and 60 F flows through a I Y2-inch Schedule 40 pipe at the rate of 144,000 cubic feet per hour at standard conditions (14.7 psia and 60 F). Find: The flow rate in pounds per hour and the velocity in feet per minute. I. W 2. P 11 000, using So 2.16 ......... page 8-2 1.0 ............. . .... page A-IO Re~d Connect J. 4· 0 n 0 3 ... ...!a. "0 CD 0- Solution: 3.7 7600 ,.n... u d' p p = 2.16 ,--_In_d_cx W I = 11000 Y2" Sched 40 CI> "lI'I c c.. In Index. ::J V = 6 000 -ij' .." CI> 3:: c: ;;: 0 z 0 3:: 0 ",.,.... x '" ,.0 0 ~ ...,.:x~ 0 c :x " ,.< :;: m yo ~ ~ z ",. yo .___._______ Condition of Steam __. ___~..~lSonable V~.~~it~~s for."!0w._oL~!eam Throu{jh Pip_e_____._____...__ ... Pressure Service Reasonable Velocity ({') P,ig (V) ==~=~~<:<:t-J:-~-~':~~~~t-(~-~ Heating (short lines) I 4000 t;;""6-00()--I 25 and up I p~;:h,;;;.-;;-;;~.;iP;:,;cnt, pro~~~pi~~-~;,---r--6.. 0()0 to 10000 Boiler and turbine leads, etc. ---[--7000t; 20 000-"Superheated 200 and UD T .~-------~-~--. Saturated z0 ... :;; "' o to 25 n '"» z m a ~ nI( D nU U II U II U U U U U II U II U U U II U U U U U U U U~' \ t w o d v Specific Volume of Steam '"> .8 .9 Index p =r=~;;- .03 Z ",/ m LO ~~ ~~~ct~~~~ I-~-r--=---.,.-''''-~-;;o~ ---~~-------~ ~\\-I'"U?,e: -1"-r~ =:p~o: \16u~os-~~_ - - - - - ~ ==-,.. ____ '___._- _ ____ --,7""'~~ ~ ----{ --'::::::~"'j;9f-" - 1---"' _ _ _-=~ ~ __ ~ .05 0__ ____- . _== •10 8 200 -----7·~r ,;.--f<'=----:.o~~ -- ... --=-- -~-'" ~6 .,.-::~ :;;:=--= ~ 5 - - - 2 - v---: .....-",C __ ~r-,?,cl_k:::::::- ~ --- -- -c. t==I=' ' F/C::::;;-C ~~ ;;::. -;;:.~ -.:::7'. = _-=;H ~ ~ -=-~ --\----r~~g;· --~--=-- . . - .-:--- --- - ~ "~-;:~t:-"L~~()"'~--~------- -"~--- p..-=- _ _ ____ ___ t"'_ _ C-:.:.>'t ",_ ==t=:::-t - -::;:7'~f;9.. ° =± ---. -t··· -v-- 1~ u ~ i -.4 '-' "-- 0" u ~ --=- ~~?: --'(1--/ .~. ~5:;=-- r===!=- ----\/- ~ -- -'" ~·t-= =-~ '0 0 LL t= -;.,..0 l--""?'t=:"sQ;:~~ I--~ - 2· -.5 =----;;; - - -fLO ~o=~ ---"'r-= :;; =- •6 =-: =:9~09-~--- L5~ =------=:----. - - - ~-:..,...-- - ,o::;?,-" - :.,.;-___ =f.-=- E u> 150 3 :;;-:::-.3 ,;; ~='4.v~;::tc"~~ ;'~T';;c~ :-~~~~~ ~~-~:~J-- ~ , , ; 0 0 . - - . - - " - _ -.S ~ :;; '"c -c ~ 0 "- == 1 ;;; -~~1.0 1::' ';;; .,c '0 ::=:-,8:; _ - ~~~- ~~o _ __ 1 / .!:." ., =;::::0- c ~ ./ .5 v ,-2 ___ I Q, 7Lj-7.0::C'~' ----\;; 0=-- f=,:t~~"!: ~~;t =::- .. ;L=-~~~= ::= ~:::;:z::':--::'::: 1=--=-- ~= i== F~ I---T/- --r--:.L-- --- i-- --1---- .3 4 .215 400 t - 500 600 700 aDO V ~ c :s 60 40 ~ 30 Q; ., LL 0 20 10 6 100 :;; 0" 80 '" -c c 60 50 40 '" '"'" 2~ -c ~ c .6 15 .=! ",I.e. '03 .=! .2 ':; ., > I .e., 20 .e '" .1 '" "'" 900 1000 II 00 ~. 3 3.5 .. r:::: '" I 10 ~ i± 1200 .10 --10 ""-=:==== ;.g:::t-:= ----=EJcc= .- - :::;;' --. =--a". -f--' -*"'..=1= 1"-: ---"''- 8 9 ¢p~ it'vJ...I- ~k ~I- ~i-- k:- t-::[., !;; I-c-f- --I~~ 20 ok .X "< - j...- "::I0 ::-. ::I C flI ~ [ t!f: n 0 3 ... -. C'" "C i (!) til til ~ i (!) .." } ," !:. a.. J til ::J _. ." "C (!) ~ ::; ::! z Cl ,. !" Z 0 ~ :;; m . 1-- 1--1- _+=(:::: Schedule Number ! i: I I t t } I: 25 30 'i> 'b0 <2> '<2"~b ~~ •Ii [ p 0 ~ If Ii~; ,-\-:: ?o" p-F- ~- ~F'" 2 Temperature, in Degrees Fahrenheit 1- k-p.-I-e:: 15 -t--".f-'1I--+-r-.':l-~_ 1.5 - I ~ 0 A~ f-- 6 ,-- Cl EO ., < 1-=;]:'1= - =.= __ _ c '" '" ~;--=;,:~ E '0 E m . I=:~"l-_-_ ~",j _ 0" '"'" = f- !- 2.5 = -i= c .,- 4.5i -EE c : 3.:t;Z; EI_ _L2i' -o- '" c -0 1 £, .4 u .= "- ~ ~ c ':; 0 0 = f- ~ 0 "- .., = ----_. / 300 0 :<: ". :!l 1.6 . . --- \'1>"\ .1.e l I.B =t=--~--. .i~\le ~ - -,,~= 2 - F--~-;:::: t=~~·t\~_ 5 -==f::,'-+-f--+-=:1---S 2)0 ;; .e Cl :;;; ,6i:= ,.., b:+:~~-~t=:~~{~:/~7!:::;~~~':P'~;::' -1--=___.4_1~~ -2.5 __ n x --- ~--~-=---= =+:::-=t-·=::'-'0S-1, .OS __ lU ~ :::<~=- 1.4I-'~~~~ .06 15 f! ,\;~ 1.2 ~120 I w 'I t I' ¥ ! ! I '·· .. "-..,...."...., ..~""':"'-"""'''~-''-''r .. -'''~..,...'"''''''''' .. _.,.,....''·_~' . -_ _ _ _ _ _ _ . ,...... ~;:L:::..!-~::>I7.;;:';'l:"':!2/:.w.w'm'1..c:;:u:~"'_""_.~.:J,;;;_.: "-'.l':m'.$~Tt-"t4~-.:.;Wt"i.~{I'l'it1."~~$'.mcV$"""ITW'~~:f:l~''fJ,":,'·· ··::::,:',;r.7:_..,,::>·;:;-,~g,[ <"..;~~.~. ____~o: .• ._<_".~" .~ ,,,,_,""£--~'., '"~"" "'.~''''''''"'''~'.,,,u __ I-., .. ,.~.->. '" __ ""."-' """~.:...:.,~ __ ..... ,-"'~'";~...."'.... _, "',"H."'""""'''''''''----'''''''' ,"""~_~_ ....... ~., __ .................,......... ..,_~_,~-_o........ __ '"' ...........~.....__ •.__..... _ _ . _....__ "...._·_·~......-.----- -.-~. ~---" j j w D:I I! I t The Reynolds number may be determined from the formula below or from the nomograph on the opposite page. The nomograph is a graphical solution of the formula. w p. d The friction factor ior ciean steel and wrought iron pipe can be obtained from the chart in the center of the nomograph. Friction factors for other types of pipe can be determined by using the calculated Reynolds number and referring to pages A-2 3 and A-24. ; ,I W R, 0.4 82 6.31 dp. 'l 2. jJ. f ... 0 0 tll l~ead Connect I ), 1 69000, using So = 0.75 .... page B-2 0.011 .... ".""" .... ,." .. ,.pageA-5 ------ ~ 4, $. W 0 0- n dp. Find: The flow rate in pounds per hour, the Reynolds number, and the friction factor. .~ 0 --.. q'. So Given: Natural gas at 250 psig and 60 F, with a specific gravity of 0.75, flows through an 8-inch Schedule 40 clean steel pipe at a rate of 1,200,000 cubic feet per hour at standard conditions (scfh). = '< - = 69000 Index p. 0,011 18" Schcd 40 pipe -R ,= 5000000 I horizontal! to: 8" I.D.y 0 VI Given: Steam at 600 psig and 850 F flows through a 4-inch Schedule 80 steel pipe at a rate of 30,000 pounds per hour. Find: The Reynolds number and the friction factor. Solution: 1. d 2. jJ. 0 0.14 Note: Flowing pressure of gases has a negligible effect upon viscosity, Reynolds number, and friction factor. tll (!) Q ::I ... 3,826 0.029 .. ", .. ,.""" ., .. ,.", ,. ,page .. C ::r Read---I 1 .____Index I FZ' 7000il0 If = 10.017 = • . . ' _ . . . __ " .. - CO .. page A-2 Connect L 0 B-17 m '" CO :s III Z C 3 IT ... .... 0 ::I :9- "D (!) 0 '"c '" ;;: '"> Z "z 0 0Cl '" > :x: ro ." 0 '" 0 '" () 0 .. 3 0.."0 ~ IR, = 5 000 000 = > ." - -.. ::J Example 2 Indcx If ::c 1"1 Example 1 Solution: 1. W :;.c "Tl Q r. "TI (For v,>lues of d. see pages B-16 to 8-18) 1 ..._. o· ::J tll <It ~ 0 :;: ... '" 0'"c Cl :c III -. IT < > (!) !" "TI 0 ~ < m ~ ~ z Cl !" > z 0 ~ ." m n ~ ~ Z m I nn ,! ~ D V Uli--il--U U HUH H w l' II H II· U · I+~*n Index I~Z d J.I. .3.., j m .44 I '1 Internal Pipe Diameter in Inches .6 .7 _____- - - 3 6 ____ _ - - - - - 24 .R .9 1.0 ~_______ l~ :=::=-::: ~_____ :; e Re Co V> -0 10000 8000 1=1 6000 4000 3000 __ 2000 <= => e "- "0 I, V> -0 I __ <= N V> => 0 .c '::J .:: BOO1_ 600 400 300 i" 200 ,=> 0 '<I' u.. "0 '" '" \' -'" :\-1-_ :z " 100 .80 60 _ 40 30 20 '"o -0 <= >, '"'" ~ - -l V2-H •. ~\\ i~t:~_~kd= 1-- - . _.--- ~\' 10 8 6 4 3 2 '6~- .5 .4 "0 6 '" N V> '"<= I -1 .c ro 5 <= E ~ 0 z 10 12 14 15--1-16 .' 0 Z L~ 1- .02 f - .3· _ -Ll .03 ~ --1.04 20 ::I- '" .045~ 30 0 1'1 :J ::I VI :i" CD 0 c CD ----' _~_., CD 0 - CD n 0 Q ::J 3 0.." .... :E ... 0 c: to -... :r 0 :J ." -. "C CD III ;;: '"» z 0 Z 0 3: 0 Q .. > '" :I: '" ~ 0 '" 5 ~ 1: ... :I: '"0c Q :I: !!!. < > CD !" IT ." 0 ~ ~ ~ ~ z Q .V> » z 0 .."' ~ - 40J -0 .,.,.. "",~'...,~,"?~~""'-i"_~~""''''''''',-'''' ........."'...~". IT 0 3: '"c: I~ .05 Friction Factor for Clean Steel and Wrought Iron Pipe :J 0 0.. en .& -0 V> <= -... '"u 0 .". Cl Q; H - J.--H .01 ............... -4 '" LJ "I. 3V, '" '" E CD "< CD .8 """...,...-.,-'.,.,....".""""'.""~".~.,.,..,."""-"'-.,- ~§l I' E '" -3/4 --r4 -3 ;;ra '" ""5 "- 0 ..." - ... ., - -... 2V, .; - ~ w I :I: n c: 3 CD <= "'- I~ -H 1 I, - c:: n :::!'. 0 :J ." -.. u <= =: "» 0 IV, .c ::; ",' =~ ~r==J=j~~~\~~ - f:. e 4 \ 2:'" I 000 f- 1.5 "TI on I~ .: 2 :t=l ~ ril _ '"'" 3/4 _, .c u 4 =1=1 =+=I 3 2 IV, :::~ (IlHf j 10 III~; ::t: Q; 12 ..-. -1/2 _ _ _ .-."., _, ",,.~,~.u~~, ...... ,~,' ,."<...--"'",.....'t"'"!'~"" .........,..,...,,...... _ ....,.....,..........,... _ _ _~- •. n·¥,."",«?""' .. ·, , '~ I ! t,,, ,_~"""~""'''-'''''''''''''''''''''''~~_A''''~'''''''''"'''''''''H"""""",,;,,,,,,,,>.,,,,,'_r~ ~ .• ~" ~"d,"'~~~""'~'~;';'_""'-"''';_'''''~''_"'--'''-', .... ,,__ ,<, ,,-,.-. "" ..""l/,,_, ",l> .'",'",b.~;".L.",,,,,".'w._ . ~"""""""-'. ~~ _'_M'~.~._~_ "~- j ) I ~ I ~ 1 Co> , I-) The pressure drop of flowing compressible fluids can be calculated from the Darcy formula below, or, from the nomograph on the opposite page. The nomograph is a graphical solution of the formula. /::"P IOO 0.00033 61 /::"P 'OO W'V d' 0.000 001 959 f o f drIp W' 0.0003)6 p V I, /:>.r iOO w n ::l: > ... (q' .)' S,' •. ~ m - '".., ... "'tJ .. (For values of d', sec pages 13-16 to 13-18) i! I, I I W = 0.0764 $ lI ,I 1 1 I ~ 1 I 1 c: ... II> ...0 0 q'. S, ~ c >= V> > z 0 Z 0 "0 ~ ::I > '" 0 Cl Air: For pressure drop, in pounds per square inch per 100 feet of Schedule 40 pipe, for air at 100 psig and 60 F, see page B-15. 1 I II> When the flow rate is given in cubic feet per hour at standard conditions (q'.) , use the following equation or the nomograph on page B-2 to convert to pounds per hour (W). I ~ 0 Example 1 n 0 3 Example 2 Given: Natural gas at 250 psig and 60 F flows through an 8-inch Schedule 40 pipe at a rate of 1,200,000 standard cubic feet per hour; its specific gravity is 0.75. Given: Steam at 600 psig and 850 F flows through a 4inch Schedule 80 steel pipe at' a rate of 30,000 pounds per hour. Find: The flow rate in pounds per hour and the pressure drop per 100 feet of pipe. Find: The pressure drop per Solution: Solution: /, d 2. J. 4· 100 feet of pipe. /, ........ page 13-17 3.826 J1. 0. 02 9 . page A-2 f 0.017 . page 3-19 V J. 22 .. page 3-17 or A-17 5· W = 30 ~-fd-~6 6. Index 7· Index ~_ _ 2 1 f = I_V 0,017 1,22 !!!. 69000 .. using S, = 0.75; page 13-2 2, J1. 0.011 . , pai:e A-5 J. f 0.014 " .page 3-1'1 4· P 1. 0 3 .. paile A-IO " ~ 0 :E ~ ::l: 0" 'TI < > ~ W ~ 0 0II> 0 C .. ::I II> c: Cl ::l: :;:m .'" ~ ~ z Cl .'" > Z 0 ---, Index 2 Index 1 ---/::"P 'OO II> ::l: '" ...~ m Read Connect .... "0 ... 7.5 Connect 5, W = 69 00018-;; 6, Index 2 7, Index _1_ _ 1 Rend S~ 40 pi~ i Index 2 f = 1 Index I 0,014 I_~_~~_J /::"P 'OO = 0.68 ..,n > Z m .~;::J 3 -21 CHAPTER 3 - fORMULAS AND NOMOGRAPHS fOR HOW THROUGH VALVES, fITIINGS, AND PIPE CRANE ~ Pressure Drop in Compressible Flow Lines {continued) ~ ;::.; JOOH Jad spunod 0001 U! 'MOlj g gg __ gg g g eo~a.noo:::t"M 80 000 0 ...-fooc.oL..n~('Y) gC'oJ 0 N )0 8jBIl-"11 0 _oo(,O'"'"'~~ _~~I.C?~C'"t':? ('oJ ~ C'! !'I!!IIr1dd!l,1 II! II!!!!!!!!!!!!"'!,! I,I[!,! I I!!!,i!!!!illtddddd,t! i! :'tj,I!!1!I!!!!!,1r1d.!r!' I! jll!t!!!!!!!!!!! JOpe:l UO!P!J:l- J Ln~ ........ ,:,! ~ I!! I ! ! ~ N (Y:J ...,,~~ .- ~ <::::> ![!!!!)!!! I",! ~ ,I! i ! I I ! (op alnpa4JS - ad!d pJBpURlSJ S84JUI U! 'Jaj8WB!O IBU!WON qo ('oJ 0 N (,Oq-N _ __ 0_ 00 (,0 U"'> I 1 I ! I r'IIFIfI I ! ( i i j i l l j i l ' ( I ~ I !! J ~ ~oor-(,O ""::I'" i ~ C"')~ ) ~ C'J ~ "'$. ............ N I! J! I ~ _ ! [ to:) ..... ~ ~ ~ _:-;!: s_" I I -f I I Ililililii\iitljilii\QQ'lllil!ilii(liil\ 1.0....... -~oql':~ cry......... u: ~ sa4JUI U! 'ad!d )0 Jajawe!o leUJajul--1' ijJUI aJRnbs Jad sPunod U! 'jaa.::l 00 I Jad dOJO aJnssaJd -- oo'cl'i7 L.t1 !! N C"') U"'> Ln(,Or-OOC':l 0 _ _ ....... ,I"!I!,!!!!,,!!!!!!!!!!!!I!! J 0 0 0 N "<:t'0 U"'> ~ I f l , I , ! , ! ! ,i"!!!!!ld!I!!I!!!!!!!!!! ..... >< ~----------------.---------------------------------------------------------------- .= ~ ~ ~ ~ g I'I'I!'I I!i 1!"II'I"j!!! I I r 1 J ct. ~ q ~ q punod Jad laa.:l J!qn3 U! 'P!nl:l ZU!MOI:l )0 ~ c-.... I! I ~CJ")CX) ! ! I r- <D \,.l'") ...,.. ('") awnlol\ 3!)p ad S-,1 5 50;':'>':; r-.:"=! LO !! I I'" ,I,!!! 1III'I!!!!]! /'!! , I'!';' I j r I'I!! I I j I I II r i l l I I I I I 1111111l I 1, j ....~1111 I ! """"!. t ! ~ ~ ~ U? I t ~ ":CC!~~ ! ,-; ! ,:\, C"-I '¢ ,1",1 (I r I! ("I") N ("I") I ! ' - " I ! ! ! ! '," j oo::t- I \,.l'") 3 -22 CRANE CHAPTER 3- FORMULAS AND NOMOGRAPHS FOR flOW THROUGH VALVES. FITTINGS. AND PIPE Simplified Flow Formula for Compressible Fluids Pressure Drop, Rate of Flow, and Pipe Size The simplified flow formula for compressible fluids is aCCllrate for fullv turbulent flow; in addition. its use provides a good ~pproximation in calculations involving compressible flt;.id now through wrought iron or commercial steel pipe for most normal flow conditions. Values of C, II" If velocities are low. friction factors assumed in the simplified formula may be too low; in such cases, the formula and nomograph shown on pages 3-20 and 3-21 may be used to provide greater accuracy. (\ 2500 2000 1500 The Darcy formula can be written in the following form: W·2(O.OO~/36f)v = (W'210-9)(336~00f)v lOoo 900 BOO c. = 700 EOO The simplified t90w formula can then be written: 500 -- = C,C, CJ C211 f':"P 1oo 400 P :; f':"P IOO P f':"P lOo P C2 C1 C1 = discharge factor from chart at right. = C2 size factor, from table on next page. The limitations of the Darcy formula for compressible flow, as outl.ined on page 3-3, apply also to the Simplified flow formula. 0 DJ ::t: Q; 2SO c- '" '0 100' § 0 a.. '0 ISO C '0 '" '0 '"'"'" '" .c '" '"'" 100 -,;; 90 > 80 70 0 f- .=,,0 li: Example 1 '0 ill ro'" 50 Given: Steam at H5 psig and 500 F flows through 8-inch Schedule 40 pipe at a rate of 240,000 pounds per hour. a:: Find: The pressure drop per 100 feet of pipe. := Solution: 01 40 3l 57 0.14 6 1.45 .page 3-17 cr A-16 57 x 0.146 x 1.45 = 12 2S 20 15 Example 2 LO Given: Pressure drop is 5 psi with 100 psig air at 90 F flowing through I()O feet of 4-inch Schedule 40 pipe. .9 Find: The flow rate in standard cubic feet per minute. Solution: f':"P 1oo = 5.0 5.17 P 0.564 ....... pageA-1O C1 (5.0 x 0.564) + 5.17 = 0.545 10 .8 C2 W q'm q'm 2)000 W +- (4-58 Sf!) ................ pageB-2 000 + (4.58 x 1.0) = 5000scfm 2) For C~ va/vel cnd on example on "determining pipe size"~ see the opposite page. CHAPTE~ CRANE 3·23 3 - FORMULAS AND NOMOGRAPHS FOR flOW THROUGH VALVES, FITTINGS, AND PIPE Simplified Flow Formula for Compressible Fluids Pressure Drop, Rate of Flow, and Pipe Size - continued Values of C, ~ominal j Schedule Pipe Size I Number Inches I 40 s 80 x Value of C, 40 s I ' 160 . ,II 319000. 71S 000. Ii ." xx 405 80x 160 ... xx 1 40. 80x 160 ." xx 40. 80 x 160 .. xx IV:! 40. 80x 160 ... xx 2 40. 80 x 160 .. xx 2 V:! SO x .. xx 4 II i; 950. Ij 640. I 1.59 2.04 2.69 3.59 4.93 G 40. 80x 120 160 ... xx 0.610 0.798 1.015 1.376 1.861 20 30 40 s 60 80x 0.133 0.135 0.146 0.163 0.185 8 100 120 140 160 10 20 30 40. 60 x 169. 236. 488. 899. 100 120 140 160 0.0661 0.0753 0.0905 0.1052 20 30 ' .. s 40 0.0157 0.0168 0.0175 0.0180 0.0195 _.. x 0.007 00 0.00804 0.00926 0.01099 0.012 44 80 100 120 140 160 18 I II 0.00247 0.00256 0.00266 0.00276 0.00287 0.00298 10 20 .. s 30 .. x 40 60 80 100 120 140 160 0.00335 0.00376 0.00435 0.00504 0.00573 0.00669 10 0.00141 0.00150 0.00161 0.00169 0.00191 20 30x 40 60 14 i 0.0206 0.023 I 0.0267 (}.031 0 0.0350 0.0423 0.00949 0.00996 0.01046 0,01099 O.Oll 55 0.01244 0.01416 0.01657 0.01898 0.021 S 0.0252 .' xx 40. 80 x 10.0 13.2 10 20 30. 40 " .x 60 5.17 6.75 8.94 I I1.S0 I, IS.59 80 100 120 140 160 II 80 100 120 140 160 \' 80 100 120 140 160 2S.7 48.3 96.6 40. 80 x 120 160 . xx 0.00463 0.00421 0.00504 0.00549 0.00612 lOs 12 21.4 10 20 30. 40x 60 16 0.0397 0.042 1 0.0447 0.051 4 0.0569 SO I 627. 904. 1656. 4630. 40 s 80x 160 Value of C, 0.211 0.252 0.289 0.317 0.333 ... :xx I. 40S. 66.7 91.8 146.3 3S0.0 Schedule Number II, !I 2110. "490. B640. I Pipe Size I I Inches ! I 40. 80 x 120 160 ... xx " 21 200. 3& 900. 100100. 62? 000. 22500. 114100. I 5 !I Ii Nominal i Value of C, 60 40. 160 3 93500. 186100. 4300000. 11180000. Inches II 1590 000. 4290000. I, 405 SO x Ii II I 2~ i~,g ggg: II 40 s 80 x SOx :1 Nomina1 I Schedule Pipe Size i Number 24 1'1 0.00217 0.00251 0.00287 0.00335 0.00385 10 20. 30 40 60 0.000534 0.000565 0.000597 0.000614 0.000651 0.000741 80 100 120 140 160 0.000835 0.000972 0.001 119 0.001274 0.001478 ., x I III I I ,:1 I Note The letters s, x, and xx in the columns of Schedule Numbers indicate Standard, Extra Strong, and Double Extra Strong pipe respectively. .~----~------~------~---------------------- Example 3 - Chen: /I.n 85 psig saturated steam line with 20,000 pounds per hour flow is permitted a maximum pressure drop of 10 psi per 100 feet of pipe. Find: The smallest size of Schedule 40 pipe suitable. Solution: 6.P"o C, 10 v= = 0·4 C, = = 4.4 10';- ,.pagc3-17or,\-13 (0.4 X 4·5) = 5.56 Reference to the table of C2 values above shows that the 4-inch size is the smallest Schedule 40 pipe having a C, value less than 5.56. The actual pressure drop per 100 feet of 4-inch Schedule 40 pipe is: 6.P100 = 0.4 x 5·17 x 4·4 = 9.3 3 _ 24 ---- CRANE CHAPTER 3 - FORMULAS AND NOMOGRAPHS FOR HOW THROUGH VALVES, FITTINGS, AND PIPE Flow of Compressible Fluids Through Nozzles and Orifices 6P The flow of compressible fluids through nozzles and orifices can be determined from the following formula, or, by using the nomograph on the next page. The nomograph is a graphical solution of the formula. W = ./I:;.p 0.525 Y d'o C.y I:;.p PI = 0.525 Y cPo C",,! =- W = 1891 Yd'OC-,jUPPI = 1891 YcPoC ~ (Pressure drop i~: V, measured across the flange taps) Example 2 Given: A differential pressure of 3 psi is measured across the flange taps of a 0.75o-inch I.D. square edged orifice assembled in I-inch Schedule ~o wrought iron pipe, in which, dry ammonia (NH3) gas is flowing at 40 psig pressure and 50 F. Example 1 Given: A differential pressure of I 1. 5 pSI IS measured across the flange taps of a I.ooo-inch I.D. nozzle assembled in a z-inch Schedule 40 steel pipe, in which, dry carbon dioxide (C0 2 ) gas is flowing at 100 psig pressure and 200 F. Find: The flow rate in pounds per second and in cubic feet per minute at standard conditions (scfm). Find: The flow rate in cubic feet per hour at stand- Solution: I. R S, 3. k 2. I. 2. 3· 35. I } .' 1. 5 16 ........,' ... for CO, gas; page A-8 1.28 -. . 4· P't = P + 14·7 = 100 + 14·7 = 114·7 5· I:;.P/P't = 11.5 + 114.7 = 0.1003 6. dl = 2.067 ....... . Z' Sched 40 pipe; page B-I6 7· do/d. = I.CO + 2.067 = 0.484 8. Y 0·93 ........................ page A-21 I .003 .. turbulent flow assumed; page A-ZO 9· C 10. T 460 + t = 460 + 200 = 660 12. 13· 14· .... _ ................... page A-IO 0·71 II. m I I Connect I:;.P = 11.5 PI 0·71 I Read Index ·---+----------~--------I 1C Index J: 15· 16. q'h do 1.000 I Y 0·93 I Index 3 W = 5000 I 44 000 scfh .................. page B-Z 0.018 .................. page A-5 860000 or 8.6 x 10' ........ page 3-21 C 1.003 I,S correct for 19· R, = 8.6 X 10' ... page A-20 20. When the C factor assumed in Step 9 is not in agreement with page A-20, for the Reynolds number based on the calculated flow, it must be adjusted until reasonable agreement is reached by repeating Steps 9 through 19. 17· I" 18. R, k for NH, gas; page A-7 1. 2 9 to determine the Y factor. 4· P', = P + 14-7 = 40 + 14·7 = 54·7 5· I:;.P /P\ = 3·0 + 54·7 = 0.0549 6. d , = 1.049 ........ 1' Schcd 40 pipe; page B-I6 7. do/d. = 0.750 + 1.0~9 = 0.716 8. Y 0.98 ........................ page A-21 0·702 .. turbulent flow assumed; page A-ZO 9. C 10. T 460 + t = 460 + 50 = 510 I I. PI 12. 13· Index I Index 1. _ _-;--,.C___I_.00 __3+I--::-In _d_e_x__ 2 __ I R = 90.8 } S. = 0.5 8 7 ........... Steps 3 through 7 are used Steps 3 through 7 are used to determine the Y factor. j w I~P '-.. 'V Solution: , \\"' VI ard conditions (scfh). ! do ........................ page A-IO 0.17 Connect I Read I:;.P = 3. 0 I PI = 0.17 Index 1 IC = 0·702 I Index I I Index 14· Index· 2 15· Index 3 16. I Index 3 Ido I 1 I 2 = 0·75 I Index 3 Y = 0.9 8 I W =.0.145 Y = 0.9 8 IW = 520 1·7- q'm 18. I" 19· R, 0.010 ....................... page A-S 310000 or 3.10 x 10' ...... pageJ-ZI 20. C 0.702 is correct for R, = 3.10 X 10' .. page A-ZO 21. When the C factor assumed in Step 9 is not in agreement with page A-20. for the Reynolds number based on the calculated flow, it must be adjusted until reasonable agreement is reached by repeating Steps 9 through 20. CRANE -------- 3·25 CHAPTER :1- FORMULAS AND HOMOGRAPHS FOR flOW THROUGH VALVES, FITIINGS, AND PIPE ;;:::1 Flow of Compressible Fluids ;::::t Through Nozzles and Orifices (continued) - " -it 6.P do 1, TV I, 600 3)00 500 <DOD 400 .~~ ~. I ~ , -400 =:::::'j ZOO 200 400 300 100 150 <DO 100 100 80 60 = 80 .:: Q 3 '" '" 40 3) ~ = '":u '-5 "- 40 ~ <D o· " " "- 10 8 6 0 ~ Q: 4 3 ZO ce ~ 15 ~ ~ "- 10 2 ~ ~ ~ ,":::=) 1.5 '" 1.0 .8 •6 .4 I ~ <J '::=8 ;::p 5 1.0 X '" ".::'" ~ '" ;;; " 0:: "- '" "C =3 = ~ .8 " "<=> <=> 1.5 ::=.l :::::) X "C '=:& ~ ",. '" "- 1.0 =3 - .9 10 8 6 :; " "Q .8 = ~ ;;; ~ '-' '" "'~ " " "- 2 ~ ~ .2 " "- = ~ 1.0 .8 .6 = .;;; " = "'~ .4 .3 .2 ~ '" '"'";;; u "- "'"= " "~ = ,; " "- ~ ~ '"I '"I ~ '" = ,:: .6 .25 I ::.. ~ = '" >< Cl UJ .55 :;; .. "" '" t '"'" 2: " N .1 -;; :: :u"'"- -;; ~ =l 1.0 <D t "i 6 ::::::3 Y u ~ 30 80 60 40 30 ~ ~ -:::=II 300 3J0 60 50 P lOOO 800 600 1000 800 600 ~ =;::J~ V 1, w Q. N = ~ N x "'" .:: '"'" -=" ~ !, 0 .g = '" " "'" u '" .2 "I u I .1 j .09 !j .08 I .07 ! l, ! " j .0625 t~ :.:=:JI A -1 ~ ::::) :=;) Physical =.) and Flovv Characteristics of ::=:3~ ::=i~ Properties of Fluids Valves, fittings, and Pipe ! APPENDIX A :=:i~ i ii ::::j. I >:=:1. I :::3 ::=:I. .==1t :=D :=:I~ ~ ==t The physical properties of many commonly used fluids are required for the solution of flow problems. These properties, compiled from many varied reference sources, are presented in this appendix. The convenience of a condensed presentation of these data will be readily apparent. I ~ I t Most texts on the subject of fluid mechanics cover in detail the flow through pipe, but the flow characteristics of valves and fittings are given little, if any, attention, probably because the information has not been available. A means of estimating the resistance coefficients for valves, deviating in minor detail from the standard forms for which the coefficients are known, is presented in Chapter 2 . ~ . :::::::n i ~ I The Y net expansion factors for discharge of compressible fluids from piping systems, which are presented here for the first time, provide means for a greatly simplified solution of a heretofore complex problem. :b~ ~ ! II I I i A _2 APPENOIX ,,- PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE CRANE . 0 f Steam 14 V·ISCOSlty .050 1\\ \\ .048 .046 .044 .040 I ! :::; ~ .042 , « \ : I Q .036 l- a ~ ~ I, ~ Vl Ie , ';1 ...... ~ <:: .034 Cll >. (/l ~ -- I - - 1 - - % V - ~~ % 1/ 0 ~ 7~ ll~~~ % ~ \1-"'' ' ' ",,,,,,,/ ~ 'I "./" 'V /" (/l = « .026 ./ V'o\)\)~ '>.\)\) .~ ~ ?f/ /' V' / /~~~ I L/ //%V~/ I .024 .022 / ~v I I 0 0/'1~ I .020 I , I I~ .018 ;; V' I I V .016 .014 .,V / \ ~",(J I ~ .028 I :t V V V ,. / I ~ .030 .... ---- ---- L,. .-: .032 :> '" 1860 ........... ....... c: u on 2600 -2200- 10.. VI U a '-- 1 « (/l 0. "- =>'" l Cl.> '-.....""1 " ~ PSIG 319 1.5 -3000 1-,\ « I i \ '" UJ .038 I I ... \ ~RESSURE '- ) I I l/ 200 I 300 400 500 600 700 800 I 900 1000 1100 1200 t - Temperature, in Degrees Fahrenheit Example: Viscosity of 600 psig, 8;0 F steam is 0.02Q centipoise. Adapted from: Philip ). Potter Steam Pou'er Planls, Copyright 1949, The Ronald Press C'..ompany. CRANE <:i APPENDIX A - PHYSICAL PROPERTIES Of flUIDS AND flOW CHARACTERISTICS OF VALVES, fITiiNGS, AND PIPE • Viscosity of Wafer and Liquid Petroleum Products8 ,12,23 400 0 300Ill.. ~ 200 18 17 1\ ~ \1\1 I 1\1\ 16 \ 1 \ 100 80 60 , , Cl. c: 40 30 ;:;. 20 12 I I o <f) 10 8 6 ::t 10 9 r,i 2 b :6, :=3, 6 1.0 I 5. Gasoline I \ i\ 6. Water \ I \ i 4 I \1 \ \:\ 7 r. . . . . ~ li b \ \ I"'-.,"'\. 1- "1\ ~~\! N...,I' 1 ......... \ I ~ i' J. \ \ \ 1\\ \ ~ I ' , r-t- r--r-I T- ~2 NN 1 .08 .0 6 ,..-1. , 20 11. 35.6 Oeg. API Crude I r--: "'-., I, I 17. SAE 30 lube (100 V.I.) \ 18. fuel 5 (Max.) or Fuel 6 (M;n.) ' 1 1\ I' ~ '\.1 -1 _L \J :\ ! ,\l-- - - 1\ I l"\. 1'\ I ~ J 30 40 60 80 100 200 300 400 t - Temperature, in Degrees Fahrenheit 20. Bunker C Fuel (Max..) and 21. Asphelt 1\ f"\.- 1')"-......., 19. SAE 70 lube (100 V.I.l M.e. Residuum i,\ '\\ ' \ \\1\ '\. ~! ~I~ \, I 15. fuel 5 (M;n.) 16. SAE 10 lube (100 V.I.) 11 \ 14. fuel 3 (Mex.) , \ \\\\\ l'\. ~ I 13. Solt Creek Crude , 1\ \ l\\11 \ f0'\, '\' 12. 32.6 Oeg. API Crude I -.... I. i ~ 1\ \' \\ \ '\ ~ ~', ~ 8. Distillate 10. 40 Oeg. API Crude \ II \ \ ~ ,-::::::: 7. Kerosene 9. 48 Oeg. API Crude I ,\ \ r----i ' 1"t'-l,I ~~~J, t - t- 1 I I 1 \ '( '\ ,,\ I' i' 3L .2 1 , D' , 1 I i\ \ 1\ _\ \ I I:::: .4 .3 I , 1\ ~ \ 4. NQtu~a' Gasoline I 5 8 .6 .04 .03 lD ,- \ ~ 8t-- 4 3 \ I \ " \ 15~ r\ 1\\ 1\ \ \ I~ 14 b- I" 1 ~l \' \ I "'-., "b, ~ ~}. \ \\ \\ ~ ~\ , u I \ ~ \ 11 1-....... Vl > \ -......., _Ll -.1 1 \ \ 1\[\ \ \ ~ 13 2. Propene (C,H s) , 1\ \ I 1\ \1 \ I 20 0 c: I. Ethene (C ,H,) , ....\ I i '" '-' 1\ \ _l 400 300 ~ \ , 6010- o \ l~ \ 1\ 1000 800 '"Vl 21 I 119 I II Ill.. - I; A-3 \ \ 600 800 1000 Example: The viscosity of ,,'ater at 125 F is 0.)2 centipoise (Cur\"c No. b). Data extracted in part by' permission from the Oil and Cas Journal. A-4 APPENDIX fti,- PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES. FITTINGS. AND PIPE ~-'---- CRANE Viscosity of Various Liquids S,8. II 10 6.0 1,\ \ 4.0 \\ \ 3.0 18\~ 11 2.0 16~ ~ ZJ r-- '\ i II - Ii ~5/ 12 7 ~S= '\. "- ~ c: '" .5 C,) c: ..:::- .4 '" .3 '" > 0 u I ::t. .2 r\ \.\ \ , l\. 1\ 1\'"-, ~ ~\' "", '\. ""- 6 .8 ,.~ .7 '"0 l'.. 0. .6 Q.) \\, ~ ~\ i 1.0 .9 1\ i( 1\ \ 5.0 '\. ...., ~. '\. ~ r\""'" '\. -.\. "" ..... \. I'-... I'\.. " "'-"" '''''~ I~ --1\ ~\ ~~ ~ p::::::: .06 \. 11 \ "- a '" I"-...... "- "- ----- "- "i I~ \\ .04 -............. I'.. \ .05 .03 -40 '" ~ "" ~ r:::::- I-"' -~ 0.1 .09 .08 .07 ......... ............ "- ....... .......... ............. '" '" ~,'" ;~ " ~"" & " ......... ..... ""- ..... \ 40 80 160 240 120 200 t - Temperature, in Degrees Fahrenheit . 280 320 360 1. Carbon Dioxide •• CC~2 2. Ammonia ••• " •••• NH::;. 3. Methyl Chloride •• CH;>Ci 4. 5. 6. 7. 8. Sulphur Dioxide •. SOI~ Freon 12 ...• F-12 Freon 114 ....•.. F-114 Freon 11 ..•....• F-l 1 Freon 113 ....... f·113 0 ••• 9. Ethyl Akohol 10. Isopropyl Alcohol 11. 12. 1 3. 14. 15. 20% Sulphuric Acid ••.••• 20% H t S0 4 Dowtherm E 16. 17. j 8. 19. 10% 20% 10% 20% Sodium Chloride Brine ••. 10% Sodium Chloride Brine ••• 20% Calcium Chloride Brine .. 1 0% Colcivm Chloride Brine •• 20% Noel Noel Coel: CaCt: Dowtherm A 20% Sodium Hydroxide .. 20% NoOH Example: The viscosity of am- Mercury monia at 40 F is 0.14 centipoise. eRA N E APPEND I)( -'-'-:.-.----- A-PrYSICAl PROPERTIES OF FLUIDS AND flOW CHARACTERISTICS OF VAlVES< FlnINGS< AND PIPE Viscosity of Gases and Vc;pors Viscosity of Various Gases . The curves for hydrocarbon vapors and natural gases in the chart at the upper right are taken from \lax\\·cll 15 ; the cun·es for all other gases (except heli um 27) in the chart are based uJXln Sutherlamfs formula. as follows: /1- = /1-0 where: =t /1- <:=1t /1-0 ::=3_ ==l. ==:I. .:=9 - :=1~ ::=1. +C T = absolute temperature, in de- . grees Rankine (460 + deg. F) for which viscosity is desired. To = absolute temperature, in degrees Rankine, for which viscosity is known . C = Sutherland's constant. Note: The variation of viscosity with pressure is small for most gases. For gases given on this page, the correction of viscosity for pressure is less than 10 per cent for pressures up to 500 pounds per square inch. ~ .==11 ==:S~ Fluid 0, Air :=:I, ,03 N, Approxi:mate Values of ~4C" i 6 I 0, / / / / Helium / / Air N, ' / //.CO, / / /:/!/V0 SO, /i//VY~ I .03 2 / 8 i II I To viscosity, in ce:1tipoise at temperature To. ! i I viscosity, in centipoise at temperature T. = I : .04 0 (0<555 7:0 + C;) (~)3:, 0.555 7 =D I ! V/V/Y~ Y/V'XY,,{ J---I t VA'hc<;Y/' i/r ::;. .;;; ,02 4 8 :;;: ~ :::I.. .02 Y ~ Vh [t' V i ;.-.! /1'a~; V ,.¥1/10-1 ;,,/.;/ i / V~ VV ~/ 1/ I o~ .01 6'.#' ~ VV ~/~/, ~ /iv'~/)ffi I , I I i ,I / ~j//.~ i ! ).---V . , /7 ~~ ~ ~, .01 2 ~. i ~~ IVV, ! II ~ I .00 i~' 8~ o 1-- H, i ! 100 200 300 400 500 GOO 700 800 900 1000 t - Temperature, in Degrees Fahrenheit Viscosity of Refrigerant Vaporsll (saturated and sup·arhealed vapors) 127 120 III CO, CO SO, 41b NH, H, 370 72 240 JIB Upper chart example: The viscosity of sulphur dioxide gas (SO,) ,at 200 lis o.olb centipoise. Lower chart example: The viscosity of carbon dioxide gas (CO,) at about 80 l- is 0.015 centipoise. t - Temperature, in Degrees Fahrenheit A-5 A-6 APPENDIX A-PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES. FITTINGS. AND PIPE CRANE Physical Properties of Water Saturation Pressure Specific Volunlc Weight Density P' \' P Pounds per Square Inch Absolute Cubic Feet Per Pound Pounds per Cubic Foot Pounds Per Gallon 32 40 50 60 0.08859 0.12163 0.17796 0.25611 0.016022 0.016019 0.016023 0.016033 62.414 62.426 62.410 62.371 8.3436 8.3451 8.3430 8.3378 70 80 90 100 0.36292 0,50683 0.69813 0.94924 0.016050 0,016072 0.016099 0.016130 62.305 62.220 62.116 61.996 8.3290 8.3176 8.3037 8.2877 1.2750 L6927 2.2230 2,8892 0.016165 0.016204 0.016247 0.016293 61.862 61.7132 61.550 61.376 8.2698 8.2498 8.2280 8.2048 3.7184 4.7414 5.9926 7.5JlO 9.340 0.016343 0.016395 0.016451 0.016510 0.016572 61.188 60.994 60.787 60.569 60.343 8.1797 . 8.1537 8.1260 8.0969 8.0667 11.526 14.123 14.696 17.186 0.016637 0.016705 0.016719 0.016775 60.107 59.862 59.812 59.613 8.0351 8.0024 7.9957 7.9690 24.968 35.427 49.200 67.005 0.016926 0.017089 0.017264 0.01745 59.081 58.517 57.924 57.307 7.8979 7.8226 7.7433 7.6608 134.604 247.259 422.55 680.86 0.01799 0.01864 0.01943 0.02043 55.586 53.648 51.467 48.948 7.4308 7.1717 6.8801 6.5433 0.02176 0.02364 0.02674 0.03662 45.956 42.301 37.397 27.307 6.1434 5.6548 4.9993 3.6505 Temperature 11 "f\~ater Degrees Fahrenheit -- 110 120 130 140 150 160 170 180 190 200 210 212 220 240 260 280 300 350 400 450 500 550 600 650 700 I I I I I I I'I IiIi II I' I Ii II II 1\ i II Ii I' II IIII I 1045.43 1543.2 2208.4 3094.3 I, \Veight 1 1I I I 1 j j Specific gravity of water at 60 F = 1,00 Weight per gallon is based on 7.48052 gal!ons per cubic foot. ; All data on volume and pressure are abstracted from ASME Steam Tables (1967), with permiSSion of publisher, The American Society of Mechanical Engineers, 345 East 47th Street, New York, N.Y. 10017. , ., \ J CRANE APPENDIX A-I'HYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTiCS OF VALVES, FITTINGS, AND PIPE Specific Gravity-Temperature Relationship for Petroleum OilS A·7 l2 (Reproduced by permission from the Oil and Cas Journal) ro o o ± ~I lI ' i =::.:3 0.2 !;--'----,~--L-:':_:_--'.-~-L--:L:-L---::L--L.._:l~-L___::!_:_--'.-~---.JL-_:l:_:-.l.--~ o 300 400 500 600 700 800 900 1000 C1Ha=Propane C.H]o=·Butane ~ t - Temperature, in Degrees Fahrenheit C:Hs=Ethone iC 4 H1 (l=lsobutane ;C;;.H 12 =Jsopentone To find the weight density of a petroleum oil at its flowing temperature when the specific gravity at 60 F/60 F is known, multiply the specific gravity of the oil at flowing temperature (see chart above) by 62.4, the density of water at 60 F. Example: The specific gravity of an oil at 60 F is 0,85 The specific gravity at 100 F = 0,83, Weight IDensity and Specific Gravity* of Various Liquids Liquid Temp ./ Weight Specific : Density Gravity I IpS ~cc Deg. t Ll';, Fahr. I Cu. for. Temp.' Weight Specific Density Gravity I I Des· Fahr. S p Lbs. Cu. fer "t. I Mercury 849]4 I ... 20 :\mmonia, Saturated! 10 .,. I\1ercufV 40 848m . B,'nccnc ' 32 .,. I Mercury 846,32 13,570 60 I I 1v1c rcury Brme, 10'; Ca CI 32 . I ... I (3Tr~ 844,62 , B~ iric, 10'; :--:a CI 32 I ... l\/fcrcury 100 I 842.93 I . I 1014 ! !\lilk [It:nkns c: Furl \ lax I'D ... II t ! . .. l . . nt . . pn D:-..ulphIJc J2 ~O_·~") Oltw 0,1 59 ,7,3 0,919 1),,, !111M ,,0 52,99! 0,850 Pentane 59 38,9 0.624 l-.:~~~:rf!\-1dX---- - ~(f--5W)2~Q8 S,,\E 1O"L-uLbe-'!~---:--"7bOC;-+--;5~4-;,6-;4--';--"0;-;.8"7;;bFuel 5 \Im, bO ,,0_~3 O,9(m SAE )0 Lube! 60 5b,02 0,898 Fuel 5 \Ia, l'(l 61,92 0,993 SAE70 Lubct. 60 57,12 0.916 Fuell' \Iin, bO , 61,<12 0,993 Salt Creck Crude 60 525b 0,84J ) 2,,," A P I Crude --i--76"7C Ca'<)line 60 4b);J 0751 0 -i---;5"'3""]"'7;--CC-CO"",8"'6'c2=Casoline, Natural 60 42 A2 0,6S0 35,6" API Crude 60 52,81 0.847 Kerosene 60 50)!5 0,815 40" API Crude 60 5145 0.825 M, C Residuum 60 58),2 0,935 48" API Crude 60 49.16 0]88 :\Ct."tone ,- , . Liquid I 60 494 I 40,9 I 5b,1 I ! 6B.05 I 67.24 b3.25 0]92 I I I I I I - .. .. .. 'Liquid at 60 F referred to water at bO F· tMilk has a weight density of 64,2 to 64,6, t 100 Viscosity Index, Values in the table at the left were taken from Smithsonian Physical Tables, Mark's' Engi~eers' Handbook, and "Nelson's Petroleum Refinery Engineering. A -8 MPENDIX A-PHYSICAL PROPERTIES OF FLUIDS AND HOW CHARACTERISTICS OF VALVES. FITTINGS. AND PIPE eRA N E ~~------------------------------------------------------------ Physical Properties of Gases l ! = specific heat at constant pressure c, = specific heat at constant volume Cp Name of Gas. · l ,CheITlical Approx. , Weight Formula Moleeu-II Density, or Pounds Symbol Weight 1 per I Cubic lIar I Acetylene Air Ammonia Argon Carbon Dioxide Carbon MonoxidE' Ethylene Helium Hydrochloric Acid I I ,i Hydrogen Methane Methyl Chloride Nitrogen Nitric Oxide Nitrous Oxide Oxygen Sulphur Dioxide Specific 1 lndiSpecific Gravity I vidual I Heat Rela- I Gas Per Pound tive Constant! at Room To Air Temperature --,--;-, R cp j Cf) 1 III M A HCI H, CH, CH,CI I 26.0 29.0 17.0 40.0 44.0 28.0 28.0 4.0 36.5 2.0 16.0 50.5 28.0 30.0 44.0 32.0 64.0 NH, C~~. He FO:t> I C,H, CO 2 I I II I l N, NO N,O 0, SO, .06754 .07528 I' .04420 I .1037 I I Heat Capacity Per Cubic Foot at Atmospheric Pressure and 68 F .350 I .2737 i .897 59.4 I' 1.000 .1725 53.3 .241 .587 90.8 .523 .4064 38.7 .124 .0743 I 1.377 1. 516 .1599 35.1 I .205 .1721 .965 55.2 I .243 I' .3292 .967 55.1 .40 .138 1.25 .754 386. .191 .1365 1. 256 I 42.4 3.42 .0695 1 767. 2.435 .593 .4692 .553 96.4 .24 .2006 1.738 1 30.6 55.2 I .247 .966 .1761 i I .231 1.034 .1648 51.5 .221 .1759 1.518 I' 35.1 .1549 1.103 48.3 .217 .154 24.1 .1230 , I 2.208 II, I I k equal to cplc, -I Cp I' .07269 .0728 .01039 .09460 .005234 .04163 .1309 .07274 .07788 .1143 .08305 .1663 I --1--------,-1 I .1142 I I C" .0185 .0236 .0130 .0181 .0179 .0231 .0077 .0129 .0234 .0183 .0177 .0125 .0291 .0240 .0130 I .0078 .0181 .0129 .0179 .0127 .0247 .0195 .0314 I .0263 .0179 .0128 .0180 .0128 .0253 .0201 .0180 .0129 .0256 .0204 I 1.28 1.40 1.29 1.67 1.28 1.41 1.22 1.66 1.40 1.40 1.26 1.20 1.40 1.40 1.26 1.40 1.25 *\\'eight density values are at atmospheric pressure and 68 F. For yalues at 60 F, multiply by 1.0154. Volumetric Composition and Specific Gravity of Gaseous Fuels 13 , Chemical Composition Percent by Volume I Ii • HYdrO-I Carbon Paraffin gen Mon- Hydrocarbons Type of Gas I oxide I MethI r Natural Gas, Pittsburgh Producer Gas from Bituminous Coal I 14.0 Blast Furnace Gas 1.0 Blue Water Gas from Coke 47.3 Carbureted Water Gas 40.5 Coal Gas (Cont. Vertical Retorts) 54.5 I II Coke-Oven Gas Refinery Oil Gas (Vapor Phase) Oil Gas, Pacific Coast il 46.5 13.1 48.& ane 27.0 27.5 37.0 34.0 10.9 6.3 1.2 12.7 83.4 3.0 1.3 10.2 24.2 32.1 23.3 26.3 I Ethane I IlluITlinants EthYl-II Benzene ene I Oxy- I, gen I I I 15.8 0.6 21.7 6.1 1.5 3.5 39.6 2.7 2.8 1.3 0.5 1.1 ! Specific Gravity Relative Nitro- Carbon to Air gen DioxS. ide 0.7 0.5 0.2 0.8 1.0 0.3 0.8 50.9 60.0 8.3 2.9 4.4 8.1 3.6 Data on this page reproduced by permission from Mechanical En[!,ineers' Handbook by L. S. Marks. Copyright. May. 1954; McGraw-Hili Book Company. Inc. 4:5 11.5 II 5.4 3.0 3.0 II 2.2 0.1 4.7 II 0.61 0.86 1.02 0.57 0.63 0.42 0.44 0.89 0.47 A-9 APeENDly. A-PHYSICAl PROPERTIES Of flUIDS AND flOW CHARACTERISTICS OF VALVES, FITIINGS. AND PIPE CRANE Steam - Values of k Ratio of Specific Heat at Constant Pressure to Specific Heat at Constant Volume k = epIc. 1.34 ~ 1.3 2 ""'- "- § 1.30 c 8. x L.LJ .0.. __ £H",!e",o,J - !o-_"i"'_ ......r- g . c a:> (/) I ~o~~ ~o~ I IOOO~ ~o~ ""'" 1.26 I"- ;-;::. ~ I 500 F - __ I .. -r-::t,_~ -r-I·h __~ -~OO-L..ro 400 F --- 12 8 !>;os> 300 F J...l40...ru;., .... - -- ~- .- -- I--- -...... ~ ~-- ---~- -- --- ~- ~- :: ~ ~ ~ ~/ - - ~ ~ ~Rl/' - --- ........... \~\\ .// .J~ I' ~- 1.2 4 '"" \~ t 1.22 I 2 5 10 20 50 100 200 500 pi _ Absolute Pressure, Pounds per Square Incil For sma'] changes in pressure (or volume) along an isentropic, pv k = constant j ::::II ::::=3 ::::::'1 . ==:1 .==8 Reprinted from "Thermodynamic Properties of Ste2.m" by J. H. Keenan and F. G. Keyes, 1936 edition, by permission of the publishers, John Wiley &1 Sons, Inc. ~ A - 10 CRANE APf'<!'<PIX A - PHYSICAL PROPERTIES OF FLUIDS AND flOW CHARACTERISTiCS OF VALVES, FITIINGS, AND PIPE '-'--'-=---- Weight Density and Specific Volume Of Gases and Vapors The chart on page A-I 144 p = P' ~ = where: I is based on the formula: MP' 2.70 10.72 T P" = 14.7 .11 It "..; P' S. T p p p I +P Problem: What is the density of dry CH, if the temperature is gauge pressure is 1.5 pounds per square inch? 100 F and the Solution: Refer to the table on page A-8 for molecular weight, specific gravity, or individual gas constant, Connect 96.4 of the R scale with 100 on the temperature scale, t, ana' mark the intersection \vith the index scale. Connect this point with 15 on the pressure scale, P. Read the answer; 0.08 pounds per cubic foot, on the weigh: density scale p. Weight Density of Air Temp, Air \Veight Density of Air. in Pounds per Cubic Foot For Gauge Pressures Indicated (Based on an atmospheric pressure of 14.696 and a molecular weight of 28.(7) II DegF. o 5 psi psi i 10 I psi 20 '1 psi 30 psi 't I 40 psi Ii 50 PSI 60 psi 70 psi 80 90 psi psi i 100 psi 110 120 130 pSI psi psi .140 psi 150 psi 30" II ,0811 I', ,10871.1363 .1915 .247 1 ,30~ I ,3~7 .412 .467 .522 .578 .633 .688 .743 .798 .853 .909 40 11.0795 " .1065 .133,5 .1876 .242 .29, 1.3,0 .404 .458 ,512 .566 I .620 .674 .782 .836 .890 50 I' .0782 .1048 1 .>314. .1846 .238 .291 .. 344 .397 .451 .504 .557 .610 .663 .770 ,823 ,876 60 .0764" .1024 .1284 .1804 .232 1,.284 i .336 .388 .440 .492 .544 .596 .752 .804 .856 1 70 ,1.0750 i .1005 .. 1260 .1770 .228 .279 I .330 .381 .432 .483 .534 .585 .738 .789 .S40 -""8"'0~I! 0736 I .09861"--;,C;;2~36~':".1~7~3~7+1-'."'22::-C4;'--;lcc.C;;27"'4~'.:;;3"'247-.-'-:.3i:7c;.4-'---'.-;4~24;-':-'-.'-'47"'47-'---'C.50:;2-;4-'c-~~.--'~c--'7;;:.-"-.:;.7"'2:O-4-+-"':."'77"'4~---'C.8"'2~4 90 1.0722' .0968 .1.214 .17051.220.! .269 .318 .367 .416 .465 .515 .711 .760 .809 100 I .07091.0951 .un .1675 .216 ,.264 .312 .361 0409 .457 .505 .698 .747 .795 lIO I'j ,069: .0934 I... n:1 .1645 .212 '.259 .307 .354 .402 .449 . . 497 ,686 .734 .781 .. i, 1 ~1~20~~I.~0~68~'~~.0~9~18~c'2.~'I~~~I~.,~1~61~7rl-.~2~08?-~I~.2~5=.5-+~.3~0~2~...:.~34;8:~~.3~9~5~~.44~I~!_...:.~48~8~:~~_~~~~~~-,...:.~67i4~~.7~2~1-+-~.768 130 Ii .0673 1 .0902 .H31 .1590! .205 .251 I .296 .342 .388 .434 .480 .663 .709 .755 1401.06621.0887 .11U .1563'1.201 .246 1.291 .337 .382 .427 Ail .652 .697 .742 150 I, .0651 .0873 .n094 .1537 .1981 i .242 .287 .331 .375 .420 .464 .641 .686 '.730 'I I' I' 175 200 225 250 275 300 350 400 450 500 550 600 30 0 40 50 60 70 ~g 1'[.06261.0834 .H151 !. 0602 .0807,. IOn .0580' .0777 i .0974 1.0559 .0750' .0940 II' .0540, .07241 .()'JiOS ,.0523, .0700 ',.0078 if .0490, .0657 i .0824 1,.0462! .O?I~: .O:,§6 I, .0436 1.0080 i .(),,33 1.0414 'I .0555 : .()695 1'.0393 .0527' .Ol>f>l ii.0375! .05021 .06.3!l I' i i 175 1 200 1'1' 1 I 225 .1477 i .1903 i .233 .275 .318 .361 i ,403 .446 .616 .659 .701 .1421 i .1831 1 .224 ,. 265;'--;"':'c;.30",6o--'---'C'3",4",7-'..-,,3.:,.8:,c8;-,-'...:.-;4",29.-+--,-::~_~~---'C'50:;5:0'2-,'..::.~59;c3;.--;---'C.6C;3.4;;'~"::'767~5 .13691.1764 i .216 .255 .295 .334 .374 .413 .492 .531 .571 .610 .650 .1321 .17021.208 .246 .284 .322 ,361 .399 .'44~95 ".513 .551 .589 .627 .1276 .1644 i .201 .238 .275 .311 .348 .385 ".495 .532 .569 ,606 .1234, .15901.1945 .230 .266 .301 .337 .372 .443 .479, .515 .550 .586 .lI58 1 .1491 .182:-o5c+":.;:2~16:c--~.2c4,~9-+..:.~28;:c3~''':':.;:3~16~.....:.:.3",4",9-+-~:.::o-'--'-'4~16 .449' .483 .516 .550 .1090 1.14051 .1719' .203 .235 .266 .298 .329' .392 0423 .455 .486 .51S .1030 !.1327 : .1624 ', .1921 .222 .252 .281 .311 .370 ADO i .430 .459 .489 .0977 .1258 ' .1540 ! .1821 .210 .238 .267 .295 .323 .351 .379 ,407 .436 .464 .0928 .1196,1 .1464 i .1731 .1999 .227 .253 .280 .307 .334 .360 .387 .414 .441 .0885 i .1140 i .1395' .1649 .1904 .216 .241 .267 .292 .318 .343 .369 .394 ,420 250 I' 300 i 400 500 600 700 2.78 2.74 2.68 3.32 3.27 3.20 3.86 3.80 3.72 4.40 4.33 4.24 ,2.63 3.14 3.65 4.16 1 800, 900 1000 psi' psi l~I~I~ ~ ~I~I~ ~ ~ ~ 1. 047 1.185 i l. 3Z3~"'1C'."'46"0"'1c-,1'-.-7"'36;-7-1'2.-'2"'9--+co 2"'.8"4'--:''''3C'.3"'9--''''3'''.'OC94~~4-.4'"9C-:-'''5~.0;;-;5~"'5'-.760OC- 1.026 1.161,1.1.% 1.431',1.70212.24 11.00911.142 '11.V5 1.408: 1.674 2.21 i .986 i 1.116 1.2:-*6 1.376' 1.636 2.16 ii .968,11.09511.213 li:m: J:g~~ l::i~ 1.350 i 1.605 r 2.12 U6f i i:~~; IU~ I ~:~~ tg~ n~ 4.95, 5.49 4.87 5.40 4.76 I 4.67 !:g~ ::~~ 100 Ii .916: 1.036 ! 1.157 1.2781,1.51912.00 12.48 2.97 3.45 3.93 4.42 lID .1: .900: 1.0181 LU7 1.255,1.492 1.967 2.44 2.92 3.39 3.86 4.34 120 ".884 I 1.001 ! 1.1.;;:17;.-'-01'0'2'73i-4-c1~1:..4o-:6",7-:-;1c:..",93,"3,-1c:2""-o4;:-0c-:-2~'c;:8~6-"_~3.:;.3:;;3--+..:3c:.,,,80~_40'c;2",6-i-7-7' 130 .869 I .984' Li.lI>8 1.213 \1.442 1 1.900 1 2.36 2.82 3.27 3.73 4.19 140 .855'.967 1..05'j 1.193 11.41811.868 1 2.32 2.77 3.22 3.67 4.12 150 .8411 .951! l,.1l!(,2 1.'17311.395,1.83812.28 2.72 3.17 3.61 4.05 175 .807, ,9!411.ll'.l1l 1.127 1.340 i 1.765 I 2.19 2.62 3.04 3.47 3.89 200 .777 I .879 I .982 1.08411.289 I 1.698 (2.11 2.52 2.93 3.34 3.75 225 .7491 .847: .'146 1.044 i 1.242 , 1.636 i 2.03 2.43 2.82 3.21, 3.61 i 4.00 250 .722 .817 ', ""13,' 1.08811.198 1.5791' 1.959 2.34 2.72 3.10' 3.48 3.86 275 .698 .790 .!!lSi .973 i 1.157 11.525 1.893 2.26 2.63 3.00 i 3.36 3.73 i .675 .764 .852 .941 '11.11911.475.1.830 2.19 2.54 2.9013.25 3.61 i 300 1 1 ..",.m~OO","~:..8~8~3~1c:.''OC05~0~1~1~.~3~84~1_",I.~7~1~7772~'0i:5~~2:..3",8o--'~2.~7~2-+-c;.3~'0i:5~~J~.39 , ~3",50__~_.~63~3~1~.,7~16~_ 400 .596' .6751 .;;'53 .8321 .98911.30311.618 1.932 2.25 i 2.56 2.87 3.19450 .5631 .6381 .712 .786 .93411.232,1.529 1.826 2.12 '2.42 2.72 3.01 500 .534 .~£~ i .675 .745 .886 1.16711.449 1.73J 2.01 2.29 2.58 2.86 550 .508 1 " n I ,M1 .708, .84211.110 1.377 1.645 1.912 i 2.18 2.45 2.72 600 .484 i .547 i .611 .675 i .802 I 1.057 1.312 1.567 1.822, 2.08 1 2.33 2.59 I i I I Air Density Table The table at the left is calculated for the perfect gas la\\' shown at the top of the page. Correction for supercompressibility, the deviation from the perfect gas law, \\'Quld be less than three percent and has not been applied. The weight density of gases other than air can be determined from this table by multiplying the density listed for air by the specific gravity of the gas relative to air, as listed in the tables on page A-8, APPENDIX A - PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES. FITTINGS. AND ~ CRANE A-ll Weight Density and Specific Volume Of Gases and Vapors R continued 8g 0.35 V 0.4 p 60 Index 50 40 30 0.5 15,----1- 20 0.6 ~ 0 0 "0 c:: => LL. u 0.7 .0 => Q:; Q:; Q; u Cl. Cl. D ~ =='" OJ => u '" - ~ c:: 0.8 0 V> - C-'>'" 0 0.9 ..... ~ - => :.0 a.. u I => c ~ C-'> <1> '"I '" :0: ~ Cl.. 0 I- 100 U 2::l '" 0 .0 '" ""I a. .6 .7 => C-'> '" =u E :': => ""= ""Q:; "'- '" "0 SO V> u '" I 120 Q:; > 0;, CQ c. E 0;>- Cl c. 140 E => '" u '" :0; ro c .?5 c'" <..) 1.0 ::E I Z;> > <1> 00 160 U 0 c::- '-' 180 u. '" c:: OJ t 200 OJ "0 :;; T 0 a.. co => 0 a.. <C I c 60 I;;;. &.. ",- 100 .8 .9 :0; V> '" i''".L 1 I 0.. 150 2 50,--- 3 €Ol---=I for application of cho,." 701--~r - explanation on the Fe:'!er to prece#.~ng the poge. Molecular weight, specific gravity,. r:mo individual 78 - constants for various gases are give;; on page A~8. CRANE APpENDIX A - PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE A-12 Properties of Saturated Steam and Saturated Water* Vacuunl Inches of Hg Absolute Pressure Lbs. per --I-i~Ches of Hg Sq. In. pi Temperature t Degrees F. I I I I Heat of the Liquid Specific Volume Latent Heat Total Heat of of Steam Evaporation V Water Btu/lb. Btu/lb. Steam Cu. ft. per Ih. Btu/lb. Cu. {t. per lb. I 0.0087 0.02 29.90 32.018 0.0003 1075.5 1075.5 0.016022 3302.4 0.10 0.20 29.72 35.023 3.026 1073.8 1076.8 0.016020 2945.5 0.15 (1.31 29.61 45.453 13.498 1067.9 1081.4 0.016020 2004.7 0.20 0041 29.51 53.160 21.217 1053.5 1084.7 0.016025 1526.3 0.25 0.51 29.41 59.323 27.382 1060.1 1087.4 0.016032 1235.5 0.30 0.61 29.31 64.484 32.541 1057.1 1089.7 0.016040 1039.7 0.35 (i.7l 29.21 68.939 36.992 1054.6 1091.6 0.016048 898.6 0.40 0.81 29.11 72.869 40.917 1052.4 1093.3 0.016056 792.1 0.45 0'.92 29.00 76.387 44.430 1050.5 1094.9 0.016063 708.8 0.50 1.02 28.90 79.586 47.623 1048.6 1096.3 0.016071 641.5 0.60 1.22 28.70 85.218 53.245 1045.5 1098.7 Ii 0.016085 540.1 0.70 1.43 28.49 90.09 58.10 1042.7 1100.8 0.016099 466.94 0.80 1.63 28.29 94.38 62.39 1040.3 1102.6 0.016112 411.69 0.90 1.83 28.09 98.24 66.24 1038.1 1104.3 0.016124 368.43 -~I~.O~--+-~2".~04T-~~27~.i88~-f~IOil~.7~4~-r-~6~9~.7~3-+--~10~3i6~.I--r'I~lo05i.~8-i-Aor.0·'16~1~36~-r~3~33'.7.60~1.2 'U.44 27.48 107.91 75.90 1032.6 1108.5 0.016158 280.96 1.4 2.85 27.07 113.26 81.23 1029.5 1110.7 0.016178 243.02 1.6 3.26 26.66 117.98 85.95 1026.8 1112.7 0.016196 214.33 __~1~.8~___, 3.~.6~6__+-~2~6~.2~6__~_~1~272.~2;2__-+~9~0~.1~8~~__~1~02~4~.3~-+~11~174~.5~-r~0~.Oi1~6~2~13~~~1~9~1.~8~5__ 2.0 I' 4.07 25.85 126.07 i 94.03 1022.1 1116.2 0.016230 173.76 2.2 4.48 25.44 129.61 97.57 1020.1 1117.6 0.016245 158.87 2.4 I 4.89 25.03 132.88 100.84 1018.2 1119.0 0.016260 146.40 2.6 5.29 24.63 135.93 103.88 1016.4 1120.3 0.016274 135.80 1O;c;1",4__ _---;2"'.800-___L--Z.."o7-=-0-+--,;2-o;-4."'2-=-2--+---:o1-,-38;-:.-';-78i;--+-0-;1O"'6:".7"'3---t--7 .7.--+_1~lco;2-o;-1.-;"5_-+---;0,-;.0~176",18;-;;7:----t---.1726;;-,"",67.-_ 3.0 ! 6.11 23.81 141.47 109.42 1013.2 1122.6 0.016300 118.73 3.5 , 7.13 22.79 147.56 115.51 1009.6 1125.1 0.016331 102.74 4.0 8.14 21.78 152.96 120.92 1006.4 1127.3 0.016358 90.64 4.5 I, 9,16 20.76 157.82 125.77 1003.5 Il29.3 0.016384 83.03 ____~5.~0__--~---=-10~.,~1~8--+-~1~9~.7~4~-+--=-16~2~.~24~--+'-713~0~.~20~-+__~10~0~0~.9~-+-71~13~1~.1i;-~~0-,;-.0~1-=-64-=-0;-;;7:--_~__~7~3~.5~3~2__ 5.5 11.20 18.72 166.29 'I 134.26 998.5 1132.7 0.016430 67.249 6.0 12..22 17.70 1170_05 138.03 996.2 1134.2 0.016451 61.984 6.5 13,,23 16.69 173.56 141.54 994.1 1135.6 0.016472 57.506 7.0 14,,25 15.67 170.84 144.83 992.1 1136.9 0.016491 53.650 7.5 15.27 14.65 ,179.93 147.93 990.2 1138.2 i 0.016510 50.294 8.0 16,29 13_63 182.86 150.87 988.5 1139.3 0.016527 47.345 1140.4 0.016545 44.733 8.5 17.31 12.61 185.63 153.65 986.8 9.0 18.32 11.60 188.27 156.30 985.1 1141.4 0.016561 42.402 9.5 19.34 10.58 190.80 158.84 983.6 1142.4 0.016577 40.310 10.0 20.36 9.56 193.21 I 161.26 982.1 1143.3 0.016592 38.420 11.0 22.40 7.52 197.75 165.82 979.3 1145.1 0.016622 35.142 12.0 24.43 5.49 201.96 170.05 976.6 1146.7 0.016650 32.394 13.0 26.47 3.45 205.88 174.00 974.2 1148.2 0.016676 30.057 14.0 I · 38.50 1.42 209.56 177.71 971.9 1149.6 J 0.016702 28.043 11 I I II I I Pressure Lbs. per Sq. In. Absolute Gage pi I p I 0.0 I Temperature t Degrees F. I Heat of the. Liquid Btu/lb. I I I Latent Heat Total Heat of of Steam Evaporation Btu/lb. Specific Volume V ho Water Btu/lb. Cu. ft. per lb. 1150.5 212.00 180.17 970.3 0.016719 213.03 181.21 969.7 J150.9 0.016726 216.32 184.52 !l52.l 967.6 0.016749 I 2..3 219.44 187.66 965.6 J153.2 0.016771 3.3 222.41 190.66 1154.3 963.7 0.016793 4.3 225.24 193.52 1155.3 0.016814 961.8 5.3 227.96 196.27 I 960.1 1156.3 0.016834 I 0.016854 230.57 958.4 1157.3 6.:l 198.90 I 233.07 201.44 7.3 956.7 1158.1 0.016873 8.:l 235.49 203.88 955.1 1159.0 0.016891 9.3 237.82 206.24 953.6 1159.8 0.016909 10.;; 240.07 208.52 952.1 1160.6 0.016927 ILl 242.25 210.7 950.6 1161.4 0.016944 12.J 244.36 212.9 949.2 1162.1 0.016961 13.a 246.41 214.9 1162.8 947.9 0.016977 I I,Ll 248.40 217.0 946.5 1163.5 0.016993 i I 15.:> 250.34 218.9 945.2 1164.1 0.0170G9 , 16.~. 252.22 220.8 943.9 1164.8 0.017024 17.,1 254.05 222.7 942.7 1165.4 0.017039 18.3 255.84 941.5 1166.0 0.017054 , 224.5 !, 19.:> 257.58 226.3 940.3 1166.6 0.017069 I I - , Steam fables (1967), With perm,:O:Slon of the pubH~hcr, --Ihe American */\bstracted from AS\1E Society of Mechanical Engineers, 345 East 47th Street. New York. New York 10017. 14.696 15.0 16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 29.0 30.0 31.0 32.0 33.0 34.0 0.3 1..3 I Steam Cu. ft. per lb. I I I I , I I I I I I I I I 26.799 26.290 24.750 23.385 22.168 21.074 20:087 19.190 18.373 17.624 16.936 16.301 15.7138 15.1684 14.6607 14.1869 13.7436 13.3280 12.9376 12.5700 12.2234 {confinued on the next page) (; C=f:I~ e::r=i ~i 9~~ =::bt :::::::::s ::=:9 ~ =:$ A-13 APPENDIX A - PI-YSICAl PROPERTIES Of flUIDS AND flOW CHARACTERISTICS OF VAItfft£S, FITTINGS. AND PIPE CRANE Properties of Saturated Steam and Saturated Wafer-continued Temperature Pressure Lbs. per Sq. In. Gage Absolute P' 35.0 36.0 37.0 38.0 39.0 40.0 41.0 42.0 43.0 44.0 45.0 46.0 47.0 48.0 49.0 50.0 51.0 52.0 53.0 54.0 55.0 56.0 57.0 58.0 59.0 60.0 61.0 62.0 63.0 64.0 65.0 66.0 67.0 68.0 69.0 70.0 71.0 72.0 73.0 74.0 75.0 76.0 77.0 78.0 79.0 80.0 81.0 82.v 83.0 84.0 85.0 86.0 87.0 88.0 89.0 90.0 91.0 92.0 9.3.0 94.0 %.0 96.0 97.0 98.0 99.0 100.0 101.0 102.0 103.0 104.0 105.0 106.0 107.0 108.0 109.0 I P t I Degrees F. 20.3 21.3 22.3 259.29 260.95 262.58 264.17 265.72 267.25 268.74 ".,+ 23.3 24.3 25.3 26.3 II I, 28.3 29.3 30.3 31.3 32.3 ~ 33.3 34.3 I 35.3 36.3 37.3 38.3 39.3 40.3 41.3 I I 43.3 44.3 'U 45.3 46.3 47.3 48.3 49.3 50.3 51.3 52.3 53.3 54.3 55.3 56.3 57.3 58.3 59.3 60.3 61.3 62.3 63.3 64.3 I m." 271.65 273.06 274.44 275.80 277.14 278.45 279.74 281.02 282.27 283.50 284.71 285.90 287.08 288.24 +'' ." 290.50 291.62 292.71 293.79 294.86 295.91 296.95 297.98 298.99 299.99 300.99 301.96 302.93 ;303.89 304.83 ,105.77 ,106.69 ,107.61 ;;08.51 ;;;09.41 310.29 311.17 312.04 312.90 313.75 314.60 315.43 316.26 317.08 3.17.89 3.18.69 3:!9.49 65.3 66.3 67.3 68.3 69.3 70.3 71.3 72.3 73.3 74.3 75.3 76.3 77.3 78.3 79.3 80.3 81.3 82.3 83.3 84.3 85.3 86.3 87.3 88.3 89.3 90.3 91.3 92.3 93.3 94.3 I I I 3:!D.28 I 321.06 321.84 322.61 323.37 324.13 314.88 325.63 32&.36 327.10 327.82 328.54 329.26 329.97 330.67 331.37 33,'.06 332.75 333.44 334.!l I I Btu/lb. 228.0 229.7 231.4 233.0 234.6 236.1 237.7 239.2 240.6 242.1 243.5 244.9 246.2 247.6 248.9 250.2 251.5 252.8 254.0 255.2 256.4 257.6 258.8 259.9 26 I.! 262.2 263.3 264.4 265.5 266.6 267.6 268.7 269.7 270.7 271.7 272.7 273.7 274.7 275.7 276.6 277.6 278.5 279.4 280.3 281.3 282.1 283.0 283.9 284.8 285.7 286.5 287.4 288.2 289.0 289.9 290.7 291.5 292.3 293,1 293.9 294.7 295.5 296.3 297.0 297.8 298.5 299.3 300.0 300.8 301.5 302.2 303.0 303.7 304.4 305.1 Total Heat of Steam Latent Heat of Evaporation Heat of the Liquid I I I I I I Specific Volume h. i Btu/lb. Btu/lb. ~ 939.1 938.0 936.9 935.8 934.7 933.6 932.6 931.5 930.5 929.5 928.6 927.6 926.6 925.7 924.8 923.9 923.0 922.1 921.2 920.4 919.5 918.7 917.8 917.0 916.2 915.4 914.6 913.8 913.0 912.3 911.5 910.8 910.0 909.3 908.5 907.8 907.1 906.4 905.7 905.0 904.3 903.6 902.9 902.3 901.6 900.9 900.3 899.6 899.0 898.3 897.7 897.0 896.4 895.8 895.2 894.6 893.9 893.3 892.7 892.1 891.5 891.0 890.4 889.8 889.2 888.6 888.1 887.5 886.9 886.4 885.8 885.2 884.7 884.1 883.6 1167.1 1167.7 1168.2 1168.8 1169.3 1169.8 1170.2 1170.7 I!71.1 1171.6 1172.0 !l72.5 1172.9 1173.3 1173.7 1174.1 1174.5 1174.9 1175.2 1175.6 1175.9 1176.3 1176.6 1177.0 1177.3 1177.6 1177.9 1178.2 1178.6 1178.9 1179.1 1179.4 1179.7 1180.0 1180.3 1180.6 1180.8 118 I.! 1181.4 1181.6 1181.9 1182.1 1182.4 1182.6 1182.8 1183.1 1183.3 1183.5 1183.8 1184.0 1184.2 1I84.4 !l84.6 1184.8 1185.0 1185.3 lI85.5 !l85.7 l!85.9 1186.0 1186.2 1186.4 1186.6 1186.8 1187.0 1187.2 1187.3 1187.5 1187.7 1187.9 !lS8.0 1188.2 1188.4 1188.5 1188.7 I II I I V ~ I I Water Cu. ft. per lb. , I I i I! I i r, ,\j I ,! Ir r I, I I O.Oi7083 0.017097 0.017111 0.017124 0.017138 0.017151 0.017164 0.017177 0.017189 0.017202 0.017214 0.017226 0.017238 0.017250 0.017262 0.017274 0.017285 0.017296 0.017307 0.017319 0.017329 0.017340 0.017351 0.017362 0.017372 0.017383 0.017393 0.017403 0.017413 0.017423 0.017433 0.017443 0.017453 0.017463 0.017472 0.017482 0.017491 0.017501 0.017510 0.017519 0.017529 ().017538 0.017547 0.017556 0.017565 ;).017573 (1.017582 0.017591 i).017600 v.017608 (}.017617 fI.017625 0.017634 i).017642 ').017651 0.017659 0.017667 /).017675 0.017684 (;.017692 0.017700 0.017708 0.017716 0.017724 0.017732 (>.017740 0.01775 0.01776 0.01776 0.01777 0.'1l778 0.D1779 0.01779 0.01780 0.01781 I I I I I I . Steam Cu. ft. per lb. 11.8959 11.5860 11.2923 11.0136 10.7487 10.4965 10.2563 10.0272 9.8083 9.5991 9.3988 9.2070 9.0231 8.8465 8.6770 8.5140 8.3571 8.2061 8.0606 7.9203 7.7850 7.6543 7.5280 7.4059 7.2879 7.1736 7.0630 6.9558 6.8519 6.7511 6.6533 6.5584 6.4662 6.3767 6.2896 6.2050 6.1226 6.0425 5.9645 5.8885 5.8144 5.7423 5.6720 5.6034 5.5364 5.4711 5.4074 5.3451 5.2843 5.2249 5.1669 5.1101 5.0546 5.0004 4.947" 4.8953 4.8445 4.7947 4.7459 4.6982 4.6514 4.6055 4.5606 4.5166 4.4734 4.4310 4.3895 4.3487 4.3087 4.2695 4.2309 4.1931 4.1560 4.!l95 4.0837 II I , i I II ~ A .. 14 APPENDIX C-'-.'--'-_ __ _ CRANE A - PHYSICAL PROPERYIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE Prop'2 iies of Saturated Steam and Saturated Water-continued Y -------'- Pressure Lbs. per Sq. In. ___ 1 AbSOpl,utc I I Gap!;c 95.3 96.3 97.3 98.~ i I I i I 99.c, 100' .0 101.3 102.3 103.3 104.3 105:3 106.3 107.3 108.3 109.3 110.3 111.3 112.3 113.3 114.3 I ,I I i I I I I i ! iI ! I I I 115.3 116.3 117.3 118.3 119.3 120..3 121.3 122.3 122,.3 124,.3 12S.3 126.3 -, 128.3. 129.3 130.3 131.3 132.3 13,1.3 13'1.3 13S.3 137.3 139.3 141.3 14,1.3 145.3 147.3 149.3 151.3 15:1.3 15';.3 15;i.3 159.3 161.3 16:;.3 16;;.3 167.3 169.3 171.3 ~U ,i II , I ! i Tcmpcrature I Ii --I ==c~=;:==*.===i.. 110.0 111.0 112.0 113.0 114.0 11-~. 0 116.0 117.0 118.0 119.0 120.0 121.0 122.0 123.0 124.0 125.0 126.0 127.0 128.0 129.0 130.0 131.0 132.0 133.0 134.0 135.0 136.0 137.0 138.0 139.0 140.0 141.0 14'-. 0 143.0 144.0 145.0 146.0 147.0 148.0 149.0 150.0 152.0 154.0 156.0 158.0 160.0 162.0 164.0 166.0 168.0 170.0 172.0 174.0 176.0 178.0 180.0 182.0 184.0 186.0 188.0 190.0 192.0 194.0 196.0 198.0 200.0 205.0 210.0 215.0 220.0 225.0 230.0 235.0 240.0 245.0 I 17".3 177.3 179.3 181.3 18:3.3 183.3 190.3 19.1.3 200.3 20:;.3 210.3 215.3 220.3 nu 130.3 I : ! Degrees F. 334.79 335.46 336.12 I 336.78 337.43 33808 I I 338.73 339.37 340.01 340.64 341.27 341.89 342.51 343.13 343.74 344.35 I I 344.95 345.55 346.15 I 346.74 347.33 347.92 l 348.50 349.08 II 349.65 350.23 350.79 351.36 351.92 , 352.48 353.04 353.59 3~4 14 354.69 355.23 355.77 356.31 356.84 357.38 357.91 358.43 359.48 360.51 361.53 362.55 363.55 364.54 365.53 366.50 367.47 368.42 369.37 . 370.31 371.24 372.16 373.08 373.98 374.88 375.77 376.65 377.53 378.40 379.26 II 380.12 380.96 381.80 383.88 385.91 387.91 389.88 391.80 393.70 395.56 397.39 399.19 I _~~~!b_ I I i I I I, I I Heat of the Liquid I I I I I I , II ! . I Ii I I I I 305.8 306.5 307.2 307.9 308.6 3093 309.9 310.6 311.3 311.9 312.6 313.2 313.9 314.5 315.2 315.8 316.4 317.1 317.7 318.3 319.0 319.6 320.2 320.8 321.4 322.0 322.6 323.2 323.8 324.4 325.0 325.5 .>26 1 326.7 327.3 327.8 328.4 329.0 329.5 330.1 330.6 331.8 332.8 333.9 335.0 336.1 337.1 338.2 339.2 340.2 341.2 342.2 343.2 344.2 345.2 346.2 347.2 348.1 349.1 350.0 350.9 351.9 352.8 353.7 354.6 355.5 357.7 359.9 362.1 364.2 366.2 368.3 370.3 372.3 374.2 . Latent Heat Total Heat o f ; of Steam Evaporation! h I g I I I I ! ! ,I I i I , I I I I I I L I I Btu/lb. Btui!!'. 883.1 882.5 882.0 881.4 880.9 8804 879.9 879.3 878.8 878.3 877.8 877.3 876.8 876.3 875.8 875.3 874.8 874.3 873.8 873.3 872.8 872.3 871.8 871.3 870.8 870.4 869.9 869.4 868.9 868.5 868.0 867.5 8671 866.6 866.2 865.7 865.2 864.8 864.3 863.9 863.4 862.5 861.6 860.8 859.9 859.0 858.2 857.3 856.5 855.6 854.8 853.9 853.1 852.3 851.5 850.7 849.9 849.1 848.3 847.5 846.7 845.9 845.1 844.4 843.6 842.8 840.9 839.1 837.2 835.4 833.6 831.8 830.1 828.4 826.6 1188.9 1189.0 il89.2 1189.3 1189.5 ;; . 11'96 1189.8 1189.9 1190.1 1190.2 1190.4 1190.5 1190.7 1190.8 1190.9 1191.1 1191.2 1191.3 1191.5 1191.6 1191.7 1191.9 1192.0 1192.1 1192.2 1192.4 1192.5 1192.6 1192.7 1192.8 1193.0 1193.1 11932 1193.3 1193.4 , ! I I ! 1 I I, i II II 1193.5 I I I I I I , 1193.6 1193.8 1193.9 1194.0 1194.1 1194.3 1194.5 1194.7 1194.9 1195.1 1195.3 1195.5 1195.7 1195.8 1196.0 1196.2 1196.4 1196.5 1196.7 1196.9 1197.0 1197.2 1197.3 1197.5 1197.6 1197.8 1197.9 1198.1 1198.2 1198.3 1198.7 1199.0 1199.3 1199.6 1199.9 1200.1 1200.4 1200.6 1200.9 Specific Volume v- Water Cu~~per I~. I -0"])1782 Tl4-:-048.f-0.01782 4.0138 0.01783 3.9798 0.01784 3.9464 0.01785 3.<)136 001-838813 I ~ 0.01786 3.8495 0.01787 3.8183 0.01787 3.7875 I 0.01788 3.7573 0.01789 3.7275 0.01790 3.6983 0.01790 3.6695 0.01791 3.6411 0.01792 3.6132 0.01792 3.5857 0.01793 3.5586 0.01794 3.5320 0.01794 3.5057 0.01795 3.4799 0.01796 3.4544 0.01797 3.4293 0.01797 3.4046 3.3802 0.01798 3.3562 0.01799 0.01799 3.3325 0.01800 3.3091 0.01801 3.2861 0.01801 3.2634 0.01802 3.2411 0.01803 3.2190 0.01803 3.1972 001804 0.01805 3.1546 0.01805 3.1337 0.01806 3.1130 3.0927 0.01806 3.0726 0.01807 0.01808 3.0528 0.01808 3.0332 0.01809 3.0139 2.9760 0.01810 2.9391 0.01812 2.9031 0.01813 2.8679 0.01814 0.01815 2.8336 0.01817 2.8001 0.01818 2.7674 0.01819 2.7355 0.01820 2.7043 0.01821 2.6738 0.01823 2.6440 0.01824 2.6149 0.01825 2.5864 0.01826 2.5585 0.01827 2.5312 0.01828 2.5045 0.01830 2.4783 2.4527 0.01831 0.01832 2.4276 2.4030 0.01833 0.01834 2.3790 0.01835 2.3554 2.3322 0.01836 0.01838 2.3095 2_28728 0.01839 2.23349 0.01841 I 0.01844 2.18217 0.01847 2.13315 2.08629 0.01850 0.01852 2.01143 1.9984& 0.01855 1.95725 0.01857 1.91769 0.01860 1.87970 0.01863 I I I I I I I I I I I ii I I I I t I I I Steam--- I ~~~~~ A-IS APPENDIX A - PHYSICAL PROPERTIES OF FLUlDS AND flOW CHARACTERISTICS Of VAlVES~ FlnINGS, AND PIPE CRANE Properties of Saturated Steam and Saturated Water-concluded , I P' I '9=.~. ,~lji '--"J-1lilI .. .,jilt 250.0 255.0 260.0 265.0 270.0 275.0 280.0 285.0 290.0 295.0 300.0 320.0 340.0 360.0 380.0 JOO.O - ~ ~ ":=:t. ~ 420.0 440.0 460.0 480.0 500.0 520.0 540.0 560.0 580.0 600.0 620.0 &40.0 &60.0 680.0 700.0 720.0 740.0 760.0 780.0 800.0 820.0 840.0 8&0.0 880.0 900.0 920.0 940.0 960.0 980.0 1000.0 1050.0 1100.0 1I50.0 1200.0 1250.0 1300.0 1350.0 1400.0 1450.0 1500.0 1600.0 1700.0 1800.0 1900.0 2000.0 2100.0 2200.0 2300.0 2400.0 2500.0 2&00.0 2700.0 2800.0 2900.0 3000.0 3100.0 3200.0 3208.2 I I I I I I, , I I I I .I I I I ,, Heat of the Liquid Temperature Pressure Lbs. per Sq. In. Gage Absolute t p II I Btu/lb. Btu/lb. Degrees F. 400.97 235.3 402.72 240.3 404.44 245.3 406.13 250.3 255.3 407.80 260.3 409.45 265.3 411.07 412.67 270.3 414.25 275.3 280.3 415.81 417.35 285.3 423.31 305.3 428.99 325.3 434.41 345.3 365.3 439.61 444.60 385.3 I 449.40 405.3 425.3 454.03 458.50 445.3 465.3 462.82· 467.01 485.3 505.3 471.07 525.3 475.01 545.3 478.84 482.57 565.3 486.20 585.3 489.74 605.3 &25.3 493.19 496.57 645.3 665.3 499.8& 685.3 503.08 705.3 506.23 725.3 509.32 745.3 512.34 765.3 515.30 785.3 518.21 805.3 521.06 ;;23.86 825.3 ;;26.60 845.3 ;;29.30 .865.3 885.3 S31.95 905.3 534.56 925.3 ii37.13 945.3 539.&5 965.3 542.14 E;44.58 985.3 0,50.53 1035.3 1085.3 556.28 1135.3 I 561.82 1185.3 I 567.19 1235.3 n n . 3 8 1285.3 577.42 1335.3 582.32 1385.3 587.07 1435.3 591.70 1485.3 596.20 1585.3 &04.87 1685.3 613.13 1785.3 621.02 1885.3 628.56 1985.3 635.80 2085.3 642.76 2185.3 649.45 2285.3 &55.89 2385.3 6b2.1I 2485.3 668.11 2585.3 &i'3.91 2685.3 679.53 2785.3 684.96 2885.3 690.22 2985.3 M5.33 3085.3 700.28 3185.3 705.08 3193.5 705.47 . Latent Heat of Evaporation II I I I II i I I : I II I I,, I 376.1 378.0 379.9 381.7 383.6 385.4 387.1 388.9 390.6 392.3 394.0 400.5 406.8 412.8 418.6 424.2 429.6 434.8 439'.8 444.7 449.5 454.2 458.7 463.1 467.5 471.7 475.8 479.9 483.9 487.8 491.6 495.4 499.1 502.7 50&.3 509.8 513.3 516.7 520.1 523.4 526.7 530.0 533.2 536.3 539.5 542.6 550.1 557.5 564.8 571.9 578.8 585.6 592.2 598.8 605.3 611.7 624.2 636.5 &48.5 660.4 672.1 683.8 695.5 707.2 719.0 731.7 744.5 757.3 770.7 785.1 801.8 824.0 875.5 906.0 I ; I 1 I I I I I 825.0 823.3 821.6 820.0 818.3 816.7 815.1 813.6 812.0 810.4 808.9 802.9 797.0 791.3 785.8 _ 780.4 775.2 770.0 765.0 760.0 755.1 750.4 745.7 741.0 736.5 732.0 727.5 723.1 718.8 714.5 710.2 706.0 701.9 697.7 693.& 689.6 685.5 681.5 677.6 673.6 669.7 665.8 661.9 658.0 654.2 650.4 640.9 631.5 622.2 613.0 603.8 594.6 585.6 567.5 567.6 558.4 540.3 522.2 503.8 485.2. 4&6.2 446.7 426.7 406.0 384.8 361.6 337.6 312.3 285.1 V ho 1201.1 1201.3 1201.5 1201.7 1201.9 1202.1 1202.3 1202.4 1202.6 1202.7 1202.9 1203.4 . 1203.8 1204.1 1204.4 - _.t204.6_ 1204.7' 1204.8 1204.8 1204.8 1204.7 1204.5 1204.4 1204.2 1203.9 1203.7 1203.4 1203.0 1202.7 1202.3 1201.8 1201.4 1200.9 1200.4 1199.9 1199.4 1198.8 1198.2 1197.7 1197.0 1196.4 1195.7 1195.1 1194.4 1193.7 1192.9 1191.0 1189.1 1187.0 1184.8 1182.6 1180.2 1177.8 1175.3 1172.9 fi70.1 1164.5 1158.6 1152.3 1145.6 1138.3 1I30.5 1122.2 1113.2 1103.7 , 1093.3 1082.0 1069.7 1055.8 Ou. ft. per lb. Cu. ft. per lb. 0.01865 0.01868 0.01870 0.01873 {l.01875 0.01878 0.01880 0.01882 0.01885 0.01887 0.01889 lJ.01899 0.01908 0.01917 0.01925 .0.01934 11.01942 0.01950 0.01959 0.01967 0.01975 0.01982 0.01990 .0.01998 0.02006 0.02013 0.02021 0.02028 0.02036 0.02043 0.02050 0.02058 0.02065 0.02072 0.02080 0.02087 0.02094 0.02101 0.02109 0.02116 0.02123 0.02130 0.02137 0.02145 (j.02152 0.02159 0.02177 il.02195 0.01214 0.02232 0.02250 0.02269 0.02288 0.02307 l)'O2327 0.0234& 0.02387 0.02428 0.02472 0.02517 0.02565 0.02615 0.02669 0.02727 0.02790 0.02859 0.02938 0.03029 0.03134 ;).03262 -6-.03428 0.03681 0.04472 -'.05078 1.84317 1.80802 1.77418 1.74157 1.71013 1.67978 1.65049 1.62218 1.59482 1.56835 1.5427-< 1.44801 1.36405 1.28910 1.22177 1.1&095 1.10573 1.05535 1.00921 0.96677 0.92762 0.89137 0.85771 0.82637 0.79712 0.76975 0.74408 0.71 995 0.69724 0.67581 0.6555& 0.63639 0.61822 0.60097 0.58457 0.5&896 0.55408 0.53988 0.52631 0.51333 0.50091 0.48901 0.47759 0.46662 0.45609 0.4459& 0.42224 0.40058 0.38073 0.36245 0.34556 0.32991 0.31536 0.30178 0.28909 0.27719 0.25545 0.23607 0.21861 0.20278 0.18831 0.17501 0.16272 0.15133 0.14076 0.13068 0.1211 0 0.11194 0.10.l05 0.09420 0.08500 0.07452 0.05663 0.05078 I ~--- I I 1020.3 993.3 931.6 906.0 Steam Water Btu/lb. 'Itt"'" 218.4 1&9.3 5&.1 0.0 Specific Volume Total Heat of Steam I I A - 16 APPEN:0IX A - PHYSICAL PROPERTIES OF flUIDS AND flOW CHARACTERISTICS OF VALVES, fITTINGS, AND PIPE CRANE Properties of Superheated Steam* v = specific volume, cubic feet per pound h, = total heot of steam, Btu per pound Pressure Lbs. per Sq. In. SflI,tt-. Abs. Gage P' P 3500 213.«13 5.31 227.% I 30.0 15.3 250.34 267.25 40.0 25.3 50.0 i 35.31 281.02 60.0 45.3 292.71 80.0 65.3 312.04 90.0 75.3 ;)20.28 100.0 85.3 327.82 120.0 125.3 35J:.04 145.3 180.0 165.3 363.55 373.08 185.3 381.80 205.3 389 . 88 225.31397.39 25.428 I 28.457 i! 31.466, 34.465 I " 40.447! 43.435 37.458! 1239.2 1286.9' 1334.9 1383.5 1432.911483.2 1534.3 46.420 1586.3 52.388 1693.1 58.352 1803,3 V 15.859 1213.6 245,3 404.44 265.3 411.07 300.0 320.0 I 285.3 417,35 423.:11 325.3 428.99 I I 345.3 434.41 28.943 1534.0 30.936 1586.1 34.918 1692.9 38.896 1803.2 18.699 20.199 21.697 23.194 26.183 29.168 9.424 1209.9 10.0621 11.306 1234.9 I 1284.1 12.529 1332.9 13.741 1382.0 14.947116.150 1431.7 1482.2 17.350 1533.4 18.549 1585.6 20.942 1692.5 23.332 1802.9 V 7.815 1208.0 8.354 1233.5 9.400 1283.2 10.425 1332.3 11.438 1381.5 12.446 1431.3 I 13.450 1481.8 14.452 1533.2 15.452 1585.3 17.448 1692.4 19.441 1802.8 V 6.664 1206.0 7.133 1232.0 8.039 1282.2 8.922 1331.6 9.793 10.659 1381.0 I 1430.9 11.522 1481.5 12.382 1532.9 13.240 1585.1 14.952 1692.2 16.661 1802.6 V 5.801 1204.0 6.218 1230.5 7.018 1281.3 7.794 I 8.560 1 9.319 1330.9 1380.5 1430.5 10.075 1481.1 10.829 1532.6 11.581 1584.9 13.081 1692.0 14.577 1802.5 17 5.128 1202.0 5.505 1228,9 8.277 6.2231 6.917 1 7.600 1280.3 1330.211380.0 I 1430.1 8.950 1480.8 9.621 1532.3 10.290 1584.6 11.625 1691.8 12.956 1802.4 h, V 4.590 1199.9 4.935 1227.4 5.588 1279.3 6.216 1329.6 7.443 1429.7 8.050 1480.4 8.655 1532.0 9.258 1584.4 10.460 1691.6 11.659 1802.2 V 3.7815 1195.6 4.0786 1224.1 4.6341 1277.1 5.163715.6813 6.1928 1328.2 1378.4! 1428.8 6.7006 1479.8 7.2060 1531.4 7.7096 1583.9 8.7130 1691.3 9.7130 1802.0 4.411914.858815.2995 1326.8 1377.4 1428.0 5.7364 1479.1 6.1709 1530.8 6.6036 1583.4 7.4652 1690.9 8.3233 1801.7 h, hg V i I 1432.1 1 1482.5 1533.7 1585.8 1692.7 1803.0 1 I 3.4661 3.9526 1220.811275.3 1 6.833 I 1379.5 h, ... 3.0060 1217.4 3.441313.8480 1273,3 1325.4 4.2420 I 4.6295 1376.411427.2 5.0132 1478.4 5.3945 1530.3 5.7741 1582.9 6.5293 1690.5 7.2811 1801.4 V ... ... 2.6474 1213.8 3.0433 1271.2 3.4093 1324.0 3.7621 4.1084 1375.311426.3 4.4508 1477.7 4.7907 1529.7 5.1289 1582.4 5.8014 1690.2 6.4704 1801.2 V 2.3598 1210.1 2.i247 3.0583 1322.6 3.3783 1374.3 I 1425.5 3.6915 4.0008 1477.0 4.3077 1529.1 4.6128 1581.9 5.2191 1689.8 5.8219 1800.9 V 2.1240 1206.3 2.4638 1266.9 2.7710 3.06421 3.3504 1321.2. 1373.211424.7 3.6327 1476.3 3.9125 1528.5 4.1905 1581.4 4.7426 1689.4 5.2913 1800.6 1.926812.246212.531612.80241 3.0661 1202.11 1264.6 I 1319.7. 1372.1 11423.8 3.3259 1475.6 3.5831 1527.9 3.8385 1580.9 4.3456 1689.1 4.8492 1800.4 12.061912.3289! 2.58081 2.8256 1262.4 1318.2 1371.1 i 1423.0 3.0663 1474.9 3.3044 1527.3 3.5408 1580.4 4.0097 1688.7 4.4750 1800.1 V V .. V ... V V V V h, 360.0 26.949 1482.8 V hg ... I I I I 1.90371 2.1551 I ii 1316.8 2.3909 1370.0 2.6194 1422.1 2.8437 1474.2 3.0655 1526.8 3.2855 1579.9 3.7217 4.1543 1688.4' 1799.8 1.7665 1257.7 2.0044 1315.2 2.2263 2.4407 1368.91 142 1.3 2.6509 1473.6 2.8585 1526.2 3.0643 1579.4 3.4721 1688.0 3.8764 1799.6 1.6462 1255.2 1.8725 1313.7 2.08231 2.2843 1367.8 1420.5 2.4821 1472.9 2.6774 1525.6 2.8708 1578.9 3.2538 1687.6 3.6332 1799.3 .. 1.5399 1.7561 1252.8 1 1312.2 1.9552 1 2.1463 1366.7 I 1419.6 2.3333 1472.2 2.5175 1525.0 2.7000 1578.4 3.0611 1687.3 3.4186 1799.0 ... 1.445411.6525 1250.3 11310.6 1.8421 12.0237 1365.61 1418 .7 2.2009 1471.5 2.3755 1542.4 2.5482 1577.9 2.8898 1686.9 3.2279 1798.8 I ! V h, 1269.0 1260.0 hg 340.0 24.952 1432.5 15.685. 17.195 1333.61 1382.5 h, 305.3 22.951 1383.0 12.624 14.165 1236.41 1285.0 h, I 20.945 1334.2 18.929 1286.0 11.838 121 1.7 h, 280.0 16.892 1237.8 I V hg hg 260.0 , i 'Abstracted from ASME Steam -rables (1967) with permission of the publisher. the American Society 01 Mechanical Engineers. 345 East 47th Street, "ow York. ~. Y. 10017. 1 ! 1500' 23.900 1215.4 h, 240.0 1300' V hg h, 220.0 I 77.807 1803.4 hg 200.0 I , 69.858 1693.2 h. 160.0 --: 1000' 1 11 00' 61.905 1586.5 hg 140.0 900' 800' 37.985l41.986. 45.978 49.964 53.946157~9Z6 1287.3 I 1335.211383.811433.211483.4: 1534.5 hg 105.31 34l'..27 700' 33.963 1239.9 h, 55.31 302 . 93 600' 31. 939 1216.2 \' h, 70.0 500,1 I h, 20.0 400' t 0.3 15.0 Total Temperature-Degrees Fahrenheit (t) Ten'>p. (continued oil 'he ~.l{' pog.) CRANE A.17 APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND FLOW CHARACTERISTICS Of VALVES, flnINGS. AND PIPE Plroperties of Superheated Steam - continued v = specific volume, cubic feet per pound hg = total heat of steam, Btu per pound Pressure Lbs. per 1 I Sat. Temp. Total Temperature-Degrees Fahrenheit (t) Sq. In. AbS'1 Gage P' 380.0 P 365.3 500' t ~ 439.61 h, 400.0 385.3 444.60 405.3 449.40 425.3 454.03 460.0 445.3 458.50 ., :: 465.3 1.2148 1 1.4007 1242.4 1305.8 485.3 505.3 540.0 525.3 1.424211.57031 1.7117 1360.0 1414.41 1468.0 V 1.0409 i 1.2115 1.3615 1234.1 1300.8 1 1358.8 V 475.01 hg i 560.0 545.3 478.84 - 'v' h, '~ ==-3 1 '~. i ~~ 580.0 565.3 482.57 V h. 600.0 585.3 486.20 V h. 650.0 635.3 494.89 - II h. 700.0 750.0 685.3 735.3 503.08 510.84 800.0 785.3 518.21 850.0 835.3 525.24 ==t# :::=t :::::a 900.0 885.3 531.95 935.3 538.39 1000.0 985.3 544.58 =- 1050.0 1035.3 550.53 1085.3 556.28 1135.3 561.82 2.4998 2.6384 1741.2 , 1797.7 Ii 2.5230 2.12261 2.2569 1629.9 1685.1 2.3903 1740.9 2.0330 1629.5 2.1619 1684.7 2.2900 1740.6 2.4173 1797.2 1797.4 1.4508 1465.1 1.570411.6880 1519.111573.4 1.8042 1628;2 1.9193 1683.6 2.0336 1739.7 2.1471 1796.4 1.0217 1293.9 1.155211. 2787 1354.2 1410.0 1.3972 1464.4 1. 5129 11.6266 1518.6 I 1572.9 1.7388 1627.8 1.8500 1683.3 1.9603 1739.4 2.0699 1796.1 0 ..9824 1.1125 1353.0 1.3473 1463.7 1.4593 1518.0 i 1409.2 1512.4 1.6780 1627.4 1.7855 1682.9 1.8921 1739.1 1.9980 1795.9 I 1.2324 1 ,1 1.5693 I I 0.9456 1290.3 1.0726 1351.8 1.1892 1408.3 1.3008 1463.0 1.4093 1517.4 1.511iO 1571.9 1.6211 1627.0 1.7252 1682.6 1.8284 1738.8 1.9309 1795.6 0.7173 1207.6 0.8634 1285.7 0.9835 1348.7 1.0929 1406.0 1.1969 1461.2 1.2979 1515.9 1.3%<); 1570.7 1.4944 1625.9 1.5909 1681.6 1.6864 1738.0 1.7813 1794.9 0.7928 1281.0 0.9072 1345.6 1.0102 1403.7 1.1078 1459.4 1.2023 1514.4 1.2948 1569.4 1.3858 1624.8 1.4757 1680.7 1.5647 1737.2 1.6530 1794.3 0.7313 1276.1 0.8409 1342.5 0.9386 1401.5 1.0306 1457.6 1.1195 1512.9 1.2063 1568.2 1.2916 1623.8 1.3759 1679.8 1.4592 1736.4 1.5419 1793.6 I 1271.1 , 0.6774 0.7828 1339.3 0.8759 1399.1 0.9631 1455.8 1.0470 1511.4 1.1289 1566.9 1.2093 1622.7 1.2885 1678.9 1.3669 1735.7 1.4446 1792.9 0.6296 1265.9 0.7315 1336.0 0.8205 1396.8 0.9034 1454.0 0.9830 1510.0 1.0606 1565.7 U366 1&21.6 1.2115 1678.0 1.2855 1734.9 1.3588 1792.3 0.5869 1260.6 0.6858 1332.7 0.7713 1394.4 0.8504 1452.2 0.9262 1508.5 0.9998 1';64.4 1.0720 1620.6 1.1430 1677.1 1.2131 1734.1 1.2825 1791.6 0.54851 0.6449 1255.1 1329.3 0.7272 1392.0 0.8030 1450.3 0.8753 1507.0 0.9455 1563.2 1.0142 1619.5 1.0817 1676.2 1.1484 1733.3 1.2143 1791.0 I 0.5137 0'.6080 0.6875 1249.3 1325.911389.6 0.7603 1448.5 0.8295 1505.4 0.8966 1561.9 0.9622 1618.4 1.0266 1.0901 1675.3 . 1732.5 1.1529 1790.3 1.0973 1789.6 ... ... V 1 ... \ ... i 0.4821 0.5745 1243.411322.4 0.6515 1387.2 0.7216 1446.6 0.7881 1503.9 0.8524 1560.7 0.9151 0.9767 1.0373 1617.41 1674 .4 ; 1731.8 0.4531 0.5440 1237.3 ,1318.8 0.6188 1384.7 0.6865 1444.7 0.7505 1502.4 0.8121 1559.4 fJ.8723 i 0.9313 : 0.9894 1616.3 1673.5 1731.0 1.0468 1789.0 0.4263 1230.9 0.5889 1382.2 0.6544 1442.8 0.7161 1500.9 0.7754 1558.1 U.8332 f 0.8899 ,615.21 1672.6 0.9456 1730.2 1.0007 1788.3 I \ V 2.7647 1798.0 0.7944 1215.9 V h. 2.6196 1741.6 1.3284 1410.9 I 1292.1 h. 1I50.0 2.4739 1685.8 2.2302 1796.7 0.8287 1219.1 hg 1100.0 2.7515! 2.9037 1741.9 1798.2 2.1125 1740.0 0.8653 1222.2 .. \ 2.5987 1686.2 I 1.87461 1.9940 1628.7 1684.0 1.2010 1355.3 hg '=::J 2.897313.0572 1742.2 1798.5 1. 6323 11.7542 1519.7 1573.9 1.0640 1295.7 \' hg 1686.5 1.5085 1465.9 0.9045 1225.3 .. V- 1.85041 1.9872 1521.5 1 1575.4 1 1.7716 i 1.9030 1520.91, 1574.9 I 1500' I I 2.7366 ' I 1400' 1.3819 1411.8 1.2504 1356.5 h. 950.0 I 2.3200 1796.9 1.1094 1297.4 ... hg 0 2.1977 1740.3 .; 0.9466 1228.3 h. :=:$ 1300 I 9507 2.0746 1. 1 1684.4 1629.1 1.4397 1412.7 V - , 1.69921 1.8256 1520.3 1 1574.4 1.3037 1357.7 h. \I I 1.5708 1466.6 1.1584 1299.1 hg ~ 1.5023 1.6384 1413.6 I 1467.3 0.9919 1231.2 f 1200' 1.936312.0790 1 2. 2203 1 2.3605 1522.1 1575.'1 1630.4. 1685.5 1.2691 1302.5 i 1362.31 i, 1.7918 1468.7 1.9759 1.0939 1236.9 h. 1100" 1.8795 1469.4 2.0825 1470.8 V V 471.07 I 2.2484,1 2~'!.U4iI 2.5750 1 1523.811017.4: 1631.6, j I 2.1339 2.2901 i 2,4450 I 1523.3 i 1576.9 J 1631.21 1 j 2.0304 i 2.1795) 2.32731 1522.711570.411630.8 1.3319 1304.2 V 1000' i ,1.1517 hg 520.0 900 0 800' , V - 467.01 I I I 1470.1 h. ' 1239 .7 hg 500.0 0 1.567611.72581 1416.21 , 1 1.492611.6445 1 1361.1 I 1415.31 V 462.82 700 1.9139! 1417.91 1 . . 1 1.4763, 1.649911.8151 I 1307.411363.4 I 1417.0 - hg 480.0 I 1.559811.7410 1309.011364.5 1.2841 1245.1 ng 440.0 1.3606 1247.7 0 V hg 420.0 600 ... . .. 0.5162 1315.2 i I A -18 APPENDIX A- PHYSICAL PROPERTIES OF FLUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE Properties of Superheated Steam - T' = speciflc volume, cubic feet CRANE concluded per pound h, = totcil heat of steam, Btu per pound p",""" So< Lbs. per ~ Temp, Total Temperature-Degrees Fahrenheit (t) Sq. In. Abs. P' , I Gage 650' P t 1200.0 1185.3 567.19 1300.0 1285.3 577.42 1 1400.0 I 1385.3 I 1500.0 11485.3 1600.0 . 1700.0 I 587.07 1585.3 604.87 1685.3 61:1.13 1785.3 621.02 \' 2000.0 1885.3 1985.3 628.56 636.80 2085.3 642.76 2185.3 649.45 2300.0 2285.3 655.89 2400.0 2385.3 662.11 2500.0 2485.3 668.11 2600.0 2585.3 673.91 2700.0 I2685.3 679.53 2800.0 2785.3 684 . 96 2900.0 2885.3 690 ..22 2985.3 695.33 3100.0 3085.3 700.28 3185.3 705.08 3400.0 1 I I! 3285.3 3385.3 ... . . I 1200' I 1300' 1400' 1500' 0.7974 1614.2 0.8519 1671.6 0.9055 1729.4 0.9584 1787.6 i? h, 0.4052 1261.9 0.4451 1303.9 0.4804 1340.8 0.5129 1374.6 0.57291 0.6287 1437.1 . , 1496.3 0.6822 1554.3 0.7341 1612.0 0.7847 1669.8 0.8345 1727.9 0.8836 1786,3 V 0.3667 0.4059 1251.411296.1 400 0.4712 0.4 1334.5 1 1369.3 0.528210.5809 1433.2 1493.2 0.6311 1551.8 0.6798 1609.9 0.7272 1668.0 0.7737 1726.3 0.8195 1785,0 0.3328 1240.2 I 0.3717 0.4894 1429.2 0.5394 1490.1 0.5869 1549.2 0.6327 1607.7 0.6773 1666.2 0.7210 1724.8 0.7639 1783.7 n, 0.3026 1228.3 0.3415 1279.4 0.4049 1 0.4350 1328.0 1364.0 1 0.37411 0.4032 1321.4 1358.5 0.4555 1425.2 0.5031 1486.9 0.5482 1546.6 0.5915 0.6336 1605.6 1664.3 0.6748 1723.2 0.7153 1782.3 V 0.2754 1215 ..1 0.3147 1270.5 0.3468 1314.5 0.3751 1352.9 0.4255 1421.2 0.4711 1483.8 0.5140 1544.0 0.5552 1603.4 0.5951 1662.5 0.6341 1721.7 0.6724 1781.0 0.2505 1201.2 0.2906 1261.1 0.3213 1307.4 0.3500 1347.2 0.3988 1417.1 0.4426 1480.6 0.4836 0.5229 1541.4 1601.2 0.5609 1660.7 0.5980 1720.1 0.6343 1779,7 0.2274 1185.7 0.2687 1251.3 0.3004 0.32751 0.3749 1300.21 1341.4 . 1412.9 0.4171 1477.4 0.4565 1538.8 0.4940 1599.1 0.5303 1658.8 0.5656 1718.6 0.6002 1778.4 0.2056 0.2488 1168.31 1240 . 9 0.1847 0.2304 1148.5 . 1229.8 0.2805 1292.6 0.3072 1335.4 0.3534 1408.7 0.39421 0.4320 0,4680 1474.1 1536.2', 1596.9 0.5027 1657.0 0.5365 0.5695 1717.0 1777.1 0.2624 1284.9 0.2888 1329.3 0.3339 1404.4 0.3734 1470.9 0.4099 1533.6 0.4445 1594.7 0.4778 1655.2 0.5101 1715.4 0.5418 1775.7 0.16361 0.2134 1123.9 1218.0 0.2458 1276.8 0.2720 1323.1 0.3161 1400.0 0.3545 1467.6 0.3897 1530.9 0.4231 1592.5 0.4551 1653.3 0.4862 1713.9 0.5165 1774.4 ·. 0.1975 1205.3 0.2305 1268.4 0.2566 1316.7 0.2999 1395.7 0.3372 1464.2 0.3714 1528.3 0.4035 1590.3 0.4344 1651.5 0.4643 1712.3 0.4935 1773.1 ... ·. 0.1824 1191.6 0.2164 0.2424 1259.71 1310.1 0.2850 1391.2 0.3214 1460.9 0.3545 1525.6 0.3856 1588.1 0.4155 1649.6 0.4443 1710.8 0.4724 1771,8 n, ·. ·. 0.1681 1176.7 0.20321 0.2293 1250.6 1303.4 0.2712 1386.7 0.3068 0.3390 I 0.3692 0.3980 0.4259 0.4529 V ... 0.1544 1160.2 0.1909 1241.1 0.2171 . 0.2585/ 0.2933 ,0.3247 1296.5 ' 1382.1 , 1454.1 11520.2 0.3540 1583.7 0.3819 10.4088 1646.0 1707.7 0.4350 1769,1 0.1411 1142.0 0.1794 1231.I 0.2058 1289.5 0.2468 1377.5 0.2809 0.3114 0.3399 1450.711517.511581.5 0.3670 1644.1 0.3931 1706.1 0.4184 1767.8 ·. ·. 0.1278 1121.2 0.1685 1220.6 0.1952 1282.2 0.2358 1372.8 0.26931 0.2991 1447.2 1514.8 0.3268 1579.3 0.3532 IM2.2 0.3785 1704.5 0.4030 1766.5 ·. ... 0.1l38 1095.3 0.1581 1209.6 0.1853 1274.7 0.2256 1368.0 0.2585 1443.7 1512.1 0.3147 1577.0 0.3403 1640.4 0.3649 1703.0 0.3887 1765.2 V ... ... 0.09821 0.1483 1060.5 1197.9 0.2161 1363.2 0.2484 1440.2 0.2770 1509.4 0.3033 1574.8 0.3282 1638.5 0.3522 1701.4 0.3753 1763.8 V .. . ... ·. · . I 0.1759 1267.0 0.1389 1185.4 0.1671 1259.1 0.2071 1 0.2390 0.2670 1358.4. 1436.71 1506.6 0.2927 1572.6 0.3170 1636.7 0.3403 1699.8 0.3628 1762.5 ·. .. . ... I 0.1300 1172.3 0.1588 1250.9 0.198710.2301 1353.4 1433.1 0.2827 0.3065 1570.3 1 1634.8 0.3291 1698.3 0.3510 1761.2 h, ... · .. .. 1 0.1213 0.1510 1 11158.2/1242.5 0.1908 1348.4 0.2218 0.248810.2734 1429.511501.011568.1 0.2:f.6 162.9 0.3187 1696.7 0.3400 1759.9 V ... ." .. 1 0.1129 0.1435 11143.21 1233.7 0.1834 1343.4 0.21401 0.2405 1425.911498.3 0.2872 1631.1 0.3088 1695.1 0.3296 1758.5 V n, i/ Ii V n, V V V h, V nJ V h, V .. .. h, V V h, V h, hg V h. 3300.0 1100' 0.6250 1 0.68451 0.7418 1440,911499.4 ! 1556.9 h. 3200.0 I 0.5615 1379.7 h, 3000.0 1000' 0.5273 1346.9 h, 2200.0 900' 0,4905 1311.5 ii, 2100.0 I 0.4497 1271.8 h, 1900.0 800' n, h, 1800.0 I 1 ii, 596.20 750' 700' V , h. ... 1287.9 i, I I 1 I 1457.5 1522.9 1585.9 1647.8 1709.2 1770.4 I 0.2877 I I 0.2576 1503.8 0.2646 1565.8 CRANE A-19 APPENDIX II - PHY,ICAL PROPERTIES OF FLUIDS AND FLOW CHARACnRISTICS OF VALVES. FITTINGS. AND PIPE Properties of Superheated Steam and Compressed Water* v = specific volume, cubic feel per pound h.= 10101 heal of sleam, Btu per pound Absolute Total Temperature-Degrees Fahrenheit (t) Pressure =L=~~S.=.l=p;=.r=l==*=2=0=O'=io=40=0~o~I==5=0=O'=*=60=0='~1=7=OO='=4=80=0='=-,\=9=0°='=4,=l=O=OO='=*I=l1=O=O'=*,1=1=200' 1 1 i7 3500 h. 3600 0.0164 176.0 0.2'195 1693.6 0.3198 1757.2 0.2908 1692.0 0.3106 1755.9 0.0183 0.0198, 0.0225 379.3 Ii 487.6 608.1 3800 "\ 0.0164 h. 176.7 0.018.11 0.0198 379.51' 487.7 0.0224 0.029410.1169 607.5, 768.4 1195.5 0.157410.1868 1322.411411.2 0.21161 0.2340 10.2549 0.2746 1487.01 1556.8 1623.611688.9 0.2936 1753.2 4000 V 0.0164 h. 177.2 0.0182 379.8 0.1752 1403.6 0.19941 0.2210 1 0.2411 1481.311552.2 1619.8 0.2601 1685.7 0.2783 1750.6 0.2470 1682.& 0.2645 1748.0 V 0.0164 177.6 0.0302 I 0.12% 775.11 1215.3 0.0198 487.7 1 0.01821 0.0197 487.8 380.1 0.02231 0.0287 606.91 763.0 0.1052 1174.3 0.1463 1311.6 0.0222 606.4 0.0282 758.6 0.0945 1151.6 0.1362 1300.4 0.1647 1396.0 0.1883 'I 0.2093 1475.5 1547.6 0.2287 1616.1 0.2174 0.2351 0.2519 1612.311679.411745.3 'I • 4400 V 0.0164 h. 178.1 0.0182 380.4 0.0197 487.9 0.0222 605.9 0.0278 754.8 0.0846 1127.3 0.1270 0.1552 1289.011388.3 0.17821 0.1986 1469.7 1543.0 4600 V 0.0164 h, 178.5 0.0182 380.7 0.0197 487.9 0.0221 605.5 0.0274, 0.0751 751.511100.0 0.11861 0.1465 1277.2 1380.5 0.1691 0.1889 1453.'l! 1538.4 0.2071 0.2242 160R.5!1670.3 0.2404 1742.7 \" 0.0164 179.0 0.0182 380.9 0.0196 488.0 0.0220 605.0 0.0271 I 0.0665 748.6' 1071.2 0.1109 1255.2 0.1385 1372.6 0.1&061 0.1800 1458.0 i 1533.8 0.1977 0.2142 1604.711673.1 0.2299 1740.0 V 0.0181 381.5 0.01% 488.2 0.0219 604.3 0.0265 743.7 0.1244 1356.6 0.14581 0.1642 1446.21 1524.5 0.1810 1597.2 0.1966 0.2114 5600 \' 0.0163 0.0181 h. 180.8 382.1 0.0195 488.4 0.0217 603.6 0.0260 10.0447 739.6 975.0 0.0856 1214.8 0.1l241 0.1331! 0.1508 1340.21 1434.3! 1515.2 0.16671 0.1815 1589.6 1660.5 0.1954 1729.5 6000 V 0.0180 382.7 0.0195 488.6 0.0216 602.9 0.0256 1 0.0397 736.1' 945.1 0.0757 1188.8 0.1020 1323.6 0.1544 1 0.1684 1505.91 1582.0! 1654.2 0.1817 1724.2 V 0.0163 182.9 0.0180 383.4 0.0194 488.9 0.0215 602.3 0.0252 732.4 0.0358 919.5 0.0655 1156.3 0.0909 1302.7 O.llM 1407.3 1494.2 0.1411 1572.5 0.1544 1646.4 0.1669 1717.6 V 0.0163 184.0 0.0180 384.2 0.0193 489.3 0.0213 601.7 0.0248 729.3 0.0334 901.8 0.05731 0.0816 1124.9 1281.7 O.lOM 1392.2 0.1160 1482.6 0.1298 1563.1 0.1424 1638.6 0.1542 1711.1 0.0163 185.2 0.0179 384.9 0.0193 489.6 0.0212 601.3 0.0245 726.6 0.0318 889.0 0.0512 1097.7 0.0737 1261.0 0.0918, 0.1068 1377.1':1 1471.0 0.1200 1553.7 0.13211 0.1433 1630.8 1704.6 0.0162 186.3 0.0179 385.7 0.0192 490.0 0.0211 600.9 0.0242 724.3 0.0306 879.1 0.0465 1074.3 0.0671 1241.0 0.0845! 0.0989 1361.2:1 1459.6 0.1115 1544.5 0.1230 1623.1 0.1338 1698.1 0.0162 h. 188.6 0.0178 3·87.3 0.0191 490.9 0.0209 600.3 0.0237 720.4 0.0288 864.7 0.0402 1037.6 0.0568 1204.1 0.07241 0.0858 1333'()i! 1437.1 0.0975 1526.3 0.1081 1607.9 0.1l79 1685.3 \' 0.0161 0.0177 0.0189 0.0207 0.0233 0.0276 0.0362 0.0495 J O.0633~,: 0.0757 0.0865 1508.6 0.0963 1593.1 0.1054 1672.8 0.0776 1491.5 0.0868 1578.7 0.0952 1660.6 4800 h. 5200 h. 0.0164 179.9 0.0163 h. 181.7 - 6500 h. 7000 h. V 7500 h. V 8000 h, 10000 h, 0.0531 0.0973 1016.9· 1240.4 1 ! i I . ! I 1666.8 1734.7 o.l2n . 0.1391 1422.3 j 0.1266 i! V 9000 190.9 388.9 491.8 600.0 717.5 854.5 11000 0.0161 h. 193.2 0.0176 390.5 0.0188 492.8 0.0205 599.9 0.0229 715.1 0.0267 846.9 12000 Ii 0.0161 0.0176 0.0187 0.0203 0.0226 0.0260 0.0,317 0.0405 0.0508': 0.0610 0.0704 0.0790 0.086'1 V h, 13000 14000 1 0.0335 992.1 0.0562:1 0.0676 1280.2:i 1394.4 0.0443 1146.3 :: 713.3 841.0 977.8 1124.5 1258.0 1374.7 1475.1 1564.9 1648.8 V 10.0160 0 . 0175 0.0186 0.0201 195.5 392.1 493.9 0.0376 1106 .7 0.0466! 0.0558 In8.5 i, 1356.5 0.0645 1459.4 0.0725 1551.6 0.0799 1637.4 0.0354 1092.3 0.0432 1221 ... 0.0515 1340.2 0.05% 1444.4 0.0670 1538.8 0.07-10 1626.5 393.8 495.0 600.1 0.0213 711.9 0.0253 836.3 0.0.,02 197.8 "\ 0.0160 h. 200.1 0.0174 395.5 0.0185 496.2 0.0200 600.5 0.0220 710.8 0.0248 832.6 0.0291 958.0 966.81 ,i \' 0.0159 0.0174 0.0184 0.0198 0.0218 0.OH4 0.0282 0.0337 0.0405:'. 0.0479 1 0.0552 0.0624 0.0690 h, 15500 1305.3 Ii 1415.3 599.9 h. 15000 1011. 3 1 1172 . 6 ] 1 - 0.176410.206610.232610.256310.2784 1338.21 1422.21 1495.51 1563.61 1629.2 I I ! I 0.16971 0.1996 1 0.22521 0.2485 0.2702 1333.011418.6 1492.6: 1561.31 1627.3 V 0.0164 176.3 h. ~=::::. , 0.0225-10.030710.1364 608.4 i 779.4 1224.6 1400' 115000 .- - - h. 4200 ·.::f3 0.018310.0199 379.11 487.6 I 1300' 202,4 397.2 497.4 600.9 710.0 829.5 -;;c 0.0159 0.0173 h. 203.& 398.1 0.0184 498.1 0.0198 601.2 0.0217 709.7 0.0242 828.2 950.9 1080.6 1206.8: 1326.0 1430.3 1526.4 1615.9 0.02781 0.0329 947.81 1075.7 0.0393 i {).0464 1200.J 1319.6 0.0534 1423.6 0.0603 1520.4 0.0668 1610.8 i *Abstracted from :\?~'1E Stl"am Tubles (lc}{)7) with pcrmj~.:-i()n of [he puhlbhcr. The American Society 01 ~lcchanicai Engineers, 3-15 East 47th Street. :\ew York, :\. Y. 10017 A.20 API'ENDIX A - PHYSICAL PROPERTIES OF flUIDS ANO flOW CHARACTERISTICS OF VALVES, FITTINGS, ANO PIPE Flow Coefficient C for Nozzles CRANE 7 (' 1.1 Data from Regelnfuet die Durch- 8 I I] 'III " Ii 1.1 6 ' 4'f i! Illi' ,I , 1.1 flussmessung mit genormten Due- sen und Blenden. VDI-Verlag G. m.b H., Berlin, SN\V, 7, 1937. Published as Technical Memorandum 952 by the NACA. 1.1 1 : ': I, I I I i ! !! I'! I ", 1.08, 1.0 6 , -~ 0.9 rnrr iii 0.l+!, I f I f II 'I ' " I : ' " --'"" , VI.)':'i :;?Vf......-: . ' I I 0.94 4 .7 .72 s .. .60 .SO .40 fY~V.n Illrvl 810' ,77 .S \;,.~~ : III 0.9 ,80 .70 , " I Fiow i Irr Ii J{f' f ').11',. 1.02 " l-i--i+-' , , 1.0 0" ExalTlple: The flow coefficient C for a diameter ratio do/d , of 0.60 at a Reynolds number of 20,000 (2 X t04) equals 1.01. f , ,I J ;, i .1 "i i"'1 '' 1.04 I,' i ' " I -, " 'I 1.10' I , ! Ii! 11 1 I .30 ' '0-0.2 i 1 II 46810' R, - Reynolds Number based on d l Flow Coefficient C for Square Edged Orifices 7 17 • C 1.3 l. 2 t 1. I I 1.0 I I I I I",Itt I 0, I 0,' v 1 --- L r, f I I , """" \\ '" t-~ :::: '-..., I I -..;. - 11Wl/ *=1#]1 8 10 , i- - , --~ F=:: 3OI'V - 6 ,t-- 1"-... 1 , I!I~ ~ I i~:;:::;:,r....L: ~ ~ \':: W " T r-:---... . i , \ \ I I v.---t" i I ,/ /' n- :50i--\Y~ !L~~ ,4~ f\\\ - 0., i "~vr :.65! 1111 i IIIIII/i I' I, i'rl o. 7 . " I ' , o. :' 0.6 iI %;80 '=751~ t- I I : 0",2) 4tJ 60 80 102 4 6 8 10 3 R,. - Reynolds Number based on d 1 - c = ;==~C~d=F' ~ 1 - (~)' Lower chart data from Regeln ruer die Durchflussmessung mit -gt?normtem Duesen und Blenden. Flow ---:r VDI-Verlag G mb.H.. Berlin, SNW, 7, 1937, Published as Technical Memorandum 952 by the NACA. 4 6 810' 2 4 6 810' 11, - Reynolds Number based on d, .30 ().().2 .s APPENDIX A- PHYSICAL PROPERTIES OF flUIDS AND FLOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE CRANE Net Expansion Factor, Y For Compressible Flow through Nozzles and Orifices 9,10 c: o .. E--L-=-::t~~~-2~~"""":","+-~~~':::""H-+-+-i--I Vl ~ ;'F--i--::-C7"b-...4~...o.,:~-r--+--...;'>,~-+-~~""':~l-1:";"..l-' x UJ :i:-r- :...... ,=~ .• ! , ; .55 b--r----j--+--+--+--+--+---l---";....-->-ii-l-+~ i I j ! ~~-r--__j---~.---t--+-~-~-+-~~+-~~ .- Data extracted from, Fluid l\1eters, Their Theory and Application, Fourth EJition, 1937, and Orifice Meters wilh Supercritical Flow by R. G Cunningham, with permission of the publisher, The American Society of Mechanical Engineers, 345 East 47th Street, New York, N,Y. 10017. ."I---ir---+-+-+--t---+--+---l--.f-----l-+~_+_W .<eE:--t---j--+--+-+--+--+---l--l----I--I-i*..l-1 i : ! II , ::: -a ! " \, ,I, !; r '! J ~ to ! I ,. l.2~!'! I , J ! I , ! , I 1, ' ! ! ,';'-) ,.~ !li,!,!!,·,,!.!tI' )'! l ,! I ) . ,t ! , ! :.C 1' '., ! t, •• II II [, lin I LO Pressure Ratio - Critical Pressure Ratio, rc For Compressible Flow through Nozzles and Venturi Tubes 9 a.. "" a.. ........ .58 .75 ~" .56 I I u 1.35 k=cp,c v I A·22 APPENDIX A-PHYSICAL PROPERTIES OF FLUIDS AND flOW CHARACTERISTICS OF VALVES, FITTINGS, AND PIPE CRANE Net Expansion Factor Y for Compressible Flow Through Pipe to a Larger Flow Area k rk 1.0 0.95 ~"rrr"xlm"tch' = 1.3 1.3 for CO,. SO,. 11,0. II,S. ~i Is. ~,O, 0,. CIl,. C,II,. anJ C,II,I ~ '-.. '-.. '\ 0.90 I I I .~ ~i ~ ~~~ ~~ l~ ~ ~ ~ ~ I ~~ I~ ~,~ ~~ ~~ t--... 1,\ ~ ~ ~ 8:: I ~ ~I ~ ~~ ." ""- ~ "R: '~8~ "\ ~ i'\. ~j ""~ ~t'o f:o~'01'1'0. I K ~ 0.85 0.80 y . 0.75 I I 0.70 '\ 0.65 I t' ~ 0.1 '" ~ "'~~ '0_f 11',\ "1-0 {$. "'0 f- \.' "0 <9 -00 ..':..0 t f'":"'01"0 '0 " '" I~~I l' 1'F",Y' 0.2 0.4 0.3 0.5 t::,p 0.6 O y 1.2 1.5 2.0 .525 .550 .593 .612 .631 .635 3 4 6 .642 .678 .722 .658 .670 .685 8 10 15 .750 .773 .807 .698 .705 .718 20 .831 .877 .920 .718 .718 .718 "'\,1' I o f f-,\_\.\_,\._T"l_ _\\_~ "f\, I 0.60 0.55 Limiting Factors For Sonic Velocity k = 1.3 40 100 I 0.7 0.3 0.9 1.0 p'1 k r:k ~approximatcly = 1.4 J.4 for Air. H,. 0" "'" CO. NO. and HCl) Limiting Factors For Sonic Velocity k = 1.4 0.95 K I~~I Y 0.80 1.2 1.5 2.0 .552 .57& .&12 .588 .&0& .&22 0.75 3 & .&&2 .. 697 .737 .&39 .649 .&71 8 10 15 .7&2 .784 .818 .&85 20 .839 .710 .8831.710 .92& .710 0.90 0.85 Y 4 0.70 0.65 ,f ,f ; I j 0.60 0.55 40 100 0 0.1 0.2 0.3 0.4 0.5 t::,p I P'I 0.8 0.9 1.0 .&95 .702 . APPENDIX A - F'H'rS1CA1. PROiftERTIES Of HUlDS AND flOW CHARACTERISTICS Of CRANE VAtVES~ fmINGS. AND PIPE A-23 Relative Roughness of Pipe Materials and Friction Fadors 18 For Complete Turbulence =::::::t :::::3 ~ '::=:t Pipe Diameter, in Feet - D .0045'E~.J~~I~'3t2~~I}§j.~4i~.~5t·~~1~.~8~'1~~§t'§2§~,3~S4~5~~~11~~~r'~§O'~~'~~EO~2L5 ' '07 1 . I 03"' I • "' 1 I '..:=t, ' -,: : ! " I i ' ! 1 h' I \ I': '.1 I I I Ii· I i i i I , II! 06 "'I i i I i 1 i .021---+'~'+!-Hr--+-i(-+~~'+++--+-l'-!~-+-'-H-++-, f-t--t-t-H---i--..t-+--!-.05 ~... I I i,\~ i '- I i I ,I 1"'- I "~,1 '" " I i ~ iN I I'l,I II -.04 035 t::I =::I ::=:I ==- ==~ - :::=2 ~ ~ :::::2 =:D :::::» 01 .~ ... ~~ ::::::s "==.".=."~ Pipe Diameter, in Inches - d ~ "~ ,~ -'~ i ),J{,I (.'\tr;lc{CJ ironl Fflt-lltm I ';.{~I'.~ .!t)f PIPr: F!tlll' bv L F \~, ""'I•.h. \l, nh pt:rml~~10n 'of the f'uhll··-t-k:'. The .\I1'.crtcan Soci.t't \ 01 ~ 1r,;"h;:~mci.l1 Engineer--:. 2'J \) e>( N,h l-!rcct. :\cw York. Problem: Determine absolute and relatiye roughness. and friction factor, for fully turbulent flow in Io-inch cast iron pipe (I.D. = 10.16"). Solution: Absolute roughness (.) = 0.0008; . . . . . Relative roughness (E. D) = 0.001 . . . . . Friction factor at fully turbulent flo\\" (j) = O.OlgO. lU Uu-u U U U II U U U U U U U U U U Uun .n II. IJ.. I U U ij U UU I VALUES OF 0.4 0.2 0.1 0.6 0,8 I '07Tf.li 06 I 1 I t ) •'1.: , '.' " ;, .1, Ir:! !~\. ,04 i" 1 .. i I 40 60 80 100 200 400 600 800 \.~() f·'··~" ',. .03! . i •. ~ ~ , . II T'Or'm'llhEE1'E'r rtllRT'BTUllCNctlII .i.' i '{ . 'i i' I I i' f I I i ",.J ~~~ ~ \,f'..l"}. ~ ~;" ,,,,.r ' '\': t r . t. I . "J:, I) ,.' (/)'211 .02 I 11111 J I "1 I .' .. .. I :1 ] I1 · n I I. I I I II+++-t+!-H Pipe .' inches . ~1/8 .t==',;.f~ H-ffiH+l:: ,t '1 'I', ',: rt-. . ~;'<;;~''j.li ,:~" "'" "",~ •.., TT " ,'\. I. -"" .. ~0. 'i<!.tH ' . c. ,.~ J"I 1 " 'I~~-rl ' ' ' ••. , ' ' . 1 ;.... "," \:.1') , " ,'1.'';<'1..) c. II Ilt41 +-1 F~j;;__~1 -1---- =1.....'...-....., . H _. - ..... ... - ' l' """". '1 ~~ ~. .. 1M 2 3 4 5C B10 4 f. 2 3 4 56 810 5 2 3 4 56 ./ 810 6 2 3 4 56 810 7 . ::1,=,a .t;;;;l~.=::t:, ~~ o 2 3 4 56 8 0 o 2 4 0 0 Scnutllliu Numlier 1+ ,. ~ ~ m z 0 )( ,. I .. '" -n.. ... Q. ~ -< III n ~ 0'" I~ 1 6 Q 14 '" .~ c ~ 3 3(I) ~ ,.z 0 V> ...D. 0 0 ~ 0 :0: n til iii (I) Q ,. ,.n'" :r ~ m '"'a ::I n V> :e 0 0.. g ~ ;: ffi - G'I 1" ::I z ." 'tJ CD :;; ::r" ::;- 108 '"m::; fl ::I 10 0 3Z ,. -. .. ihP He - Reynolds Number i', 6 8 - ",' ... +- '-1-- f-.. 103 3/4 +-\:.....;..,p.-,,=:;13 Ii ..ct:~~:~~ j~1Iff--l·1 I··t.·j·!.·.I··j· ... ,·[·..[·-11.···1... I·I-~~···'<I~t':'~~~r:: . '" ~~.·"r·~:·.I·.;~ ........ . ; tID tilt lnli iliittllfll j =>1J ~~J~r·:: . 1/2 BE::t:~~~ 2~i Ii , ~-;t m m H4f- I" t I fl . _ _C" I· ~t~t't~.l. .:•.:,""f'"~ _- ..' -.. _-- -i' I . t 0 iD I ~r-N. i- ." Q 0 ., "1""'" .. '+ ::I Sjl~, l 1U11 I I UUnll11l I! .'., . ,,, I' --'-- -O· I I I H-l ~·H.jl ".,~ -_... ::r 1\' r I t I t+l4-1 Nominal -\1' . . - ". -'T" » t ~,I... + I ~~tt ' ..... I ,;... ,I..l-l-W _, .. I i~~Ht-I i·· ! INN :' ttl·] 1\ . - I ~~, '. I-r---U ' i 1"', I , > ~~f:::~t! +,,'-1--11 I ;to TIJJ1JLIEIJf Zo'NE tfh~t~:~rrft?::f~ ·'I.~r 1~" ~ i: ~.' ! ft .! . " i l l Friction Faclor ~ n "'~\~~~~~ 'l,~ z I '1 I i .... 1 .... .I i i .. r T•. ·,' I "ll i- rr'f]' i I "~iIV':!<~. >. . ~.'..... "t "'},' !, 20 TR~N~~I~.N 1.' ~"'1 I ~:;l', • 8 10 ~'l!Pl'!'!Ill +.. 1 I' T ; rtl ,~. I ,05 I i t \ tN.· f 6 1 ' ~MIN:r. , FOR WATER AT 60' F (VELOCITY IN FT,/SEC, X OIAMETER IN INCHES) (I'd) }i'e For other lormJ 01 the Re equation, see page 3·2. 0 m i» Problem: Determine the friction factor for 12-inch Schedule 40 pipe at a flow haVing a Reynolds number of 300,000. Solution: The friction factor (f) equals 0.016, » I..:) UI .. ~~~k,:.'· M,."'''.,~.'''"' ~._,~~N'I~.~'!i.Iif .......~,,~........... ~.-,~ ... ·~·-,~,----- ... - .. ,~,'_.~~.'!'''".,,'':'' ...... :",-'',,.,~T· ... .... --.~ ....- - . - - -........ ~,''~,.t' .... ,_"'"." ....,....,.... .... "..,."~,.,..-'""-"I'''I"I~*~_~. ---> ....~~--.,.- .. -..-,-~-~.~-."---------......~~-,~-~,,",,"-- __ ~~_· _ _ _ _ _ • _ _ __ " '-'~..,"""'..._"' •. c,,""_,~,.'...,.,.- A-26 APPEN[)IX A-PHYSICAL PROPERTIES Of flUIDS AND flOW CHARACTERISTICS OF VALVES, flnINGS, AND PIPE CRANE Resistance in Pipe Resistance Due to Sudden Enlargements and Contractions 20 -- LO 0,9 0,8 ~ I '" y ~ 0.7 ~ <= - 'u 0.6 'r--u CD u 0.5 --- ' ii; 0 <= .l3 '" 0.4 '" CD 0::: I /' V f= '[ ~~212J 1- -- -- / - - -.-V 1\ ............. " ---- -- -7'K 0.3 II -~ ~ SUDDEN CONTRACTION 0.2 f dl ~ 0.1 Y' 0 t' 0.1 I 1\ ~~ 0.3 0.4 0.5 0.6 0.7 ""- 0.8 6.065 ---. = II.Q38 0,5 1 Note: The values for the resistance coefficient, K, are based on velocity in the small pipe. To det.erinineK values in terms of the greater diameter, multiply the chart values by (ddd,)'. ~ I 0.5 1 Sudden contraction: The resistance coefficient 1<. for a sudden contraction from 12-inch Schedule 40 pipe to 6-inch Schedule 40 pipe is 0.33, based on the 6-inch pipe size. d, -d, ~ 0.2 6.06 5 11·q38 SUDDEN ENLARGEMENT 1"'- <l> d~ l ''\ Sudden enlargement: The resistance coefficient K'for a sudden enlargement from 6-inch Schedule 40 pipe to 12cinch Schedule 40 pipe is 0.55, based on the 6-inch pipe size. r--..... 0.9 1.0 dIld2 Resistance Due to Pipe Entrance and Exit - L I I -~ r Inward Projecting Pipe Sharp Edged K = 0.23 Slightly Rounded Entrance Entrance Entrance K'= 0.78 ----r ---L K = 1.0 Projecting Pipe EJtit Jr = ---r -r L 0.50 -.J -, -~ IC = 1.0 Sharp Edged Exit - ~ I K = 1.0 Rounded exit L K = 0.04 Well Rounded Entrance Problem: Determine the total resistance coefficient for a pipe one diameter long having a sharp edged entrance and a sharp edged exit. Solution: The resistance of pipe one diameter long is small and tal1 be neglected (K = I L/ D). From the diagrams, note: Resistance for a sharp edged entrance Resistance for a sharp edged exit Then, the total resistance, K, for the pipe. = 0·5 = 1.0' 1.5 A-30 CRANE APPENDIX A - PHYSICAL PROPERTIES OF FLUIDS AND FlOW CHARACTERISTICS OF VALVES. fITTINGS. AND PIPE Schedule (Thickness) of Steel Pipe Used in Obtaining Resistance O:F Valves and Fittings of Various Pressure Classes by Test* Valve or Fitting ANSI Pressure Classification Steam Rating ICold Rating! l50-Pound and L0::JJer 500 300-Pound to 600-Pound 1440 900-Pound 2160 1500-Pound 3600 2500-Pound Yz to 6' 8' and larger psig I psig psig psig I i I 3600 6000 psig psig Schedule No. of Pipe Thickness Schedule 40 Schedule 80 Schedule 120 Schedule 160'---_ _ xx (Double Extra Strong) Schedule 160 *These schedule numbers have been arbitrarily selected only for the purpose of identifying the various pressure classes of valves and fittings with specific pipe dimensions for the interpretation of flow test data; they should not be construed as a recommendation for installation purposes. R,epresentative Equivalent Length! in Pipe Diameters (L/D) Of Various Valves and Fittings Equivalent Length In Pipe Diameters Description of Product I (LID) With no obstruction in flat. be\'c!, or plug type seat Fully open 340 \\'ith wing or pin guided disc Fully open 450 ---------~~~~~~~~~-~~---~-----~~~-------- (No obstruction in flat, bevel. or plug type seat) Y-Pattern - With stem 60 degrees from run of pipe line Fully open 175 - With stem 45 degrees from run of pipe line Fully open 145 \\'ith no obstruction in flat, bc\·cl, or plug type scat Fully open 145 Angle Valv.", With wing or pin guided disc . Fully open 200 Fully open 13 Vl edge, Disc, Threc-quarters open 35 Double Disc, Qne-hal f open ;d§Q. or Plug Disc Gate One-quarter open 900 Valves Fully open 17 Thrcc-quarters open 50 Pulp Stock One-half open 260 One-quartcr open 1200 , Fully open Conduit Pipe Lme bate, Ball, and Plug Valves 3" Stem Perpendicular to Run Globe Valves ~ Conventional Swing O.5t . . Fully open O.5t .. _Fully ope,n Clearway Swing 2.0t ... Fully open Globe Lift or Stop; SteIll Perpendicular to Run or Y -Pattern Angle Lift or Stop 2.0t ... Fully open 2.5 vertical and 0.25 hori=ontalt .. Fully open In-Line Ball With poppet lift-type disc 0.3t . . Fully open Foot Vatves with Strainer With leather-hinged disc OAt. _. Fully open Butterfly Valves (8-ineh and larger) Fully open Straight-Through 1 j , i f I f ~ II j I Cocks Three-Way I Rectangular plug port area equal to 100r~ of pipe area I Rectangular plug port area equal to J35 50 Same as Globe Same as Angle 150 420 75 40 Fully open 18 Flow straight through Flow through branch 44 80S; of pipe area (fully open) 140 Standard Elbow 30 Standard Elbow 16 Long Ra.:d.:i.cuc-s_E __lc-bo'-'-_ w _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _--:-_---,_--"k==--__ Street Elbow 50 Street Elbow 26 II~Sq~u_a_re_c~o~r.n__e_r~E_l_bo_W~~-~-~-~--------------_________+-_______5.:7______ Standard Tee With flow through run 20 1~~~~--~--~I~~~·i--t--h~fl-o-w-t--h-r--Ou~g~h~b-ra=n~c-h--__________________________~-------60~----Close Pattern Return Bend 50 - - - 1 9 0 Degree Pipe Bends See Page A-27 Miter Bends See Page A-27 Pipe Sudden Enlargements and Contractions See Page A-26 i Entrance and Exit Losses See Page A~26 -----'-"Exact equivalent length is t!\.,tinimum calculated pressure tFor limitations. see page equal to the length between drop (psi) acro<;;s valve to provide 2-1 I. For effect of end flange faces or wclding ends. sufficient flow to lift dISC fuBy. connections, see page 2-10. 90 45 90 , 90 Fittings l, 45 1 Degree Degree Degree Degree Degree I For resistance :rador "K", equivalent length in Feet of pipe, end equivalent Row coefficient .. e ..... , see pages A-31 and A-32. eRA N E A·31 APPEND'IX A -I'HYSICAl PROPEHIES OF FlUIDS AND FlOW CHARACTERISTICS OF YAl YES, FITTINGS, AND PIPE ~~.::.-~=---'-- L and LID and Resistance Coefficient K *ECIUivcJlent Lengths d L LID , j S( I 40 ! 30 20 ~ ..'!l '" '" Q. E <'0 0: Cl 0 - '" 0: / Q) Q. '" / l.L. e .: / " " <I) "" '"u .t= .E <: w- / N C;; .t= c;, e '" -' c: 0 <: / ..'!l CO :> / '" / <'0 .:::/ . / / 0- L.U / I / "- ...;:" " / .-- / w- Q. 5 0: '5 ..'!l 0- ~ 0 <U E ..'!l "'" '" 0; / <U .<:: <.> '" L.U ....,I " .E 6 .£ ..... ~ /' ~O- / ~ ,- ..'!l ,- .-- "'.-.... 10 9 8 7 .t='" '"u 6'" 3 , <: 'E "<:l 0 2: ./ '" -0 'iii .E 2 / , - ./ /,// ./ --- --- --- 1.0 0,9 0.8 0.7 .2 0.6 0.5 SCHEOUL.E 40 PIPE S(ZE:. INCHES Problem: Find the cqui"alent length in pipe Jldn1Cft.'rs and ket of Sch('duJc 40 pipe. and thl' rc.:"'I~tancc factor" for J, 5, and 12-inch fully-opened gate \·a"·cs. ·For limita,ions. see page ~!-11. Solution Valve Size I'_L~:~I~1~:J-R~~Tto Equi\'alcnt length. pipe di;Hncters : IJ I IJ Equi\'alcnt length. fcct of Schcd. ~U pipe! 1.1 I 5. 5 Resist. factor K, based on Schoo. 40 pipe; 0,30 I O.2()' I (J /I PagC::\-JOi I J II Dotted lines I 0.17 on chart,