Fluid Lab manual

A Manual for the

MECHANICS of FLUIDS LABORATORY

William S. Janna
Department of Mechanical Engineering
Memphis State University

©1997 William S. Janna
All Rights Reserved.
No part of this manual may be reproduced, stored in a retrieval system, or transcribed in any form or by any means—electronic, magnetic, mechanical, photocopying, recording, or otherwise— without the prior written consent of William S. Janna

2

TABLE OF CONTENTS
Item

Page

Report Writing.................................................................................................................4
Cleanliness and Safety ....................................................................................................6
Experiment 1
Density and Surface Tension.....................................................7
Experiment 2
Viscosity.........................................................................................9
Experiment 3
Center of Pressure on a Submerged Plane Surface.............10
Experiment 4
Measurement of Differential Pressure..................................12
Experiment 5
Impact of a Jet of Water ............................................................14
Experiment 6
Critical Reynolds Number in Pipe Flow...............................16
Experiment 7
Fluid Meters................................................................................18
Experiment 8
Pipe Flow .....................................................................................22
Experiment 9
Pressure Distribution About a Circular Cylinder................24
Experiment 10
Drag Force Determination .......................................................27
Experiment 11
Analysis of an Airfoil................................................................28
Experiment 12
Open Channel Flow—Sluice Gate .........................................30
Experiment 13
Open Channel Flow Over a Weir ..........................................32
Experiment 14
Open Channel Flow—Hydraulic Jump ................................34
Experiment 15
Open Channel Flow Over a Hump........................................36
Experiment 16
Measurement of Velocity and Calibration of a Meter for Compressible Flow.............................39
Experiment 17
Measurement of Fan Horsepower .........................................44
Experiment 18
Measurement of Pump Performance....................................46
Appendix .........................................................................................................................50

3

REPORT WRITING
All reports in the Fluid Mechanics
Laboratory require a formal laboratory report unless specified otherwise. The report should be written in such a way that anyone can duplicate the performed experiment and find the same results as the originator. The reports should be simple and clearly written. Reports are due one week after the experiment was performed, unless specified otherwise.
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, shown in Figure R.1, is to be used for formal Laboratory
Reports:
Title Page–The title page should show the title and number of the experiment, the date the experiment was performed, experimenter's name and experimenter's partners' names.
Table of Contents –Each page of the report must be numbered for this section.
Object –The object is 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 object can be as short as one sentence and it is usually written in the past tense.
Theory –The theory section should contain a complete analytical development of all important equations pertinent to the experiment, and how these equations are used in the reduction of data. The theory section should be written textbook-style.
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-

Bibliography

Calibration Curves

Original Data Sheet
(Sample Calculation)
Appendix
Title Page
Discussion & Conclusion
(Interpretation)
Results (Tables and Graphs)
Procedure (Drawings and Instructions)
Theory
(Textbook Style)
Object
(Past Tense)
Table of Contents
Each page numbered

Experiment Number
Experiment Title
Your Name
Due Date
Partners’ Names

FIGURE R.1. Format for formal reports. by-step how the experiment was performed in case someone desires to duplicate it. If it cannot be duplicated, the experiment shows nothing. Results – The results section should contain a formal analysis of the data with tables, graphs, etc. Any presentation of data which serves the purpose of clearly showing the outcome of the experiment is sufficient.
Discussion and Conclusion – This section should give an interpretation of the results explaining how the object of the experiment was accomplished. If any analytical expression is to be verified, calculate % error† and account for the sources. Discuss this experiment with respect to its faults as well
† % error–An analysis expressing how favorably 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.

4

as its strong points. Suggest extensions of the experiment and improvements. Also recommend any changes necessary to better accomplish the object.
Each experiment write-up contains a number of questions. These are to be answered or discussed in the Discussion and Conclusions section. Appendix
(1) Original data sheet.
(2) Show how data were used by a sample calculation. (3) Calibration curves of instrument 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.
(4) 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.
Graphs
In many instances, it is necessary to compose a plot in order to graphically present the results.
Graphs must be drawn neatly following a specific format. Figure R.2 shows an acceptable graph prepared using a computer. There are many computer programs that have graphing capabilities. Nevertheless an acceptably drawn graph has several features of note. These features are summarized next to Figure R.2.

0.2

•
•
•
•
•

•
•
•

Border is drawn about the entire graph.
Axis labels defined with symbols and units. Grid drawn using major axis divisions.
Each line is identified using a legend.
Data points are identified with a symbol: “ ´” on the Qac line to denote data points obtained by experiment.
The line representing the theoretical results has no data points represented.
Nothing is drawn freehand.
Title is descriptive, rather than something like Q vs ∆h.

3 flow rate Q in m /s

Features of note

Q

th

0.15

Q

ac

0.1
0.05
0
0

0.2

0.4

0.6

0.8

1

head loss ∆ h in m

FIGURE R.2. Theoretical and actual volume flow rate through a venturi meter as a function of head loss.

5

CLEANLINESS AND SAFETY
Cleanliness
There are “housekeeping” rules that the user of the laboratory should be aware of and abide by. Equipment in the lab is delicate and each piece is used extensively for 2 or 3 weeks per semester. During the remaining time, each apparatus just sits there, literally collecting dust.
University housekeeping staff are not required to clean and maintain the equipment. Instead, there are college technicians who will work on the equipment when it needs repair, and when they are notified that a piece of equipment needs attention. It is important, however, that the equipment stay clean, so that dust will not accumulate too badly.
The Fluid Mechanics Laboratory contains equipment that uses water or air as the working fluid. In some cases, performing an experiment will inevitably allow water to get on the equipment and/or the floor. If no one cleaned up their working area after performing an experiment, the lab would not be a comfortable or safe place to work in. No student appreciates walking up to and working with a piece of equipment that another student or group of students has left in a mess.
Consequently, students are required to clean up their area at the conclusion of the performance of an experiment. Cleanup will include removal of spilled water (or any liquid), and wiping the table top on which the equipment is mounted (if appropriate). The lab should always be as clean or cleaner than it was when you entered. Cleaning

the lab is your responsibility as a user of the equipment. This is an act of courtesy that students who follow you will appreciate, and that you will appreciate when you work with the equipment. Safety
The layout of the equipment and storage cabinets in the Fluid Mechanics Lab involves resolving a variety of conflicting problems. These include traffic flow, emergency facilities, environmental safeguards, exit door locations, etc. The goal is to implement safety requirements without impeding egress, but still allowing adequate work space and necessary informal communication opportunities.
Distance between adjacent pieces of equipment is determined by locations of floor drains, and by the need to allow enough space around the apparatus of interest. Immediate access to the Safety Cabinet is also considered.
Emergency facilities such as showers, eye wash fountains, spill kits, fire blankets and the like are not found in the lab. We do not work with hazardous materials and such safety facilities are not necessary. However, waste materials are generated and they should be disposed of properly. Every effort has been made to create a positive, clean, safety conscious atmosphere.
Students are encouraged to handle equipment safely and to be aware of, and avoid being victims of, hazardous situations.

6

EXPERIMENT 1
FLUID PROPERTIES: DENSITY AND SURFACE TENSION
There are several properties simple
Newtonian fluids have. They are basic properties which cannot be calculated for every fluid, and therefore they must be measured.
These properties are important in making calculations regarding fluid systems. Measuring fluid properties, density and viscosity, is the object of this experiment.

W2
W1

Part I: Density Measurement.
Equipment
Graduated cylinder or beaker
Liquid whose properties are to be measured Hydrometer cylinder
Scale
The density of the test fluid is to be found by weighing a known volume of the liquid using the graduated cylinder or beaker and the scale. The beaker is weighed empty. The beaker is then filled to a certain volume according to the graduations on it and weighed again. The difference in weight divided by the volume gives the weight per unit volume of the liquid. By appropriate conversion, the liquid density is calculated. The mass per unit volume, or the density, is thus measured in a direct way.
A second method of finding density involves measuring buoyant force exerted on a submerged object. The difference between the weight of an object in air and the weight of the object in liquid is known as the buoyant force (see Figure 1.1).

Part II: Surface Tension Measurement
Equipment
Surface tension meter
Beaker
Test fluid
Surface tension is defined as the energy required to pull molecules of liquid from beneath the surface to the surface to form a new area. It is therefore an energy per unit area (F⋅L/L2 = F/L).
A surface tension meter is used to measure this energy per unit area and give its value directly. A schematic of the surface tension meter is given in
Figure 1.2.
The platinum-iridium ring is attached to a balance rod (lever arm) which in turn is attached

FIGURE 1.1. Measuring the buoyant force on an object with a hanging weight.
Referring to Figure 1.1, the buoyant force B is found as
B = W1 - W2
The buoyant force is equal to the difference between the weight of the object in air and the weight of the object while submerged. Dividing this difference by the volume displaced gives the weight per unit volume from which density can be calculated. Questions
1. Are the results of all the density measurements in agreement?
2. How does the buoyant force vary with depth of the submerged object? Why?

to a stainless steel torsion wire. One end of this wire is fixed and the other is rotated. As the wire is placed under torsion, the rod lifts the ring slowly out of the liquid. The proper technique is to lower the test fluid container as the ring is lifted so that the ring remains horizontal. The force required to break the ring free from the liquid surface is related to the surface tension of the liquid. As the ring breaks free, the gage at the front of the meter reads directly in the units indicated (dynes/cm) for the given ring. This reading is called the apparent surface tension and must be corrected for the ring used in order to obtain the actual surface tension for the liquid.
The correction factor F can be calculated with the following equation
7

balance rod platinum iridium ring

FIGURE 1.2. A schematic of the surface tension meter.

clamp

torsion wire

test liquid

F = 0.725 + √
 0.000 403 3(σa/ρ) + 0.045 34 - 1.679(r/R) where F is the correction factor, σa is the apparent surface tension read from the dial
(dyne/cm), ρ is the density of the liquid (g/cm3), and (r/R) for the ring is found on the ring container. The actual surface tension for the liquid is given by

σ = Fσa

8

EXPERIMENT 2
FLUID PROPERTIES: VISCOSITY
One of the properties of homogeneous liquids is their resistance to motion. A measure of this resistance is known as viscosity. It can be measured in different, standardized methods or tests. In this experiment, viscosity will be measured with a falling sphere viscometer.
The Falling Sphere Viscometer
When an object falls through a fluid medium, the object reaches a constant final speed or terminal velocity. If this terminal velocity is sufficiently low, then the various forces acting on the object can be described with exact expressions.
The forces acting on a sphere, for example, that is falling at terminal velocity through a liquid are:
Weight - Buoyancy - Drag = 0
4
4 ρsg πR3 - ρg πR3 - 6πµVR = 0
3
3 where ρs and ρ are density of the sphere and liquid respectively, V is the sphere’s terminal velocity, R is the radius of the sphere and µ is the viscosity of the liquid. In solving the preceding equation, the viscosity of the liquid can be determined. The above expression for drag is valid only if the following equation is valid:

average the results. With the terminal velocity of this and of other spheres measured and known, the absolute and kinematic viscosity of the liquid can be calculated. The temperature of the test liquid should also be recorded. Use at least three different spheres. (Note that if the density of the liquid is unknown, it can be obtained from any group who has completed or is taking data on
Experiment 1.)
Questions
1. Should the terminal velocity of two different size spheres be the same?
2. Does a larger sphere have a higher terminal velocity?
3. Should the viscosity found for two different size spheres be the same? Why or why not?
4. If different size spheres give different results for the viscosity, what are the error sources? Calculate the % error and account for all known error sources.
5. What are the shortcomings of this method?
6. Why should temperature be recorded.
7. Can this method be used for gases?
8. Can this method be used for opaque liquids?
9. Can this method be used for something like peanut butter, or grease or flour dough?
Why or why not?

ρVD
< 1 µ where D is the sphere diameter. Once the viscosity of the liquid is found, the above ratio should be calculated to be certain that the mathematical model gives an accurate description of a sphere falling through the liquid. Equipment
Hydrometer cylinder
Scale
Stopwatch
Several small spheres with weight and diameter to be measured
Test liquid

d

V

FIGURE 2.1. Terminal velocity measurement (V = d/time). Drop a sphere into the cylinder liquid and record the time it takes for the sphere to fall a certain measured distance. The distance divided by the measured time gives the terminal velocity of the sphere. Repeat the measurement and
9

EXPERIMENT 3
CENTER OF PRESSURE ON A SUBMERGED
PLANE SURFACE
Submerged surfaces are found in many engineering applications. Dams, weirs and water gates are familiar examples of submerged surfaces used to control the flow of water. From the design viewpoint, it is important to have a working knowledge of the forces that act on submerged surfaces.
A plane surface located beneath the surface of a liquid is subjected to a pressure due to the height of liquid above it, as shown in Figure 3.1.
Increasing pressure varies linearly with increasing depth resulting in a pressure distribution that acts on the submerged surface.
The analysis of this situation involves determining a force which is equivalent to the pressure, and finding the location of this force.

yF

F

FIGURE 3.1. Pressure distribution on a submerged plane surface and the equivalent force.

verification of these equations for force and distance is the subject of this experiment.
Center of Pressure Measurement
Equipment
Center of Pressure Apparatus
Weights
Figure 3.2 gives a schematic of the apparatus used in this experiment. The torus and balance arm are placed on top of the tank. Note that the pivot point for the balance arm is the point of contact between the rod and the top of the tank.
The zeroing weight is adjusted to level the balance arm. Water is then added to a predetermined depth. Weights are placed on the weight hanger to re-level the balance arm. The amount of needed weight and depth of water are then recorded. The procedure is then repeated for four other depths. (Remember to record the distance from the pivot point to the free surface for each case.)
From the depth measurement, the equivalent force and its location are calculated using
Equations 3.1 and 3.2. Summing moments about the pivot allows for a comparison between the theoretical and actual force exerted. Referring to
Figure 3.2, we have
F=

For this case, it can be shown that the equivalent force is:
F = ρgycA

(3.1)

in which ρ is the liquid density, yc is the distance from the free surface of the liquid to the centroid of the plane, and A is the area of the plane in contact with liquid. Further, the location of this force yF below the free surface is yF =

Ix x
+ yc y cA

(3.2)

in which Ixx is the second area moment of the plane about its centroid. The experimental

WL
(y + y F )

(3.3)

where y is the distance from the pivot point to the free surface, yF is the distance from the free surface to the line of action of the force F, and L is the distance from the pivot point to the line of action of the weight W. Note that both curved surfaces of the torus are circular with centers at the pivot point. For the report, compare the force obtained with Equation 3.1 to that obtained with
Equation 3.3. When using Equation 3.3, it will be necessary to use Equation 3.2 for yF.
Questions
1. In summing moments, why isn't the buoyant force taken into account?
2. Why isn’t the weight of the torus and the balance arm taken into account?

10

L

level

y

Ri

pivot point
(point of contact)

torus weight hanger

zeroing weight

yF

Ro

h
F

FIGURE 3.2. A schematic of the center of pressure apparatus.

11

w

EXPERIMENT 4
MEASUREMENT OF DIFFERENTIAL PRESSURE
Pressure can be measured in several ways.
Bourdon tube gages, manometers, and transducers are a few of the devices available. Each of these instruments actually measures a difference in pressure; that is, measures a difference between the desired reading and some reference pressure, usually atmospheric. The measurement of differential pressure with manometers is the subject of this experiment.
Manometry
A manometer is a device used to measure a pressure difference and display the reading in terms of height of a column of liquid. The height is related to the pressure difference by the hydrostatic equation.
Figure 4.1 shows a U-tube manometer connected to two pressure vessels. The manometer reading is ∆h and the manometer fluid has density ρm. One pressure vessel contains a fluid of density ρ1 while the other vessel contains a fluid of density ρ2. The pressure difference can be found by applying the hydrostatic equation to each limb of the manometer. For the left leg,

p2 p1 z2
2
1

z1 h pA

pA m FIGURE 4.1. A U-tube manometer connected to two pressure vessels. p1 + ρ1gz1 = pA
Likewise for the right leg, p2 + ρ2gz2 + ρmg∆h = pA
Equating these expressions and solving for the pressure difference gives

p1 - p2 = ρ2gz2 + ρ1gz1 + ρmg∆h
If the fluids above the manometer liquid are both gases, then ρ1 and ρ2 are small compared to ρµ.
The above equation then becomes p1 - p 2 = ρ m g ∆ h
Figure 4.2 is a schematic of the apparatus used in this experiment. It consists of three U-tube manometers, a well-type manometer, a Utube/inclined manometer and a differential pressure gage. There are two tanks (actually, two capped pieces of pipe) to which each manometer and the gage are connected. The tanks have bleed valves attached and the tanks are connected with plastic tubing to a squeeze bulb. The bulb lines also contain valves. With both bleed valves closed and with both bulb line valves open, the bulb is squeezed to pump air from the low pressure tank to the high pressure tank. The bulb is squeezed until any of the manometers reaches its maximum reading. Now both valves are closed and the liquid levels are allowed to settle in each manometer. The ∆h readings are all recorded. Next, one or both bleed valves are opened slightly to release some air into or out of a tank. The liquid levels are again allowed to settle and the ∆h readings are recorded. The procedure is to be repeated until 5 different sets of readings are obtained. For each set of readings, convert all readings into psi or Pa units, calculate the average value and the standard deviation.
Before beginning, be sure to zero each manometer and the gage.
Questions
1. Manometers 1, 2 and 3 are U-tube types and each contains a different liquid. Manometer
4 is a well-type manometer. Is there an advantage to using this one over a U-tube type? 2. Manometer 5 is a combined U/tube/inclined manometer. What is the advantage of this type? 3. Note that some of the manometers use a liquid which has a specific gravity different from 1.00, yet the reading is in inches of water. Explain how this is possible. 4. What advantages or disadvantages does the gage have over the manometers?
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5. Is a low value of the standard deviation expected? Why?
6. What does a low standard deviation imply? 7. In your opinion, which device gives the most accurate reading. What led you to this conclusion? High pressure tank

Low pressure tank

Bleed valves

Gage

U-tube manometers

Well-type manometer U-tube/inclined manometer FIGURE 4.2. A schematic of the apparatus used in this experiment.

13

EXPERIMENT 5
IMPACT OF A JET OF WATER
A jet of fluid striking a stationary object exerts a force on that object. This force can be measured when the object is connected to a spring balance or scale. The force can then be related to the velocity of the jet of fluid and in turn to the rate of flow. The force developed by a jet stream of water is the subject of this experiment.
Impact of a Jet of Liquid
Equipment
Jet Impact Apparatus
Object plates
Figure 5.1 is a schematic of the device used in this experiment. The device consists of a tank within a tank. The interior tank is supported on a pivot and has a lever arm attached to it. As water enters this inner tank, the lever arm will reach a balance point. At this time, a stopwatch is started and a weight is placed on the weight hanger (e.g., 10 lbf). When enough water has entered the tank (10 lbf), the lever arm will again balance. The stopwatch is stopped. The elapsed time divided into the weight of water collected gives the weight or mass flow rate of water through the system (lbf/sec, for example).
The outer tank acts as a support for the table top as well as a sump tank. Water is pumped from the outer tank to the apparatus resting on the table top. As shown in Figure 5.1, the impact apparatus contains a nozzle that produces a high velocity jet of water. The jet is aimed at an object
(such as a flat plate or hemisphere). The force exerted on the plate causes the balance arm to which the plate is attached to deflect. A weight is moved on the arm until the arm balances. A summation of moments about the pivot point of the arm allows for calculating the force exerted by the jet.
Water is fed through the nozzle by means of a centrifugal pump. The nozzle emits the water in a jet stream whose diameter is constant. After the water strikes the object, the water is channeled to

the weighing tank inside to obtain the weight or mass flow rate.
The variables involved in this experiment are listed and their measurements are described below: 1. Mass rate of flow–measured with the weighing tank inside the sump tank. The volume flow rate is obtained by dividing mass flow rate by density: Q = m/ρ.
2. Velocity of jet–obtained by dividing volume flow rate by jet area: V = Q/A. The jet is cylindrical in shape with a diameter of 0.375 in. 3. Resultant force—found experimentally by summation of moments about the pivot point of the balance arm. The theoretical resultant force is found by use of an equation derived by applying the momentum equation to a control volume about the plate.
Impact Force Analysis
The total force exerted by the jet equals the rate of momentum loss experienced by the jet after it impacts the object. For a flat plate, the force equation is:
F=

ρQ2
A

(flat plate)

For a hemisphere,
F=

2ρQ2
A

(hemisphere)

For a cone whose included half angle is α,
F=

ρQ2
(1 + cos α)
A

(cone)

For your report, derive the appropriate equation for each object you use. Compose a graph with volume flow rate on the horizontal axis, and on the vertical axis, plot the actual and theoretical force. Use care in choosing the increments for each axis.

14

balancing weight pivot

lever arm with flat plate attached

flat plate water jet

nozzle

drain

flow control valve weigh tank tank pivot

plug

weight hanger

sump tank

motor

pump

FIGURE 5.1. A schematic of the jet impact apparatus.

15

EXPERIMENT 6
CRITICAL REYNOLDS NUMBER IN PIPE FLOW
The Reynolds number is a dimensionless ratio of inertia forces to viscous forces and is used in identifying certain characteristics of fluid flow.
The Reynolds number is extremely important in modeling pipe flow. It can be used to determine the type of flow occurring: laminar or turbulent.
Under laminar conditions the velocity distribution of the fluid within the pipe is essentially parabolic and can be derived from the equation of motion. When turbulent flow exists, the velocity profile is “flatter” than in the laminar case because the mixing effect which is characteristic of turbulent flow helps to more evenly distribute the kinetic energy of the fluid over most of the cross section.
In most engineering texts, a Reynolds number of 2 100 is usually accepted as the value at transition; that is, the value of the Reynolds number between laminar and turbulent flow regimes. This is done for the sake of convenience.
In this experiment, however, we will see that transition exists over a range of Reynolds numbers and not at an individual point.
The Reynolds number that exists anywhere in the transition region is called the critical
Reynolds number. Finding the critical Reynolds number for the transition range that exists in pipe flow is the subject of this experiment.

dye will flow downstream in a threadlike pattern for very low flow rates. Once steady state is achieved, the rotameter valve is opened slightly to increase the water flow rate. The valve at B is opened further if necessary to allow more dye to enter the tube. This procedure of increasing flow rate of water and of dye (if necessary) is repeated throughout the experiment. Establish laminar flow in one of the tubes.
Then slowly increase the flow rate and observe what happens to the dye. Its pattern may change, yet the flow might still appear to be laminar. This is the beginning of transition.
Continue increasing the flow rate and again observe the behavior of the dye. Eventually, the dye will mix with the water in a way that will be recognized as turbulent flow. This point is the end of transition. Transition thus will exist over a range of flow rates. Record the flow rates at key points in the experiment. Also record the temperature of the water.
The object of this procedure is to determine the range of Reynolds numbers over which transition occurs. Given the tube size, the
Reynolds number can be calculated with:
Re =

Critical Reynolds Number Measurement
Equipment
Critical Reynolds Number Determination
Apparatus
Figure 6.1 is a schematic of the apparatus used in this experiment. The constant head tank provides a controllable, constant flow through the transparent tube. The flow valve in the tube itself is an on/off valve, not used to control the flow rate. Instead, the flow rate through the tube is varied with the rotameter valve at A. The head tank is filled with water and the overflow tube maintains a constant head of water. The liquid is then allowed to flow through one of the transparent tubes at a very low flow rate. The valve at B controls the flow of dye; it is opened and dye is then injected into the pipe with the water. The dye injector tube is not to be placed in the pipe entrance as it could affect the results.
Establish laminar flow by starting with a very low flow rate of water and of dye. The injected

VD ν where V (= Q/A) is the average velocity of liquid in the pipe, D is the hydraulic diameter of the pipe, and ν is the kinematic viscosity of the liquid. The hydraulic diameter is calculated from its definition:
D=

4 x Area
Wetted Perimeter

For a circular pipe flowing full, the hydraulic diameter equals the inside diameter of the pipe.
For a square section, the hydraulic diameter will equal the length of one side (show that this is the case). The experiment is to be performed for both round tubes and the square tube. With good technique and great care, it is possible for the transition Reynolds number to encompass the traditionally accepted value of 2 100.

16

Questions
1. Can a similar procedure be followed for gases? 2. Is the Reynolds number obtained at transition dependent on tube size or shape?
3. Can this method work for opaque liquids?

dye reservoir drilled partitions

B

on/off valve rotameter transparent tube

inlet to tank overflow to drain

A to drain

FIGURE 6.1. The critical Reynolds number determination apparatus.

17

EXPERIMENT 7
FLUID METERS IN INCOMPRESSIBLE FLOW
There are many different meters used in pipe flow: the turbine type meter, the rotameter, the orifice meter, the venturi meter, the elbow meter and the nozzle meter are only a few. Each meter works by its ability to alter a certain physical characteristic of the flowing fluid and then allows this alteration to be measured. The measured alteration is then related to the flow rate. A procedure of analyzing meters to determine their useful features is the subject of this experiment.
The Venturi Meter
The venturi meter is constructed as shown in
Figure 7.1. It contains a constriction known as the throat. When fluid flows through the constriction, it must experience an increase in velocity over the upstream value. The velocity increase is accompanied by a decrease in static pressure at the throat. The difference between upstream and throat static pressures is then measured and related to the flow rate. The greater the flow rate, the greater the pressure drop ∆p. So the pressure difference ∆h (= ∆p/ρg) can be found as a function of the flow rate.

h
1

2

and substituting from the hydrostatic equation, it can be shown after simplification that the volume flow rate through the venturi meter is given by
Qth = A2

√


2g ∆ h
1 - (D 24/D 14)

(7.1)

The preceding equation represents the theoretical volume flow rate through the venturi meter.
Notice that is was derived from the Bernoulli equation which does not take frictional effects into account.
In the venturi meter, there exists small pressure losses due to viscous (or frictional) effects. Thus for any pressure difference, the actual flow rate will be somewhat less than the theoretical value obtained with Equation 7.1 above. For any ∆h, it is possible to define a coefficient of discharge Cv as
Cv =

Qac
Qth

For each and every measured actual flow rate through the venturi meter, it is possible to calculate a theoretical volume flow rate, a
Reynolds number, and a discharge coefficient.
The Reynolds number is given by
Re =

V2D2 ν (7.2)

where V 2 is the velocity at the throat of the meter (= Q ac/A 2).
FIGURE 7.1. A schematic of the Venturi meter.
Using the hydrostatic equation applied to the air-over-liquid manometer of Figure 7.1, the pressure drop and the head loss are related by
(after simplification): p 1 - p2
= ∆h ρg By combining the continuity equation,
Q = A1 V 1 = A2 V 2 with the Bernoulli equation, p 1 V 12 p2 V 22
+
= + ρ 2 ρ 2

The Orifice Meter and
Nozzle-Type Meter
The orifice and nozzle-type meters consist of a throttling device (an orifice plate or bushing, respectively) placed into the flow. (See Figures
7.2 and 7.3). The throttling device creates a measurable pressure difference from its upstream to its downstream side. The measured pressure difference is then related to the flow rate. Like the venturi meter, the pressure difference varies with flow rate. Applying Bernoulli’s equation to points 1 and 2 of either meter (Figure 7.2 or Figure
7.3) yields the same theoretical equation as that for the venturi meter, namely, Equation 7.1. For any pressure difference, there will be two associated flow rates for these meters: the theoretical flow rate (Equation 7.1), and the
18

actual flow rate (measured in the laboratory).
The ratio of actual to theoretical flow rate leads to the definition of a discharge coefficient: Co for the orifice meter and Cn for the nozzle.

rotor supported on bearings
(not shown)

to receiver

h turbine rotor rotational speed proportional to flow rate

flow straighteners 2

1

FIGURE 7.4. A schematic of a turbine-type flow meter. FIGURE 7.2. Cross sectional view of the orifice meter. h

1

2

FIGURE 7.3. Cross sectional view of the nozzletype meter, and a typical nozzle.
For each and every measured actual flow rate through the orifice or nozzle-type meters, it is possible to calculate a theoretical volume flow rate, a Reynolds number and a discharge coefficient. The Reynolds number is given by
Equation 7.2.
The Turbine-Type Meter
The turbine-type flow meter consists of a section of pipe into which a small “turbine” has been placed. As the fluid travels through the pipe, the turbine spins at an angular velocity that is proportional to the flow rate. After a certain number of revolutions, a magnetic pickup sends an electrical pulse to a preamplifier which in turn sends the pulse to a digital totalizer. The totalizer totals the pulses and translates them into a digital readout which gives the total volume of liquid that travels through the pipe and/or the instantaneous volume flow rate.
Figure 7.4 is a schematic of the turbine type flow meter. The Rotameter (Variable Area Meter)
The variable area meter consists of a tapered metering tube and a float which is free to move inside. The tube is mounted vertically with the inlet at the bottom. Fluid entering the bottom raises the float until the forces of buoyancy, drag and gravity are balanced. As the float rises the annular flow area around the float increases.
Flow rate is indicated by the float position read against the graduated scale which is etched on the metering tube. The reading is made usually at the widest part of the float. Figure 7.5 is a sketch of a rotameter. outlet freely suspended float

tapered, graduated transparent tube

inlet

FIGURE 7.5. A schematic of the rotameter and its operation. Rotameters are usually manufactured with one of three types of graduated scales:
1. % of maximum flow–a factor to convert scale reading to flow rate is given or determined for the meter. A variety of fluids can be used with the meter and the only variable

19

2.

3.

encountered in using it is the scale factor. The scale factor will vary from fluid to fluid.
Diameter-ratio type–the ratio of cross sectional diameter of the tube to the diameter of the float is etched at various locations on the tube itself. Such a scale requires a calibration curve to use the meter.
Direct reading–the scale reading shows the actual flow rate for a specific fluid in the units indicated on the meter itself. If this type of meter is used for another kind of fluid, then a scale factor must be applied to the readings. Experimental Procedure
Equipment
Fluid Meters Apparatus
Stopwatch
The fluid meters apparatus is shown schematically in Figure 7.6. It consists of a centrifugal pump, which draws water from a sump tank, and delivers the water to the circuit containing the flow meters. For nine valve positions (the valve downstream of the pump), record the pressure differences in each manometer. For each valve position, measure the actual flow rate by diverting the flow to the volumetric measuring tank and recording the time required to fill the tank to a predetermined volume. Use the readings on the side of the tank itself. For the rotameter, record the position of the float and/or the reading of flow rate given directly on the meter. For the turbine meter, record the flow reading on the output device.
Note that the venturi meter has two manometers attached to it. The “inner” manometer is used to calibrate the meter; that is, to obtain ∆h readings used in Equation 7.1. The
“outer” manometer is placed such that it reads the overall pressure drop in the line due to the presence of the meter and its attachment fittings.
We refer to this pressure loss as ∆H (distinctly different from ∆h). This loss is also a function of flow rate. The manometers on the turbine-type and variable area meters also give the incurred loss for each respective meter. Thus readings of
∆H vs Qac are obtainable. In order to use these parameters to give dimensionless ratios, pressure coefficient and Reynolds number are used. The
Reynolds number is given in Equation 7.2. The pressure coefficient is defined as

Cp =

g∆H
V2/2

(7.3)

All velocities are based on actual flow rate and pipe diameter.
The amount of work associated with the laboratory report is great; therefore an informal group report is required rather than individual reports. The write-up should consist of an
Introduction (to include a procedure and a derivation of Equation 7.1), a Discussion and
Conclusions section, and the following graphs:
1. On the same set of axes, plot Qac vs ∆h and
Q th vs ∆ h with flow rate on the vertical axis for the venturi meter.
2. On the same set of axes, plot Qac vs ∆h and
Q th vs ∆ h with flow rate on the vertical axis for the orifice meter.
3. Plot Qac vs Qth for the turbine type meter.
4. Plot Qac vs Qth for the rotameter.
5. Plot Cv vs Re on a log-log grid for the venturi meter.
6. Plot Co vs Re on a log-log grid for the orifice meter. 7. Plot ∆H vs Qac for all meters on the same set of axes with flow rate on the vertical axis.
8. Plot Cp vs Re for all meters on the same set of axes (log-log grid) with C p vertical axis.
Questions
1. Referring to Figure 7.2, recall that
Bernoulli's equation was applied to points 1 and 2 where the pressure difference measurement is made. The theoretical equation, however, refers to the throat area for point 2 (the orifice hole diameter) which is not where the pressure measurement was made. Explain this discrepancy and how it is accounted for in the equation formulation.
2. Which meter in your opinion is the best one to use?
3. Which meter incurs the smallest pressure loss? Is this necessarily the one that should always be used?
4. Which is the most accurate meter?
5. What is the difference between precision and accuracy?

20

manometer

orifice meter volumetric measuring tank venturi meter

rotameter

return

sump tank turbine-type meter

motor

pump

valve

FIGURE 7.6. A schematic of the Fluid Meters Apparatus. (Orifice and Venturi meters: upstream diameter is 1.025 inches; throat diameter is 0.625 inches.)

21

EXPERIMENT 8
PIPE FLOW
Experiments in pipe flow where the presence of frictional forces must be taken into account are useful aids in studying the behavior of traveling fluids. Fluids are usually transported through pipes from location to location by pumps. The frictional losses within the pipes cause pressure drops. These pressure drops must be known to determine pump requirements. Thus a study of pressure losses due to friction has a useful application. The study of pressure losses in pipe flow is the subject of this experiment.

•

•

•

With the pump on, record the assigned pressure drops and the actual volume flow rate from the rotameter.
Using the valve closest to the pump, change the volume flow rate and again record the pressure drops and the new flow rate value.
Repeat this procedure until 9 different volume flow rates and corresponding pressure drop data have been recorded.

With pressure loss data in terms of ∆h, the friction factor can be calculated with

Pipe Flow f= Equipment
Pipe Flow Test Rig
Figure 8.1 is a schematic of the pipe flow test rig. The rig contains a sump tank which is used as a water reservoir from which a centrifugal pump discharges water to the pipe circuit. The circuit itself consists of four different diameter lines and a return line all made of drawn copper tubing. The circuit contains valves for directing and regulating the flow to make up various series and parallel piping combinations. The circuit has provision for measuring pressure loss through the use of static pressure taps (manometer board not shown in schematic). Finally, because the circuit also contains a rotameter, the measured pressure losses can be obtained as a function of flow rate.
As functions of the flow rate, measure the pressure losses in inches of water for (as specified by the instructor):
1. 1 in. copper tube
2. 3/4-in. copper tube
3. 1/2-in copper tube
4. 3/8 in copper tube
•
•
•

5. 1 in. 90 T-joint
6. 1 in. 90 elbow (ell)
7. 1 in. gate valve
8. 3/ 4-in gate valve

The instructor will specify which of the pressure loss measurements are to be taken.
Open and close the appropriate valves on the apparatus to obtain the desired flow path.
Use the valve closest to the pump on its downstream side to vary the volume flow rate. 2g ∆ h
V 2 (L/D)

It is customary to graph the friction factor as a function of the Reynolds number:
Re =

VD ν The f vs Re graph, called a Moody Diagram is traditionally drawn on a log-log grid. The graph also contains a third variable known as the roughness coefficient ε/D. For this experiment the roughness factor ε is that for drawn tubing.
Where fittings are concerned, the loss incurred by the fluid is expressed in terms of a loss coefficient K. The loss coefficient for any fitting can be calculated with
K=

∆h
V2/2g

where ∆h is the pressure (or head) loss across the fitting. Values of K as a function of Qac are to be obtained in this experiment.
For the report, calculate friction factor f and graph it as a function of Reynolds number Re for items 1 through 4 above as appropriate. Compare to a Moody diagram. Also calculate the loss coefficient for items 5 through 8 above as appropriate, and determine if the loss coefficient
K varies with flow rate or Reynolds number.
Compare your K values to published ones.
Note that gate valves can have a number of open positions. For purposes of comparison it is often convenient to use full, half or one-quarter open. 22

rotameter

tank

valve motor static pressure tap

pump
FIGURE 8.1. Schematic of the pipe friction apparatus.

23

EXPERIMENT 9
PRESSURE DISTRIBUTION ABOUT A CIRCULAR CYLINDER
In many engineering applications, it may be necessary to examine the phenomena occurring when an object is inserted into a flow of fluid. The wings of an airplane in flight, for example, may be analyzed by considering the wings stationary with air moving past them. Certain forces are exerted on the wing by the flowing fluid that tend to lift the wing (called the lift force) and to push the wing in the direction of the flow (drag force). Objects other than wings that are symmetrical with respect to the fluid approach direction, such as a circular cylinder, will experience no lift, only drag.
Drag and lift forces are caused by the pressure differences exerted on the stationary object by the flowing fluid. Skin friction between the fluid and the object contributes to the drag force but in many cases can be neglected. The measurement of the pressure distribution existing around a stationary cylinder in an air stream to find the drag force is the object of this experiment. Consider a circular cylinder immersed in a uniform flow. The streamlines about the cylinder are shown in Figure 9.1. The fluid exerts pressure on the front half of the cylinder in an amount that is greater than that exerted on the rear half. The difference in pressure multiplied by the projected frontal area of the cylinder gives the drag force due to pressure (also known as form drag). Because this drag is due primarily to a pressure difference, measurement of the pressure distribution about the cylinder allows for finding the drag force experimentally. A typical pressure distribution is given in Figure 9.2. Shown in

Figure 9.2a is the cylinder with lines and arrowheads. The length of the line at any point on the cylinder surface is proportional to the pressure at that point. The direction of the arrowhead indicates that the pressure at the respective point is greater than the free stream pressure (pointing toward the center of the cylinder) or less than the free stream pressure
(pointing away). Note the existence of a separation point and a separation region (or wake). The pressure in the back flow region is nearly the same as the pressure at the point of separation. The general result is a net drag force equal to the sum of the forces due to pressure acting on the front half (+) and on the rear half
(-) of the cylinder. To find the drag force, it is necessary to sum the components of pressure at each point in the flow direction. Figure 9.2b is a graph of the same data as that in Figure 9.2a except that 9.2b is on a linear grid.

Wake

FIGURE 9.1. Streamlines of flow about a circular cylinder. separation point 0

Stagnation
Streamline

Freestream
Velocity V

p
30

60

90

120

150

180

separation point (a) Polar Coordinate Graph

(b) Linear Graph

FIGURE 9.2. Pressure distribution around a circular cylinder placed in a uniform flow.
24

Pressure Measurement
Equipment
A Wind Tunnel
A Right Circular Cylinder with Pressure
Taps
Figure 9.3 is a schematic of a wind tunnel. It consists of a nozzle, a test section, a diffuser and a fan. Flow enters the nozzle and passes through flow straighteners and screens. The flow is directed through a test section whose walls are made of a transparent material, usually
Plexiglas or glass. An object is placed in the test section for observation. Downstream of the test section is the diffuser followed by the fan. In the tunnel that is used in this experiment, the test section is rectangular and the fan housing is circular. Thus one function of the diffuser is to gradually lead the flow from a rectangular section to a circular one.
Figure 9.4 is a schematic of the side view of the circular cylinder. The cylinder is placed in the test section of the wind tunnel which is operated at a preselected velocity. The pressure tap labeled as #1 is placed at 0° directly facing the approach flow. The pressure taps are attached to a manometer board. Only the first 18 taps are connected because the expected profile is symmetric about the 0° line. The manometers will provide readings of pressure at 10° intervals about half the cylinder. For two different approach velocities, measure and record the pressure distribution about the circular cylinder.

Plot the pressure distribution on polar coordinate graph paper for both cases. Also graph pressure difference (pressure at the point of interest minus the free stream pressure) as a function of angle θ on linear graph paper. Next, graph ∆p cosθ vs θ
(horizontal axis) on linear paper and determine the area under the curve by any convenient method (counting squares or a numerical technique). The drag force can be calculated by integrating the flow-direction-component of each pressure over the area of the cylinder: π Df = 2RL

∫ ∆p cosθdθ
0

The above expression states that the drag force is twice the cylinder radius (2R) times the cylinder length (L) times the area under the curve of ∆p cosθ vs θ.
Drag data are usually expressed as drag coefficient CD vs Reynolds number Re. The drag coefficient is defined as
CD =

Df ρV2A/2 The Reynolds number is
Re =

ρVD µ inlet flow straighteners nozzle

diffuser

fan

test section

FIGURE 9.3. A schematic of the wind tunnel used in this experiment.

25

where V is the free stream velocity (upstream of the cylinder), A is the projected frontal area of the cylinder (2RL), D is the cylinder diameter, ρ is the air density and µ is the air viscosity.
Compare the results to those found in texts.

60

90

120

30
0

static pressure taps attach to manometers 150
180

FIGURE 9.4. Schematic of the experimental apparatus used in this experiment.

26

EXPERIMENT 10
DRAG FORCE DETERMINATION
An object placed in a uniform flow is acted upon by various forces. The resultant of these forces can be resolved into two force components, parallel and perpendicular to the main flow direction. The component acting parallel to the flow is known as the drag force. It is a function of a skin friction effect and an adverse pressure gradient. The component perpendicular to the flow direction is the lift force and is caused by a pressure distribution which results in a lower pressure acting over the top surface of the object than at the bottom. If the object is symmetric with respect to the flow direction, then the lift force will be zero and only a drag force will exist.
Measurement of the drag force acting on an object immersed in the uniform flow of a fluid is the subject of this experiment.
Equipment
Subsonic Wind Tunnel
Objects
A description of a subsonic wind tunnel is given in Experiment 9 and is shown schematically in Figure 9.3. The fan at the end of the tunnel draws in air at the inlet. An object is mounted on a stand that is pre calibrated to read lift and drag forces exerted by the fluid on the object. A schematic of the test section is shown in Figure
10.1. The velocity of the flow at the test section is also pre calibrated. The air velocity past the object can be controlled by changing the angle of the inlet vanes located within the fan housing.
Thus air velocity, lift force and drag force are read directly from the tunnel instrumentation.
There are a number of objects that are available for use in the wind tunnel. These include a disk, a smooth surfaced sphere, a rough surface sphere, a hemisphere facing upstream, and a hemisphere facing downstream. For whichever is assigned, measure drag on the object as a function of velocity.
Data on drag vs velocity are usually graphed in dimensionless terms. The drag force Df is customarily expressed in terms of the drag coefficient CD (a ratio of drag force to kinetic energy): CD =

in which ρ is the fluid density, V is the free stream velocity, and A is the projected frontal area of the object. Traditionally, the drag coefficient is graphed as a function of the
Reynolds number, which is defined as
Re =

VD ν where D is a characteristic length of the object and ν is the kinematic viscosity of the fluid. For each object assigned, graph drag coefficient vs
Reynolds number and compare your results to those published in texts. Use log-log paper if appropriate. Questions
1. How does the mounting piece affect the readings? 2. How do you plan to correct for its effect, if necessary? object

uniform flow

mounting stand

drag force measurement lift force measurement FIGURE 10.1. Schematic of an object mounted in the test section of the wind tunnel.

Df ρV2A/2 27

EXPERIMENT 11
ANALYSIS OF AN AIRFOIL
A wing placed in the uniform flow of an airstream will experience lift and drag forces.
Each of these forces is due to a pressure difference. The lift force is due to the pressure difference that exists between the lower and upper surfaces. This phenomena is illustrated in
Figure 11.1. As indicated the airfoil is immersed in a uniform flow. If pressure could be measured at selected locations on the surface of the wing and the results graphed, the profile in Figure 11.1 would result. Each pressure measurement is represented by a line with an arrowhead. The length of each line is proportional to the magnitude of the pressure at the point. The direction of the arrow (toward the horizontal axis or away from it) represents whether the pressure at the point is less than or greater than the free stream pressure measured far upstream of the wing.

Experiment I
Mount the wing with pressure taps in the tunnel and attach the tube ends to manometers.
Select a wind speed and record the pressure distribution for a selected angle of attack (as assigned by the instructor). Plot pressure vs chord length as in Figure 11.1, showing the vertical component of each pressure acting on the upper surface and on the lower surface. Determine where separation occurs for each case.
Mount the second wing on the lift and drag balance (Figure 11.2). For the same wind speed and angle of attack, measure lift and drag exerted on the wing. lift c drag c

uniform flow

stagnation point Cp

stagnation point drag force measurement negative pressure gradient on upper surface pressure coefficient mounting stand

lift force measurement positive pressure on lower surface

FIGURE 11.2. Schematic of lift and drag measurement in a test section.

chord, c

FIGURE 11.1. Streamlines of flow about a wing and the resultant pressure distribution.

Lift and Drag Measurements for a Wing
Equipment
Wind Tunnel (See Figure 9.3)
Wing with Pressure Taps
Wing for Attachment to Lift & Drag
Instruments (See Figure 11.2)

The wing with pressure taps provided pressure at selected points on the surface of the wing. Use the data obtained and sum the horizontal component of each pressure to obtain the drag force. Compare to the results obtained with the other wing. Use the data obtained and sum the vertical component of each pressure to obtain the lift force. Compare the results obtained with the other wing. Calculate % errors. 28

Experiment II
For a number of wings, lift and drag data vary only slightly with Reynolds number and therefore if lift and drag coefficients are graphed as a function of Reynolds number, the results are not that meaningful. A more significant representation of the results is given in what is known as a polar diagram for the wing. A polar diagram is a graph on a linear grid of lift coefficient (vertical axis) as a function of drag coefficient. Each data point on the graph corresponds to a different angle of attack, all measured at one velocity (Reynolds number).
Referring to Figure 11.2 (which is the experimental setup here), the angle of attack α is measured from a line parallel to the chord c to a line that is parallel to the free stream velocity.
If so instructed, obtain lift force, drag force and angle of attack data using a pre selected velocity.
Allow the angle of attack to vary from a negative angle to the stall point and beyond. Obtain data

at no less than 9 angles of attack. Use the data to produce a polar diagram.
Analysis
Lift and drag data are usually expressed in dimensionless terms using lift coefficient and drag coefficient. The lift coefficient is defined as
CL =

Lf
2A/2
ρV

where Lf is the lift force, ρ is the fluid density, V is the free stream velocity far upstream of the wing, and A is the area of the wing when seen from a top view perpendicular to the chord length c. The drag coefficient is defined as
CD =

Df ρV2A/2 in which Df is the drag force.

29

EXPERIMENT 12
OPEN CHANNEL FLOW—SLUICE GATE
Liquid motion in a duct where a surface of the fluid is exposed to the atmosphere is called open channel flow. In the laboratory, open channel flow experiments can be used to simulate flow in a river, in a spillway, in a drainage canal or in a sewer. Such modeled flows can include flow over bumps or through dams, flow through a venturi flume or under a partially raised gate (a sluice gate). The last example, flow under a sluice gate, is the subject of this experiment.

h0 =

In terms of flow rate, the velocities are written as
V0 =
V=

Flow Through a Sluice Gate
Equipment
Open Channel Flow Apparatus
Sluice Gate Model
Figure 12.1 shows a schematic of the side view of the sluice gate. Flow upstream of the gate has a depth h o while downstream the depth is h.
The objective of the analysis is to formulate an equation to relate the volume flow rate through
(or under) the gate to the upstream and downstream depths. sluice gate

hand crank

V 2 V 02
+h
2g 2g

Q Q
=
A bh0

Q bh where b is the channel width at the gate.
Substituting into the Bernoulli Equation and simplifying gives h0 =

Q2 1
 - 1 +h
2gb2  h 2 h 0 2 

Dividing by h 0,
1=

Q2
 1 - 1 + h
2gb 2 h 0  h 2 h 0 2  h 0

Rearranging further,
2

patm

direction of movement patm

ho

2

1 - h  = Q 2 1 - h 2  h0 
 h 0  2gb 2 h h 0 

h

FIGURE 12.1. Schematic of flow under a sluice gate. The flow rate through the gate is maintained at nearly a constant value. For various raised positions of the sluice gate, different liquid heights h o and h will result. Applying the
Bernoulli equation to flow about the gate gives p 0 V 02 p V2
+
+ h0 =
+
+h ρg 2g ρg 2g
Pressures at the free surface are both equal to atmospheric pressure, so they cancel. Rearranging gives Multiplying both sides by h2/h02, and continuing to simplify, we finally obtain h 2/h02
Q2
=
1 + h/h 0 2gb 2 h 0 3 here Q is the theoretical volume flow rate. The right hand side of this equation is recognized as
1/2 of the upstream Froude number. So by measuring the depth of liquid before and after the sluice gate, the theoretical flow rate can be calculated with the above equation. The theoretical flow rate can then be compared to the actual flow rate obtained by measurements using the orifice meters.
For 9 different raised positions of the sluice gate, measure the upstream and downstream depths and calculate the actual flow rate. In addition, calculate the upstream Froude number for each case and determine its value for maximum flow conditions. Graph h/h0 (vertical
30

axis) versus (Q 2/b 2h 03g). Determine h/h0 corresponding to maximum flow. Note that h/h0 varies from 0 to 1.
Figure 12.2 is a sketch of the open channel flow apparatus. It consists of a sump tank with a pump/motor combination on each side. Each pump draws in water from the sump tank and discharges it through the discharge line to calibrated orifice meters and then to the head tank. Each orifice meter is connected to its own manometer. Use of the calibration curve
(provided by the instructor) allows for finding the actual flow rate into the channel. The head tank and flow channel have sides made of
Plexiglas. Water flows downstream in the channel past the object of interest (in this case a sluice gate) and then is routed back to the sump tank. Questions
1. For the required report, derive the sluice gate equation in detail.
2. What if it was assumed that V 0