DEPARTMENT OF MECHANICAL ENGINEERING
KULLIYYAH OF ENGINEERING
INTERNATIONAL ISLAMIC UNIVERSITY
MALAYSIA
FLUID MECHANICS
LAB MANUAL
MEC 2600
MEC 2700
January 2008
Syed Noh Syed Abu Bakar/ Sanisah Saharin
1
TABLE OF CONTENTS
ITEMS PAGES
========================================================================
Laboratory & Reports: An Overview
3
Guidelines for Laboratory Report (Lab workbook) Writing
4
Guidelines for Final Report Writing
5
Experiment # 1: FLOW RATE MEASUREMENT
8
Experiment # 2: FRICTION LOSSES
10
Experiment # 3: IMPACT OF JET
12
Experiment # 4: REYNOLDS OSBORNE EXPERIMENT
14
Experiment # 5: PUMPS IN SERIES & PARALLEL
15
References
16
2
LABORATORY & REPORTS: AN OVERVIEW
All experiments in the Fluid Mechanics Laboratory require either a laboratory report (lab
workbook) or a final laboratory report for selective experiments, unless it is stated otherwise. The
reports should be simple and clearly written. Laboratory reports (lab workbook) are due after all
of the experiments are performed, unless it is stated otherwise. Final reports should be submitted
a week after the experiment’s day, unless it is stated otherwise. Any late submission will not be
entertained, unless there are concrete and unavoidable reasons.
The laboratory reports (lab workbook) should be in hand writing and any graphs needed should
be drawn in either an appropriate graph paper or drawn using EXCEL, whichever suitable.
However, for final laboratory reports, it should be computer-generated and any graphs should be
drawn using EXCEL.
The final laboratory reports should be submitted to the instructor directly or at the instructor’s
office.
The pre-lab questions in this lab manual should be answered and submitted during the first 5
minutes before you start your experiment accordingly.
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GUIDELINES
Workbook)
FOR
LABORATORY
REPORT
WRITING
(Lab
All experiments in the Fluid Mechanics Laboratory require a laboratory report unless specified
otherwise. The report should be written in such a way that anyone can understand and convinced with
what the experimenter will do in the experiments. The following formats are proposed as a guide. The
students may add or delete sections as needed for each specific experiment in order to obtain a logical,
self-contained document.
Title page
Specify the experiment’s number and its title. Include names of all experimenters, experimenters’
matric numbers, experimenter’s programme (Aerospace or Automotive) and dates when experiments
were carried out
Objectives
The objectives are a clear concise statement explaining the purpose of the experiment. This is one of
the most important parts of the laboratory report because everything included in the report must
somehow relate to the stated object. The objectives can be as short as one sentence and it is usually
written in the past tense.
However, for this course you just have to copy from lab manual and rewrite it in your reports.
Introduction
Indicate what the overall plan of the experiment is: what will be done and how (the procedures),
which variables will be manipulated and measured. Clearly indicate what the reader should expect to
find in each of the subsequent sections.
Results
Include all tables and graphs that document your final results. Include all relevant information so that
you can later refer to these figures in the Discussion section to support your conclusions.
Sample Calculations
Give one example of each calculation that leads to a result reported in the document. Include one
calculation for each figure or table reported in the Results section.
Discussion and Conclusion
This section should give an interpretation of the results explaining how the object of the experiment
was accomplished. Note down and discuss briefly any observations and trend that you could possibly
deduce from your results.
Pre-lab Questions
Answer the problems at ‘Pre-lab Questions’ section in this lab report and submit during the 5 minutes
of commencing your experiment accordingly.
References
List all the literature sources that are cited in the report. You may refer this lab manual References for
format reference.
4
GUIDELINES FOR FINAL REPORT WRITING
There will be only two of the experiments from the Fluid Mechanics Laboratory require a final
laboratory report unless specified otherwise. The report should be written in such a way that anyone
could duplicate the performed experiment and find the same results as the originator. The reports
should be simple and clearly written.
The report should communicate several ideas to the reader. First, the report should be neatly done.
The experimenter is in effect trying to convince the reader that the experiment was performed in a
straightforward manner with great care and with full attention to detail. A poorly written report might
instead lead the reader to think that just as little care went into performing the experiment. Second,
the report should be well organized. The reader should be able to easily follow each step discussed in
the text. Third, the report should contain accurate results. This will require checking and rechecking
the calculations until accuracy can be guaranteed. Fourth, the report should be free of spelling and
grammatical errors. The following format is to be used for formal Laboratory Reports:
Title page
Specify the experiment’s number and its title. Include names of all experimenters, experimenters’
matric numbers, experimenter’s programme (Aerospace or Automotive), date of submission, and
dates when experiments were carried out. Refer to Appendix A for the example of this title page.
Table of Contents
Lists each major section and subsection and their page numbers. You may refer this lab manual Table
of Contents as a format reference.
Objectives
The objectives are a clear concise statement explaining the purpose of the experiment. The objectives
serve as a guide to the results. This is one of the most important parts of the laboratory report because
everything included in the report must somehow relate to the stated objectives. The objectives can be
as short as one sentence and it is usually written in the past tense. Do not exceed one page.
However, for this course you just have to copy from lab manual and rewrite it in your reports.
Abstract/Introduction
Summarize the important results. The abstract must be self-contained: do not refer to figures and
tables located in other sections of the report. Do not include tables, figures, and equations, unless
absolutely necessary. Do not assume that the reader will unambiguously identify undefined symbols.
Be precise and succinct. Do not exceed one page. The Abstract should be written with great care
because it is a most important part of the Final Report and will have a very large impact on the
grade assigned to the work.
Procedure
The procedure section should contain a schematic drawing of the experimental setup including all
equipment used in a parts list with manufacturer serial numbers, if any. Show the function of each part
when necessary for clarity. Outline exactly step-by-step how the experiment was performed as there is
someone desires to duplicate it. If it cannot be duplicated, the experiment shows nothing.
Results
Include all tables and graphs that document your final results. Include all relevant information so that
you can later refer to these figures in the Discussion section to support your conclusions. If possible,
present the results in the same order that you listed the objectives. Do not discuss the significance of
the results. Include only final results that satisfy the objectives of the experiment; lengthier tables and
intermediate figures should be included in the Appendix. Introduce the reader to each figure and table
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with a brief paragraph indicating what variables are plotted or tabulated. Each figure and table must
have a unique number and a title or caption.
Sample Calculations
Give one example of each calculation that leads to a result reported in the document. Include one
calculation for each figure or table reported in the Results section. Introduce each calculation with a
brief paragraph indicating to the reader which specific point in a figure or entry in a table is being
calculated. These calculations are samples only and must be annotated. Extensive calculations should
be included in the Appendix; the Sample Calculations section can then include appropriate references
to the Appendix.
Discussion and Conclusion
This section should give an interpretation of the results explaining how the objectives of the
experiment were accomplished. Any significant observations should be noted down and discussed.
Any graphs or other relevant results should be discussed in terms of trend, importance and
other significant information that could be deduced. If any analytical expression is to be verified,
calculate % error and account for the sources. (% error – An analysis expressing how favourably the
empirical data approximate theoretical information. There are many ways to find % error, but one
method is introduced here for consistency. Take the difference between the empirical and theoretical
results and divide by the theoretical result. Multiplying by 100% gives the % error. You may compose
your own error analysis as long as your method is clearly defined.) Discuss this experiment with
respect to its faults as well as its strong points. Suggest extensions of the experiment and
improvements. Also recommend any changes necessary to better accomplish the objectives. Use the
available theory to explain why the relevant variables behaved in the observed fashion.
Appendix
(1) Original data sheet. This original data sheet should be approved by instructor(s) during
experiment day.
(2) Calibration curves of instruments which were used in the performance of the experiment. Include
manufacturer of the instrument, model and serial numbers. Calibration curves will usually be supplied
by the instructor.
(3) Bibliography listing all references used.
Short Form Report Format
Often the experiment requires not a formal report but an informal report. An informal report includes
the Title Page, Object, Procedure, Results, and Conclusions. Other portions may be added at the
discretion of the instructor or the writer. Another alternative report form consists of a Title Page, an
Introduction (made up of shortened versions of Object, Theory, and Procedure) Results, and
Conclusion and Discussion. This form might be used when a detailed theory section would be too
long.
6
Graphs
In engineering laboratory reports, one of the methods to represent the results is graph. The graph
sometimes summarized the results. An acceptable graph has several features. Some of the important
features are as following.
• Axis labels defined with symbols and units.
• Each line is identified using a legend.
• Data points are identified with a symbol: “x” on the Qac line to denote data points obtained by
experiment.
• Data points are identified with a symbol: “o” on the Qth line to denote data points obtained by
theoretical.
• Nothing is drawn freehand.
• Should have number and title; e.g. Fig. E1.1 Volumetric flow rate, Q vs. head drop, ∆h. Title is
descriptive, rather than something like Q vs ∆h
• For non-computer generated graph, a graph paper must be used.
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EXPERIMENT # 1
FLOW RATE MEASUREMENT
OBJECTIVES
The objectives of the experiment are:
1. To show the measurement of flow rate
2. To show the application of Bernoulli equation in flow rate measurement
3. To show effect of minor losses and its modification in flow rate measurement
4. To demonstrate piezometer as a method to measure pressure
LEARNING OUTCOMES
It is expected by completing the experiment, the students will be able:
1. To determine flow rate by using orifice meter, Venturi meter and rotameter
2. To explain how to calculate ideal flow rate by using Bernoulli equation
3. To determine the correction factor for by using an elbow and a sudden expansion
4. To measure pressure by using piezometer
THEORY/BACKGROUND
{More in textbook [1] section 5-4 and 8-8}
There are various ways of measuring volumetric flow rate. Some flow meters measure the flow rate
directly by discharging and recharging a measuring chamber of known volume continuously and keeping
track of the number of discharges per unit time. However, most flow meters measure the flow rate
indirectly – they measure the average velocity V or a quantity related to average velocity such as pressure
and drag, and determine volume flow rate, Q from Q = AV, where A is cross sectional area of flow.
Obstruction Flow Meters: Venturi Meter and Orifice Meter
One way to measure flow rate is to put obstruction in a pipe flow such as a throat (Venturi Meter) and
simple obstruction that reduced the cross sectional area (Orifice Meter).
Theoretical ideas behind these flow meters are the conservation of mass and the Bernoulli equation. From
conservation of mass we know that reduce of cross sectional area will contribute to an increase of velocity.
Thus, from Bernoulli equation, this will lead to a decrease of static pressure. These kinds of flow meters
did not measure the flow rate or velocity directly but it measures the drop of static pressure. Then the
velocity can be calculated from Bernoulli equation and conservation of mass.
The same idea can be applied for sudden expansion and elbow meter.
Rotameter
Rotameter is also known as variable-area flow meter or float meter. A rotameter consists of a vertical
tapered conical transparent tube made of glass or plastic with a float inside that is free to move. As fluid
flows through tapered tube, the float rises within the tube to a location where the float weight, drag force
and buoyancy force are balance each other and the net force acting on the float is zero. The flow rate is
determined by simply matching the position of the float against the graduated flow scale outside the
tapered transparent tube.
Coefficient of Discharge
For rotameter the flow rate can be read directly from scale at tapered tube. However, for obstruction flow
meter, we need to consider a loss due to viscous (frictional) effects. As we know the Bernoulli equation did
not include the viscous effects. The for, any calculation that calculated from the conservation of mass and
Bernoulli equation is an ideal volumetric flow rate, not an actual one. Thus, to determine an actual
volumetric flow rate a correction factor need to be introduced to the ideal flow rate equation. This
correction factor is called as coefficient of discharge. The coefficient of discharge can be defined as the
ratio of actual flow rate to the ideal flow rate.
Loss coefficient
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Due to viscous effects, there are losses at the obstruction. The losses at the obstruction can be considered
as minor losses. If the pressure drop and average velocity is known, then the loss coefficient can be
determined since the pressure drop is proportional to velocity.
This experiment is to demonstrate flow rate measurements.
For Orifice meter, Venturi meter,
1. Measure pressure drop (in term of head) as a function of valve opening.
2. Determine ideal flow rate and actual flow rate.
3. Determine Reynolds number
4. Determine coefficient of discharge, Cd
5. Prepare the following graph
a. On the same set of axes, plot actual volume flow rate vs. pressure head drop and ideal
flow rate vs. pressure head drop with flow rate on the vertical axis for obstruction flow
meter
b. Plot actual volumetric flow rate vs. ideal flow rate for Rotameter
c. Plot coefficient of discharge vs. Reynolds number on log-log grid for obstruction flow
meter
For Elbow meter and Sudden expansion:
6. Measure pressure drop (in term of head) as a function of valve opening.
2
7. Determine the loss coefficient by plotting graph pressure head drop vs. V /2g (where V is
average velocity and g is gravitational acceleration)
8. Compare the calculated loss coefficient with the manufacturers published loss coefficient for
Orifice meter and Venturi meter.
EQUIPMENT:
Hydraulic Bench
Flow Meter Apparatus
PRE-LAB QUESTIONS
1. Explain briefly the following terms:
i.
Pressure Head
ii.
Velocity Head
iii.
Elevation Head
2. Define Loss Coefficient
3. Define Coefficient of Discharge and what its significance in flow rate measurement.
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EXPERIMENT #2
FRICTION LOSSES
OBJECTIVES
The objectives of the experiment are:
1. To modify Bernoulli equation
2. To show one of the restriction in application of Bernoulli equation
3. To investigate pressure loss due to friction
LEARNING OUTCOMES
It is expected by completing the experiment, the students will be able:
1. To apply energy equation (integral form) to estimate the friction losses in a given pipeline
situation
2. To determine friction losses and pressure drop due to friction
THEORY/BACKGROUND
Bernoulli equation may be the most used and abused in fluid mechanics. Therefore, it is important to
know the restriction of the Bernoulli equation. This experiment is meant to show one of the Bernoulli
equation restrictions, which is the effect of viscosity. Viscosity, the tendency of a fluid to stick to
another fluid or any boundary, is one of the fluid properties. Viscous effect only can be neglect when
the viscous force is small compared to other force such as an inertia force. Friction effect is due to this
property (viscosity). If viscous effect is not negligible, then the frictional effect also not negligible.
The first part of this experiment is to show about this effect and to modify the Bernoulli equation so
that it can be use in a viscous flow.
One of the most important properties in pipe design as well as pump selection for pipe network is the
pressure drop. Pressure drop occurs because of the friction occur at the wall of the pipe as well as
because of elbows, bends and fittings that exist in a piping system. The study of pressure drop is the
purpose of the second part of the experiment.
First Part: Modification of Bernoulli Equation
{More in textbook [1] section 5-4 and 5-7}
There is several ways to derived Bernoulli equation. One of it is by using First Law of
Thermodynamics or also known in Fluid Mechanics as Energy equation. By applying an appropriate
assumptions and considerations to Energy equation, we will obtain the Bernoulli equation. Thus, in
other word we can say that the Bernoulli equation is also a statement of energy that fluid carries.
The work done on a particle by all forces acting on the particle is equal to the change of the kinetic
energy of the particle is what the Bernoulli equation express in mathematical terms.
For flow in a close conduit, the Bernoulli equation says that the energy should equal to a constant at
any point in the length of the conduit.
This experiment is to check this statement and modify the statement if it is incorrect. For that purpose,
draw Hydraulic Grade Line and Energy Grade Line. Determine whether there are effects of the
Reynolds number or the volumetric flow rate to HGL and EGL.
EQUIPMENT:
Hydraulic Bench
Bernoulli Experiment’s Apparatus
Second Part: Friction Losses in Straight Pipes, Bends and Elbows
{More in textbook [1] section 5-6 until 5-7, 8-4, and 8-6}
A pipe system usually consists of straight pipes, bends, elbows, valve and fittings. The existent of
these parts will contribute to a loss (due to friction). A loss will lead to a pressure drop. In pump
selections, there are needs to know about the pressure drop.
10
A loss in overall piping system is called major loss while loss in bends, elbows, valve and fitting is
called as minor loss.
This experiment is to study about the friction losses in straight pipes, bends and elbows.
For all studies, measure the losses as a function of volumetric flow rate.
For losses in straight pipes (7mm and 10mm diameter pipe),
1. Calculate the friction factor from Darcy-Weisbach Equation
2. Graph the friction factor as a function of Reynolds number, drawn in log-log grid.
3. Compare to Moody diagram
For losses in pipe consist of bends or elbows:
1. Determine the equivalent length (Use Table E1.1)
2. Determine friction factor (Use modified Bernoulli equation in term of head where head loss
consist of loss from straight and bends or elbows are considered)
3. Determine loss coefficient (Weisbach equation)
4. Compare the loss coefficient that have been determined with loss coefficient calculated from
Table E1.1
5. Determine if the loss coefficient varies with flow rate or Reynolds number.
The surface roughness is 0.0015 mm.
R is radius of bend; D is diameter of pipe; f is friction factor; L is equivalent length; K is loss coefficient
e
Table E1.1
EQUIPMENT:
Hydraulic Bench
10 mm diameter straight pipe
7 mm diameter straight pipe
Inlet and Outlet head
Pipe with 4 bends
Pipe with 4 elbows
PRE-LAB QUESTIONS
1. Explain the phenomena that occur at a bend that lead to a loss.
2. State Darcy-Weisbach Equation for head loss, hL..
3. What is minor loss?
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b
EXPERIMENT # 3
IMPACT OF JET
OBJECTIVES
The objectives of the experiment is to compare the momentum in fluid jet with force generated when
it strikes a flat plate, a 120° plate, a conical object and a hemispherical cup
LEARNING OUTCOMES
It is expected by completing the experiment, the students will be able:
1. To explain conservation of linear momentum
2. To apply conservation of linear momentum to estimate force exerted by an object from a fluid
jet
THEORY/BACKGROUND
{More in textbook [1] section 6-1 until 6-4}
A jet is a stream issuing from an orifice, nozzle or tube. It is not enclosed by solid boundary walls but is
surrounded by a fluid whose velocity is less than its own. The two fluids may be different or they may be
of the same kind.
From conservation of linear momentum, we know that if a jet of fluid striking an object, will exerts a force
on that object. Theoretically, the force can be estimated from conservation of linear momentum in integral
form (to get an average value) or in differential form (i.e. Euler’s equation or Navier Stokes equation).
Experimentally, the force can be determined if we connect the object to a spring balance or scale.
For this experiment,
1. Determine (For two size of nozzle)
a. Volumetric flow rate
b. Velocity of jet
c. Theoretical and actual resultant force generated when jet strikes a flat plate, a 120° plate,
a conical object and a hemispherical cup – the theoretically resultant force is found by
use of an equation derived by applying conservation of linear momentum to a control
volume about the plate/object
2. Plot, on the same set of axes, graph of actual force vs. volumetric flow rate and theoretical force vs.
volumetric flow rate with volumetric flow rate on the horizontal axis.
EQUIPMENTS:
Hydraulic Bench
Impact of Jet Apparatus
PRECAUTIONS ON HANDLING EQUIPMENT
1. Make sure the control valve is close completely every time before the pump is switch on. This is to
avoid intrusion of air into the pump. Entrapped air can reduced the force exerted by the jet thus
reducing it efficiency.
2. Reading on PU tube should be on the water meniscus to avoid parallax error.
3. When measuring the flow rate, volume difference should be taken at least 10 liters for a more
accurate reading. For high flow rate, start measuring only when the water at the measuring tank
reaches the second level of the compartment. This is to ensure a steady increment of water level in
the PU tube.
4. It is important to drain all water from the apparatus when not in use. The apparatus should be stored
properly to prevent damage.
5. The apparatus should not be exposed to any shock and stresses.
6. Always run the experiment after fully understands the unit and procedures.
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PRE-LAB QUESTIONS
1. What is the ‘conservation of momentum?
2. State the equation of flow rate in terms of velocity and cross sectional area.
3. What is the effect of nozzle diameter to the velocity of the water?
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EXPERIMENT # 4
REYNOLDS OSBORNE EXPERIMENT
OBJECTIVES
The objectives of the experiment are:
1. To demonstrate laminar, transition and turbulent flow
2. To introduce Reynolds number to classify laminar, transition and turbulent flow
LEARNING OUTCOMES
It is expected by completing the experiment, the students will be able:
1. To describe laminar, transition and turbulent flow
2. To determine critical Reynolds number for laminar, transition and turbulent flow
THEORY/BACKGROUND
{More in textbook [1] section 8-2}
Fluid flow can be classified to three regimes which is laminar, transitional and turbulent regime. Laminar
regime is a regime where the flow is characterized by smooth streamlines and highly ordered motion.
Turbulent is a regime where flow is characterized by velocity fluctuations and highly disordered motion.
Transitional regime is where the flow fluctuates between laminar and turbulent before it becomes fully
turbulent.
The transitional from laminar to turbulent flow depends on geometry, surface roughness, flow velocity,
surface temperature, and type of fluid. However, Osborne Reynolds discovered that the flow regime
mainly depends on the ratio of inertial forces to viscous forces. This ratio is what we called as Reynolds
number.
At small or moderate Reynolds numbers the viscous forces are large enough to suppress theses fluctuations
and to keep the fluid “in line”. Thus, the flow is streamlined and in ordered motion. However, at large
Reynolds numbers, the inertial forces, which are proportional to the fluid density and the square of the
fluid velocity, are large relative to the viscous force. As the results, the viscous force cannot prevent the
random and rapid fluctuations of the fluid. Thus, the flow will be in disordered motion.
The boundary of Reynolds number for laminar, transitional and turbulent regime varies by geometries and
flow condition. For example, flow in a circular pipe is laminar for Reynolds number less than 2300,
turbulent for Reynolds number larger than 4000 and transitional in between. However, we will have other
boundaries if the pipe cross sectional area is a square.
[This part was taken with some modification from textbook Fluid Mechanics: Fundamentals and
Applications; Yunus A. Cengel and John M. Cimbala; McGraw Hill, 2006.]
This experiment is to visualize the laminar, transitional and turbulent flow in a pipe and to determine the
boundary of Reynolds number for flow in the pipe.
First by controlling the flow rate, establish the laminar flow. Then by slowly increase the flow rate
observes what happened to the dye streak. Record the flow pattern change and its volumetric flow rate
reading. Determine the boundary of Reynolds number for laminar, transitional and turbulent regime.
EQUIPMENT:
Hydraulic Bench
Reynolds Experiment Apparatus
PRE-LAB QUESTIONS
1. What is Reynolds Number?
2. Explain what is the meaning is if one say ‘The flow has low Reynolds Number?
3. Draw velocity profile for fully developed turbulent flow.
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EXPERIMENT # 5
PUMPS IN SERIES & PARALLEL
OBJECTIVES
The objectives of the experiment are:
1. To demonstrate pump performance when connected in series and parallel
2. To show shut off point of pump in series and parallel
LEARNING OUTCOMES
It is expected by completing the experiment, the students will be able:
1. To estimate power requirement for a pump as a function of its throughput, pressure increase and
efficiency
2. To analyze pump network for pipelines operating under pressure
THEORY/BACKGROUND
{More in textbook [1] section 14-2}
In selecting a pump fro a given situation, we have a variety of pumps to choose among. The manufacturers
provide the pump performance information such as the pump performance curves. The engineer’s task is to
the pump or pumps that best fits in with the system characteristics.
One of the considerations in fulfilling a system characteristic is whether to combine a pump in one system
or not. The combination may be in parallel or series.
By examining pump performance curve for pumps in series and pumps in parallel, we easily can say that
the pumps in series tend to increase head but pumps in parallel tend to increase capacity.
For this experiment,
1. Determine:
a. Average velocity of the fluid flow
b. Volumetric flow rate
c. Required net head by solving energy equation
d. Pump efficiency
2. Plot on the same set of axes the graph of available net head, pump efficiency and required net head
as a function of capacity (volumetric flow rate).
3. From the graph, determine (if possible)
a. Shut off head for each pump
b. Free delivery
c. Best efficiency point
d. Operating point
EQUIPMENT
Pump in Series and Parallel Apparatus
PRECAUTIONS ON HANDLING EQUIPMENT
1. Never operate the pumps when there is no liquid in the pipeline. It will cause serious damage to the
pumps.
2. Do not operate pump above and below its limit operation as given below:
PRE-LAB QUESTIONS
1. Define shut off head.
15
2. What will happen to the total flow rate (capacity) if you put two similar pumps in parallel
arrangement?
3. What is the meaning of available head?
REFERENCES
[1] Yunus A. Cengel and John M. Cimbala, Fluid Mechanics: Fundamentals and Applications,
McGraw-Hill, 2006.
[2] Bruce R. Munson, Donald F. Young and Theodore H. Okiishi, Fundamentals of Fluid Mechanics,
th
5 ed., Wiley Asia Student Edition, 2006.
th
[3] Clayton T. Crowe, Donald F. Elger and John A. Roberson, Engineering Fluid Mechanics, 8 ed.,
Wiley, 2005
th
[4] E. John Finnemore and Joseph B. Franzini, Fluid Mechanics with Engineering Applications, 10
ed., International Edition, McGraw Hill, 2006.
th
[5] Robert W. Fox and Alan T. McDonald, Introduction to Fluid Mechanics, 5 ed., Wiley.
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