Measurement of flow rate, velocity profile and friction factor in Pipe Flow S. Ghosh, M. Muste, F. Stern Overview Purpose Experimental design Experimental Process Test Set-up Data acquisition Data reduction Uncertainty analysis Data analysis Purpose Provide hands-on experience with pipe stand facility and modern measurement systems including pressure transducers, pitot probes and computer data acquisition and data reduction. Comparison between automated and manual data acquisition systems. Measure flow rate, velocity profiles and friction factor in smooth and rough pipes. Determine experimental uncertainties. Compare results with benchmark data Experimental Design The facility consists of: Closed pipe network Fan Reservoir Instrumentation: 3 Venturi meters Contraction Diameters (mm): 12.7 25.4 52.9 3 Flow Coefficient, K 0.915 0.937 0.93 5 Simple water Manometer Differential Water manometer Pitot Probe Digital Micrometer (Accurate radial positioning) Pressure transducer Computer based Automated Data Acquisition System (DA) Experimental process Test Set-up Data Acquisition Facility & conditions Prepare experimental procedures Airflow pipe system Install model Data Reduction Statistical analysis Uncertainty Analysis Estimate bias limits Data Analysis Compare results with benchmark data, CFD, and /or AFD Remove outliers Set blower speed Set valves in proper positions N/A Data reduction equations Evaluate Eq. 3 Table 1 Estimate precision limits Evaluate Eq. 4 Calibration Use Fig 8 as reference value for velocity profile Use Fig 9 as reference value for friction factor Evaluate Eq. 5 Plot experimental velocity profile and friction factor on reference data Evaluate Eq. 6 N/A Prepare measurement systems Initialize data acquisition software Evaluate Eq. 9 Evaluate Eq. 13 Open Labview program Venturimeter Enter hardware settings Pressure transducer Valve manifold Run tests & acquire data Pitot tube Micrometer Estimate total uncertainty Measure total discharge Measure pressure drop in pipe Measure velocity profile Repeat discharge measurement Store data Write results to output file Evaluate fluid physics, EFD process and UA Evaluate Eq. 7 Evaluate Eq. 11 Measure room and pipe temperature Report difference between experimental and reference data Answer questions in section 4 Prepare report Test set-up Test Set-up: Venturi meter and Pitot-tube housing Venturimeter Pitot-tube housing Test set-up: Instrumentation The equipment used in the experiment includes: Digital thermometer with a range of – 40 to 450 F and a smallest reading of 0.1 F for measurement of the environment temperature. Digital micrometer with least significant digit 0.01 mm for positioning the Pitot-tube inside the pipe. Simple water manometer with a range of 2.5 ft and a least scale division of 0.001 ft for measurement of the head at each pressure tap along the pipes and for measurement of velocities using the Pitot-tube arrangement . Differential water manometer with a range 3 ft and a least scale division of 0.001ft for measurement of the head drop across the Venturi meters. Pressure transducer calibrated with ft of water Test set-up: Instrumentation Reservoir: Digital Micrometer: To build up pressure and force the air to flow downstream through any of the three straight experiment pipes. Allows the measurement of the position of the Pitot probe at different locations along the cross section of the pipe tested Pitot Probe: Venturi meters: Located in the glass-wall box Used to measure the Stagnation pressure and calculate the velocity profile in pipe Located on each pipe type Used to measure flow rate Q along the differential water manometer Pressure Taps: Manometers: Located along each pipe, they are connected to the simple water manometer to evaluate the head measurement They are used to calculate the friction factor To measure the head at each pressure Tap along the pipe and to make the Pitot-tube measurements (simple Manometer) To measure head drops across the venturi meters (differential Manometer) Data acquisition The procedures for data acquisition and reduction are described as follow: 1. 2. 3. 4. 5. Use the appropriate Venturi meter, (2” contraction diameter) to measure the total discharge. Increase blower setting from 15% to 35% with 5% increments and measure flow rate using both manometer and pressure transducer. Take reading for ambient air (manometer water) and pipe air temperatures. To obtain velocity data, use the Pitot-tube box to measure the ambient head and stagnation heads across the pipe. Measure the stagnation heads at radial intervals. The recommended radial spacing for one half of the diameter is 0, 5, 10, 15, 20, 23, and 24 mm. Maintaining the discharge at 35%, measure the head along the pipe by means of the ADAS the pressure heads at pressure taps 1, 2, 3, and 4 Repeat step 2 Automated Data Acquisition System Pitot-Tube Housing Tested Pipe Static Pressure from Pressure Taps To Atmosphere To Atmosphere DA 2 DA 1 Differential Manometer Static Pressure Stagnation Pressure Pressure Transducer Valve Manifold Simple Manometer Venturi Meter Return Pipe (a) (b) Layout of the data acquisition systems: a) photo; b) schematic LEGEND Tygon Tubing Connections Introduction to ADAS Software - Labview Front panel on Data Acquisition program Initial settings Flow rate measurement Friction factor measurement Velocity profile measurement Data reduction For the flow rate and friction factor, the individual measurements are performed for: Ambient air temperature Pipe air temperature Pipe pressure head Venturi meter pressure head drop Data reduction equations are: w f (Two ) o o ) air f (Tair ) air f (Tair Q KAt 2 gZ DM The experimental Results are: Manometer water density Air density Kinematic viscosity Flow rate Reynolds number Friction factor w air 4Q Re D air g 2 D 5 w f Z SM i Z SM j 2 8LQ air Data reduction equations: Flow rate pa Va2 pb Vb2 ( Bernoulli ) g 2 g g 2 g Va Aa Vb Ab (Continuity) Volumetric flow rate Q AbVb Q CD K CD Equation (1), lab handout Q KAt 2 gz DM Aa Ab 2 gh( Aa2 Ab2 Aa Ab Aa2 Ab2 w a , w 1) , a Friction factor Pitot-Tube Housing Tested Pipe Static Pressure from Pressure Taps To Atmosphere To Atmosphere DA 2 DA 1 Differential Manometer Static Pressure Stagnation Pressure Pressure Transducer Valve Manifold Simple Manometer Venturi Meter Return Pipe LEGEND Tygon Tubing Connections Friction factor (contd.) g 2 D 5 w f z SM i z SM j 8LQ 2 a Equation 2 is a form of Darcy Weisbach equation in terms of flow rate Q and pressure drop where, and A is the pipe cross sectional area. Velocity profile p0 p stat 1 V 2 , Bernoulli 2 V 2( p0 p stat ) / 2 g w u (r ) z SM Stagnationr z SM Static a Equation 3, Exercise notes pstag pstat w g ( z SM stag z SM stat ); p0 pstag 1/ 2 Appendix C: Spreadsheet for data acquisition, data reduction and uncertainty analysis for Measurement of Velocity profile and friction factor in pipe flows (smooth pipe) Table of Contents Data reduction: Spreadsheet Color code: Sections Comments Enter student data Constants Calculated or output values 1. Experimental Summary 2. Data reduction equations 3. Data Acquisition and Reduction 3.1 Input variables 3.2 Measured variables 4. Uncertainty Analysis 4.1 Bias Limits 4.2 Precision Limits 4.3 Total Uncertainty 1. Experiment summary Statement of Purpose: To measure velocity profile and friction factor in rough pipe and determine the uncertainties and compare results with benchmark data. Air-flow unit (WTA) Air flows through a pipe system Lab2 Handout: http://css.engineering.uiowa.edu/~fluids/Lab/EFDLab2.PDF Facility: Test Design: References: 2. Data Reduction Equations 2 g w u (r ) z SM Stagnation r z SM Static a 1/ 2 f Eqn. (3) g 2 D 5 w z SM i z SM j 8LQ2 a Eqn. (4) 3. Data acquisition and reduction for multiple test UA approach 3.1 Input variables Table A1. Table A2. Quantity Gravity Number of test Coverage factor for standard deviation Symbol g M K Value 9.8031 10 2 Units m/s^2 --------- 3.2 Measured variables Target Conditions Target Reynolds # Re= 100,000 Target Headdrop (ft water) ZDM= 0.59 Date Temperature(deg C) Room Pipe Initial Final Average ###### #DIV/0! Actual Flow rate Venturi Head Drop z DM (ft water) Initial Final Average #DIV/0! FRICTION FACTOR TAP # Smooth Pipe z SM fij (ft water) 1 2 f 12 = #DIV/0! 3 f 23 = #DIV/0! 4 f 34 = #DIV/0! Constant Discharge Coeff. Cross-sectionArea Symbol K At Gravity Pipe Diameter Pipe Length g D L VELOCITY PROFILE z SM stagnatio z SM static r (m) (ft n (ft 0.026 0.024 0.023 0.020 0.015 0.010 0.005 0.000 -0.005 -0.010 -0.015 -0.020 -0.023 -0.024 -0.026 Location (ft) 5 10 15 20 Value Units 0.935 0.002154 m2 9.8031 m/s2 0.05238 m 9.144 m u (m/s) 0.000 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! 0.0000 Time Fluid Property w (kg/m3) = a (kg/m3) = m a (kg/m.s) = Reynolds Number (Re) Flow Rate Q (m 3/s) from integration of velocity Initial profile Final Average Avera #IV/0! ge Repeated Measurements Smooth Pipe z SM3 z SM4 f 34 Measur.. # (ft water) (ft water) 1 #DIV/0! 2 #DIV/0! 3 #DIV/0! 4 #DIV/0! 5 #DIV/0! 6 #DIV/0! 7 #DIV/0! 8 #DIV/0! The following example illustrates the procedure for calculating Q using velocity For calculating the flow rate Q (Cell no. G66) first obtain the velocity profile with respect to radial distance. Cells D84-D98 calculates the velocity profile. The following example illustrates the procedure for calculating Q using velocity integration method. Note: The x axis on the following plot is cell A85 - A91. The Y axis is cell D85 - D91. Once the velocity profile is plotted, fit a 2nd order polynomial curve to the points and display the equation on the chart, as shown below. The y in the equation is velocity and the x is radial distance r. Finally the flow rate Q is given by the following formula. Note that the variable x in the integral equation is actually radius. Also Rmax is the radius of the pipe. Q 2 Rmas 0 (2733x2 287.11x 41.434) xdx 9 10 #DIV/0! #DIV/0! Average f 34 #DIV/0! St. Deviation Sf34 #DIV/0! Repeated Measurements (near wall) z SM stagnation z SM static Measur. # u (m/s) (ft water) (Ft water) 1 #DIV/0! 2 #DIV/0! 3 #DIV/0! 4 #DIV/0! 5 #DIV/0! 6 #DIV/0! 7 #DIV/0! 8 #DIV/0! 9 #DIV/0! 10 #DIV/0! Average #DIV/0! #DIV/0! #DIV/0! Std. Dev #DIV/0! #DIV/0! #DIV/0! Alternate measurements at various radial positions with repeated measurements. Note: The value in cell G 66 for the flow rate should be approximately 0.07 m3/s. Check your flow rate calculation of your value deviates too much from the recommended value. Conversion of pressure head from ft of water to pascals Tap # 1 2 3 4 ZSM(ft water) 0.0000 0.0000 0.0000 0.0000 ZSM pas 0 0 0 0 Uncertainty analysis Block diagram of the experimental determination of the Friction factor Block diagram of the Velocity measurement EXPERIMENTAL ERROR SOURCES EXPERIMENTAL ERROR SOURCES TEMPERATURE WATER Tw Ta B T , PT B T , PT w PIPE PRESSURE TEMPERATURE AIR a w Bz a z SM , Pz SM SM VENTURI PRESSURE Bz z DM , Pz DM = F(T ) w w a = F(Ta ) Q = F(z DM ) f = F( , , z w a 2 SM , Q) = g D 8LQ f B f , Pf 5 2 w (z - z ) a SM i SM j DM INDIVIDUAL MEASUREMENT SYSTEMS TEMPERATURE WATER TEMPERATURE AIR MEASUREMENT OF INDIVIDUAL VARIABLES Tw Ta B T , PT w w B T , PT a a DATA REDUCTION EQUATIONS z Bz SM 2( z a SM ,z stag SM ) = stat u EXPERIMENTAL RESULTS , Pz stag a w z SM stag = F(T ) w w = F(Ta ) u = F( , , z STATIC PRESSURE STAGNATION PRESSURE Bu, Pu Bz SM stag -z SM stag SM stat SM stat SM , Pz stat ) g w SM stat ½ INDIVIDUAL MEASUREMENT SYSTEMS MEASUREMENT OF INDIVIDUAL VARIABLES DATA REDUCTION EQUATIONS a EXPERIMENTAL RESULT Uncertainty Analysis The data reduction equation for the friction factor is: g 2 D 5 w f z SM i z SM j 2 8LQ a However here we will only consider bias limits for ZSM i and ZSM j . The total uncertainty for the friction is: U 2f B 2f Pf2 The Bias Limit, Bf and the precision limit, Pf, for the result are given by: j B i2 Bi2 Z2SMi BZ2SMi Z2SMj BZ2SM j 2 f i 1 Pf tS f M Uncertainty Analysis (continue) Data Reduction equation for the velocity profile is as follow: 1/ 2 2 g w u (r ) zSM Stag r zSM Stat a U B P 2 u 2 u j 2 u Bu2 i2 Bi2 Z2SMstagn BZ2SMstagn Z2SMstat BZ2SMstat i 1 tSu Pu M Data Analysis: Results and discussions Moody Chart for pipe friction with smooth and rough walls Laminar Flow Critical Zone Transition Zone 0.10 0.090 0.080 Complete Turbulence, Hydraulically Rough 2 (L/D)V /(2g) hf 0.01 0.008 0.006 0.004 /R = 64 0.030 e Friction Factor f = 0.02 0.015 f Flo w 0.040 in a r 0.050 Lam 0.060 0.025 0.002 0.020 0.001 0.0008 0.0006 0.0004 Hydraulically Smooth 0.015 Relative Roughness, k /D 0.05 0.04 0.03 0.070 Low speed = 44 m/s Smooth Pipe (2”) low speed Rough Pipe (2”) low speed 0.0002 0.0001 k /D = 0.000005 0.010 0.009 0.008 0.00005 k /D = 0.000001 10 3 10 4 10 5 10 Reynolds Number, Re = 6 0.00001 10 7 10 8 VD Benchmark data for Friction Factor 07/10/03 Data Analysis: Results and discussions (contd.) r/R u/umax 0.0000 1.0000 0.1000 0.9950 0.2000 0.9850 0.3000 0.9750 0.4000 0.9600 0.5000 0.9350 0.6000 0.9000 0.7000 0.8650 0.8000 0.8150 0.9000 0.7400 0.9625 0.6500 0.9820 0.5850 1.0000 0.4300 Benchmark data for velocity profile (Schlichting, 1968) Low speed = 44 m/s High speed = 62 m/s