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DEPARTMENT OF CIVIL ENGINEERING UNIVERSITY OF OTTAWA
Mahmoud Al-Riffai and Ioan Nistor
CVG2116 INTRODUCTORY FLUID MECHANICS LABORATORY
LABORATORY MANUAL
1. PITOT TUBE TRAVERSE 2. BERNOULLI’S EQUATION 3. FORCE ON A SLUICE GATE 4. IMPULSE TURBINE 5. PIPE FLOW HEADLOSS 6. FORCED VORTEX
2010 EDITION
CVG2116 LABORATORY MANUAL Winter 2010
TABLE OF CONTENTS A. CVG2116 Laboratory Procedures and Reports .....................................1
1.0 Objective ...............................................................................................2 2.0 Laboratory Procedure ..........................................................................2 3.0 Submission of Reports ........................................................................3 4.0 Format ...................................................................................................3
B. EXPERIMENTAL SETUPS........................................................................8
1.0 Pitot Tube Traverse ..............................................................................9 2.0 Bernoulli’s Equation...........................................................................14 3.0 Force on a Sluice Gate .......................................................................19 4.0 Impulse Turbine..................................................................................25 5.0 Pipe Flow Headloss............................................................................30 6.0 Forced Vortex .....................................................................................34
C. REFERENCES.........................................................................................38
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CVG2116 LABORATORY MANUAL Winter 2010
A. CVG2116 LABORATORY PROCEDURES AND REPORTS
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CVG2116 LABORATORY MANUAL Winter 2010
1.0 OBJECTIVE
The objective of the experimental laboratories is to enable you, a student civil
engineer, to practice and understand the methods and means of determining,
deriving, and verifying certain principles which are required for solving
engineering problems in the field of Fluid Mechanics.
It should be noted that although results do not always seem to fit the prescribed
theory, they are not necessarily incorrect. It is your task and obligation during
working on this course and certainly in your future engineering career to
determine "what went wrong". Remember that there is always an explanation, be
it your fault or not. Because this is such an important aspect of engineering, any
"cooking" of the experimental results and calculations is unacceptable.
You should also indicate in your repots the practical lessons and applications of
the theory or of the results that you have obtained. This tool is in preparation for
the "real world".
2.0 LABORATORY PROCEDURE
The experimental apparatus will be setup by the Laboratory Technical Officer
and/or by the Teaching Assistant who will be available for guidance and
questions throughout the duration of the experiment and afterwards. The
experiments will be conducted jointly by the group such that each student will
have a specific responsibility which must be defined between the group members
themselves at the beginning of the experiment. It is advised that each member
alternate their responsibility with the other members along the duration of the
experiment to give all students greater exposure. Tasks to be performed by the
group are outlined in the laboratory handout. Before conducting the experiments,
it is compulsory to watch the DVD that comes with this manual and which is
entitled Instructional Video for CVG2116 - Fluid Mechanics.
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CVG2116 LABORATORY MANUAL Winter 2010
No horseplay will be tolerated in the laboratory. Students are not to tamper with
experimental apparatus beyond adjustments specified in this handout or by the
Instructor. It is not necessary to wear a lab coat for these exercises.
3.0 SUBMISSION OF REPORTS
All data obtained will be shared among the group members, whereas each group
will submit one laboratory report. However, it is strongly advised that each
student participate in every laboratory report! Duties can be divided based on
data analysis, presentation of results, theoretical and explanations and
experimental procedures, discussions and/or conclusion and recommendations.
It is also suggested that each member of the group read the report before it is
handed in. That way, all group members will endorse the report collectively and
give it their “seal of approval”.
The text of the report must be produced using a word processor on a computer.
Though recommended, it is not always necessary to use the word processor to
enter equations or graphical material in the report; these may be hand-written.
Unless otherwise stated, the laboratory report should be handed in two weeks
after the experiment has been performed unless otherwise stated. A good
practice for report writing is to always assume that the reader is not well informed
on the report topic! Therefore it is your responsibility be as clear and detailed as
possible, especially with respect to how you layout the wording and phrasing of
your sentences.
4.0 FORMAT
Reports should have the following headings proceeding appropriate sections
(Note: Do not simply copy and paste sections from this manual into your report.
You are expected to at least rephrase the wording from the manual if you plan to
make reference to it):
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CVG2116 LABORATORY MANUAL Winter 2010
4.1 Title Page
Department of Civil Engineering, University of Ottawa, course code, course
name, title of experiment, data performed and submitted, and group number
along with student member names and their IDs.
4.2 Abstract
It is advised that this section is written last, since it is a brief summary of your
report. It should include the objective of the experiment, the method by which you
have conducted the experiment, the key findings of your experiment and your
main conclusion.
4.3 Objective
In your own words, write one brief paragraph (3 to 4 lines) outlining the
purpose(s) of the laboratory experiment. This section may be separate or
included towards the end of the introduction after presenting the reader with the
purpose behind carrying out such an experiment.
4.4 Introduction
This section is intended to present the reader the purpose behind your
experiment or investigation. It begins by familiarizing the reader with historical
developments in this particular field and by mentioning the purpose or
importance of conducting such an investigation. The authors must present the
scope of the experiment in the context of the "real world" and give examples of
practical applications.
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CVG2116 LABORATORY MANUAL Winter 2010
4.5 Theory
This section should briefly provide the reader with the background in order to
understand the framework of the experiment and the principles by which the
theory has been derived and simplified.. Derivations should include equations
numbered in sequence, where all new terms must be identified clearly with the
appropriate symbols and units (if applicable).
4.6 List of Equipment/Apparatus/Materials
This section should be in point form. At least one sketch or photograph of the
main features of the laboratory apparatus is required. Do not forget to label and
number your figure captions accordingly!
4.7 Experimental Procedure/Methodology
This section should be in point form. You may also make a reference to the lab
handout or manual (e.g., “As outlined in the laboratory manual/handout”). Note
and describe any steps taken that were different from the procedure in the
handout.
4.8 Data Collected/Raw Data
In tables (numbered and captioned), show data collected during the experiment.
Columns/row headings should be indicated using the appropriate titles, symbols
and units. This section may be included in an appendix, especially if it contains a
large set of data.
4.9 Calculations
Give a sample/example calculation for all the different types of calculations
performed. Calculations must be performed with SI units, unless otherwise
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CVG2116 LABORATORY MANUAL Winter 2010
specified. Make tables for repeated calculations in the "Results" section. Each
experiment in this manual contains a section describing the procedure for
performing the calculations. Do not forget units and always use appropriate and
consistent significant figures!
4.10 Results
Present all of your results in neat and clear tabular form where graphs should be
used for plots. A plot of the results will usually help you identify the pattern/trend
or the mathematical-physical relationship between the different variables. Give
the tables and graphs concise headings with table/figure numbers. Do not write
numerical results with insignificant digits.
Example:
Measured flume width = 12.7 cm
Measured flow depth = 6.5 cm
Area = 12.7cm x 6.5 cm
= 82.55 cm2 (incorrect)
= 82.6 cm2 (correct)
4.11 Discussion
Refer to the heading "Report" in the individual laboratory handout. You may also
include one paragraph summarizing the theory (no equations are necessary) in
this section. After a complete understanding of the theory behind the experiment,
you should be able to analyze the numerical and graphical results. You should
refer to the results in this section (using the corresponding figure/table number)
and discuss any trend or behavior that you have observed. Remember that the
results may not always fit the theory. You should be able to surmise non-trivial
reasons for deviations. You should indicate the accuracy of the results, as well as
both major and minor causes of error or inaccuracy. You must also state possible
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CVG2116 LABORATORY MANUAL Winter 2010
explanations for discrepancies in your results. Answer all questions outlined in
the laboratory handout.
4.12 Conclusion and Recommendations
Discuss whether the objective(s) have been achieved and state what indication
prompted you to conclude that. Summarize your results and percentage errors,
and comment on the main source of error (if any). If you have an original idea or
concept, you have the full right to claim it as such. However, if you use an idea or
results (not raw data!) from someone else, for example after a discussion with a
classmate, or from a published article, you must indicate that this is the case.
You will not lose marks if you do this judiciously. Simply remember that you are
expected to be able to research and think matters out; copying material from
another group is not acceptable and will not be tolerated! This section of the
report is not to be longer than one page. Keep it brief and concise.
4.13 References
Any literature sources that you have consulted in writing this report (e.g.
laboratory manual, course textbooks, scientific papers, reports, etc) must be
included in this section. Please note that Wikipedia and similar web based
encyclopedias are not considered official references! Please refer to the Guide
for writing Laboratory Reports of the Civil Engineering Department with respect to
article or book citations.
4.14 Appendices
This section (if applicable) should comprise of additional information not included
in the report such as: raw data, computer codes, sample and other calculations,
other tables and figures, other hardcopies, etc.
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CVG2116 LABORATORY MANUAL Winter 2010
B. EXPERIMENTAL SETUPS
Fig 1. Experiment 1 - Pitot Tube Traverse
Fig 2. Experiment 2 – Bernoulli’s Equation
Fig 3. Experiment 3 – Force on a Sluice
Gate
Fig 4. Experiment 4 – Impulse Turbine
Fig 5. Experiment 5 – Pipe Flow Headloss
Fig 6. Experiment 6 – Forced Vortex
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CVG2116 LABORATORY MANUAL Winter 2010
1.0 PITOT TUBE TRAVERSE
1.1 Introduction
A characteristic of a flow which is of fundamental importance in fluid mechanics
is the discharge, also known as flow rate. A basic method of determining flow
rate, which is often used in the laboratory, is to collect a known amount of fluid
expressed as volume, mass or weight in a tank and to measure the time required
to collect it. The volumetric flow rate is then found from the volume collected
divided by the time required to collect it.
The flow rate will depend upon the velocity of the flow. If, for example, there is a
flow of water from the end of a pipe with the same velocity, v0, in all parts of the
flow, an increment of volume, ΔV, will flow out of the pipe in a time increment, Δt,
and is equal to:
0V v A tΔ = Δ (1.1)
The velocity, v0, is the velocity normal to the cross-sectional area, A, of the pipe.
The flow rate, Q, can be expressed as:
0 0lim tdV VQ vdt tΔ →
Δ= = =
ΔA (1.2)
Suppose that the normal velocity varies from point to point throughout the flow.
It would be reasonable to find the flow rate by dividing the area into increments,
multiplying each area by the normal velocity through it, and summing these
partial flow rates. The general expression for the flow rate in this case is the
integral of the normal velocity times the elemental area, dA, over the total cross-
sectional area, A.
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CVG2116 LABORATORY MANUAL Winter 2010
(1.3) nA
Q v d= ∫ A
In this expression vn is the velocity normal to the differential or elemental area,
dA. The average velocity, v , for the entire cross-section can then be defined as,
QvA
= (1.4)
where, A is the total cross-sectional area of the flow.
The Pitot tube, or stagnation tube, which was invented by Henri de Pitot (1695-
1771), can be used to determine the velocity of flow at different points throughout
the flow by measuring the total or stagnation pressure head, pstagnation/γ, and the
static pressure head, pstatic/γ, at a point. The difference between the two pressure
heads is the velocity head, vn2/2g, as shown in the expression below,
2
2stagnation staticn p pv
g γ γ= − (1.5)
where, γ is the specific weight of the flowing fluid.
The most common type of Pitot tube was developed by Ludwig Prandtl (1875-
1973). For this type, the tubes for the total (or stagnation) pressure and the static
pressure measurement are combined into one piece, whereas the openings for
the static pressure measurement are located at the proper point along the body
of the probe to give the same static pressure reading, as if no tube was present.
Proper use of the instrument requires that it be correctly aligned to point directly
(or parallel) into the oncoming flow.
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CVG2116 LABORATORY MANUAL Winter 2010
1.2 Objective
The objective of this experiment is to determine the discharge in a rectangular
channel by measurement of the velocity distribution using a Pitot tube and
comparing it to a weighing method.
1.3 Experimental Procedure
1. Measure the channel width using a metallic ruler.
2. Measure the depth of the flow using the point gauge provided.
3. Lower the Pitot tube to the bottom of the channel and record the vertical
position.
4. Raise the Pitot tube such that it is right below the surface (by about
10mm) and record its vertical position.
5. Subtract the two positions obtained in step 3 and 4, and divide the
difference by 4 to obtain the vertical increment for each flow depth to be
used.
6. Place the Pitot tube on the channel bottom, as close to the wall as
possible (left or right), starting at the lowest position. Keep the tube
aligned with the flow.
7. Record the manometer readings for both the static and total pressure
head.
8. Slide the Pitot tube towards the opposite wall by adding the horizontal
increment specified on the data sheet to the horizontal position, while
recording both manometer readings.
9. Once the manometer readings have been recorded four times (i.e., wall-
to-wall), repeat readings of the Pitot tube at 1/4 depth, 1/2 depth, 3/4
depth, and near the surface by adding the vertical increment to the
vertical location. Please refer to the figure in the data sheet for more
clarification.
10. Measure the flow rate using the tank on the scale at the end of the
channel and a stop watch. Use at least 3 discharge measurements.
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CVG2116 LABORATORY MANUAL Winter 2010
1.4 Calculations
1. Calculate the velocity, v, using Eq. (1.5) at each point where the static and
stagnation pressure heads were measured.
2. Plot each point on a cross section of the flow and label it with the velocity
found there.
3. Draw lines of equal velocity (isovelocity or isovels) as you would draw
contour lines on a topographic map. It is likely that interpolation between
the data points will be required to plot the isovelocity lines. Note: There
are several programs that can do this task (e.g. Surfer, Golden Software).
4. Calculate the mean velocity between each adjacent isovelocity lines and
measure the area between them. Determine the discharge through
adjacent isovelocity lines by multiplying the mean velocity by the area
between them. Then determine the total discharge in the cross-sectional
area by summing the discharge through adjacent isovelocity lines as
indicated in Eq. (1.3).
5. Calculate the flow's mean velocity by dividing the discharge by the total
cross-sectional area.
1.5 Report
Discuss your results including comments on the following points: comparison of
flow rate found by the Pitot tube and weighing methods; variability of velocity in
the cross-section; accuracy of each method; and, distinguishing characteristics of
the method of measurement. Also discuss how this application can be used in
civil engineering field problems.
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CVG2116 LABORATORY MANUAL Winter 2010
PITOT TUBE TRAVERSE
Cross-section of the channel:
Width
Depth
Width W : _________ Depth D : _________ Pitot tube diameter: 4mm N.B. Flow going through the sheet
Left wall
1/3 2/3
1/4
1/2
3/4
Stagnation (or total) and static pressure head (cm or mm) for the cross-section:
Left wall Position: 247mm
1/3 width Position: 288mm
2/3 width Position: 328mm
Right wall Position: 370mm
Bottom Position:
¼ depth Position:
½ depth Position:
¾ depth Position:
Surface Position:
N.B. Increment of ~ 40 mm for horizontal direction and mm for vertical direction.
Flow rate in the tank: Mass in the tank: __________ 1) Starting time: ___________
2) End time: ____________
Time recorded for a given volume in the tank: _______________
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CVG2116 LABORATORY MANUAL Winter 2010
2.0 BERNOULLI’S EQUATION
2.1 Introduction
The Bernoulli equation is an important dynamic relation in fluid mechanics since
it provides a mean for calculating fluid pressures from known velocities and
elevations. The principle of this equation was stated by Daniel Bernoulli (1700-
1782), based upon the conservation of energy principle.
The form of the equation most often used in hydraulics, expresses each
parameter in terms of "heads" as shown below,
2
2p vz
gγ+ + = constant (2.1)
where, p/γ is pressure head.
z is elevation head.
v2/2g is velocity head.
The first two heads are combined to give the piezometric head, h, as shown
below,
ph zγ
= + (2.2)
In the calculations for this experiment some dimensionless plots are required.
An advantage of dimensionless plots is that the results for more than one set of
conditions may be used for other calculation based on similarity laws. Reduced
to non-dimensional terms, the results from many different situations may be able
to be expressed in a single graphical relation. This principle of similarity is very
important in physical modeling in which results from geometrically small scale
tests are applied to a similar situation on a larger scale (also known as
“prototype”).
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CVG2116 LABORATORY MANUAL Winter 2010
2.2 Objective
The objective of this experiment is to apply and validate the Bernoulli equation to
flow in a closed conduit and to observe the energy loss in a Venturi metre.
2.3 Experimental Procedure
1. Establish steady flow in the apparatus when the flow rate is near full
capacity.
2. Make sure that there is no air in the system.
3. Record the water levels in the piezometer tubes (hA to hL). Note: There is
no piezometer/station at “I”. Also, the zero mark on the piezometers scale
is 167mm above the Venturi centerline.
4. Measure the flow rate by weighing as directed by the lab demonstrator.
5. Repeat the process at three lower flow rates.
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CVG2116 LABORATORY MANUAL Winter 2010
2.4 Calculations
Table 2.1: Dimensions of the apparatus (see Figure 7 below)
Station Diameter, φ
(mm)
Area (mm2)
Spacing (mm)
A 25.99 530.5 -
B 23.97 451.3 20
C 18.21 260.4 12
D 15.75 194.8 14
E 16.01 201.3 15
F 17.65 244.7 15
G 19.29 292.2 15
H 20.94 344.4 15
J 22.50 397.6 15
K 24.22 460.7 15
L 26.29 542.8 20
1. Compute the velocity at each station using the continuity equation.
2. For each run, plot h against the distance along the conduit, where h is the
recorded piezometric head. Also plot h + v2/2g (i.e. total pressure head, H)
against the distance along the conduit. Draw curves through these points.
3. Calculate total head, HA, at tube A from the following expression:
2
2A
A AvH hg
= + (2.3)
4. For each of the four runs, compute h/HA. Plot these values (h/HA) for all
stations against the distance along the conduit, all on one graph. Use a
different plotting symbol (legend and/or colour) for each run.
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CVG21
16 LABORATORY MANUAL Winter 2010
17
Discuss your results, referring in particular to the following points:
Fig 7. Dimensions of Venturi meter and positions of piezometer tubes.
Direction of Flow
3. Discuss the uniformity of the flow through the Venturi section and any
deviation from this assumption.
2. Discussion of the components of the Bernoulli equation (p/γ, v2/2g, and z)
and how they vary along the length of the Venturi section. Indicate the
points of maximum velocity and minimum pressure.
1. Existence of an energy loss and how this is shown by the data.
2.5 Report
A B C D E F G H J K L
20 12 14 15 15 15 15 15 15 20
All dimensions in ‘mm’
CVG2116 LABORATORY MANUAL Winter 2010
18
BERNOULLI’S EQUATION
Piezometric head for a given flow rate: hA
[mm] hB
[mm] hC
[mm] hD
[mm] hE
[mm] hF
[mm] hG
[mm] hH
[mm] hJ
[mm] hK
[mm] hL
[mm] Q1 Time: Mass:
Q2 Time: Mass:
Q3 Time: Mass:
Q4 Time: Mass:
CVG2116 LABORATORY MANUAL Winter 2010
3.0 FORCE ON A SLUICE GATE
3.1 Introduction
Many engineering applications of fluid mechanics require the determination of the
force of a flowing fluid on a structural or machine element. This experiment
demonstrates two methods for estimating these forces.
Method 1: Integration of the fluid pressure exerted on a plane surface gives the
component of the fluid force normal to the plane.
nA
F pd= ∫ A (3.1)
Similarly, the force of fluid pressure on a curved surface can be obtained from a
known pressure distribution. The determination of the force by its individual
components may, in this case, be the best procedure; in some cases, the use of
a coordinate system adapted to the curved surface may be advantageous.
The method of integration is a basic technique for finding pressure forces which
can be used whenever the pressure distribution is known, either by
measurement, or by analysis. Also, the point of application of the force (or centre
of pressure) can be found by integrating the moment of the force about the
subject axis.
Method 2: Another convenient method for calculating fluid forces is the
momentum flux equation, which is a basic equation in fluid dynamics.
Consideration here will be restricted to the momentum flux equation in steady
flow; although it is applicable to unsteady flow, its application is more complex
and not as useful in engineering applications.
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CVG2116 LABORATORY MANUAL Winter 2010
For steady flow, the momentum flux equation states that the sum of the external
forces on the fluid within a certain volume, called a control volume, is equal to the
difference between the momentum flux out of the control volume and the
momentum flux into the control volume (i.e., the net rate of change of
momentum). In many cases where the flow rate, Q, is constant, the velocity can
be represented by an average velocity, v, so that this statement can be
expressed as,
( )2 1F Q v vρ= −∑ (3.2)
where, F∑ is the vector sum of the external forces.
1v and are the inflow and outflow velocity vectors within
the control volume, respectively.
2v
The above equation can also be written in component form.
The control volume is usually chosen in a way that simplifies the problem,
keeping in mind what are the known and required quantities.
The momentum equation does not give any information on the point of
application of any of the external forces. Also, when necessary, body forces,
such as the weight of the fluid in the control volume, must be included in the
summation of forces.
3.2 Objective
The main objective of this experiment is to measure the piezometric head at
different points on a gate and to calculate the resultant force acting on the gate
from the pressure distribution. The experimental result will then be compared to
that obtained by the momentum equation.
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CVG2116 LABORATORY MANUAL Winter 2010
3.3 Experimental Procedure
Note: Perform the experiment with the conditions set by the lab instructor. Do not
attempt to change any of these settings!
1. Measure the head over the V-notch weir using the manometer on the side.
2. Ask the lab instructor to adjust the height of the gate opening for the first
condition.
3. Measure the gate opening, δ, using a metallic ruler.
4. Measure the depth of water upstream, Y1, using a metallic ruler. Ensure
that the measurement is recorded as close to the gate as possible.
5. Measure the depth of the water, Y2, downstream of the gate using the
point gauge. These measurements should be made where the depth is
uniform. Use the average of three measured values.
6. Record the manometer readings for the piezometer taps connected to the
gate. Ensure that there is no air in the lines.
7. Ask the lab instructor to set conditions for a second run using a larger gate
opening and then repeat steps 3 through 6.
8. It is convenient to use the channel bottom as a reference datum. To
establish the zero of the manometers, determine the manometer reading
for the tap in the channel bottom and, at the same time, measure the
depth of at one of the tapping points on the channel (i.e., downstream the
gate). Subtract the depth of water from the manometer reading to get the
zero reading of the manometers.
9. Measure the channel width using a metallic ruler.
10. From the demonstrator, obtain the zero reading for the V-notch weir. The
height of the tapping points on the gate with respect to the bottom of the
gate is provided on the data sheet.
3.4 Calculations
1. Find both the stagnation and hydrostatic pressure heads at each tapping
point on the gate.
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CVG2116 LABORATORY MANUAL Winter 2010
stag
p h zγ⎞
= −⎟⎠
(stagnation pressure head) (3.3)
1hydr
p Y zγ⎞
= −⎟⎠
(hydrostatic pressure head) (3.4)
where, h is the measured piezometric head for any manometer;
z is the elevation of the tapping point above channel bottom;
Y1 is the depth of the upstream flow.
2. Plot the pressure head vs. distance above channel bottom for the two
runs. Each run (i.e. gate opening condition) should be on different graphs,
however, a comparison between the stagnation and hydrostatic pressure
head for the same gate opening condition should be carried out on the
same graph. Assume that the stagnation pressure head is zero at the
water surface and at the bottom of the gate (Note: The hydrostatic
pressure head is zero at the water surface only). Draw smooth curves
showing the pressure variation for the stagnation pressure head plot.
3. Find the area under the pressure head curves (for both stagnation and
hydrostatic pressure calculations), apply any scaling factors, and calculate
the normal forces on the gate for the two runs (i.e. for both gate openings).
nA
pF γγ
= ∫ dA
H
(3.5)
4. Use the standard V-notch weir formula to find the flow rate, Q,
(SI units) (3.6) 2.51.365= ΔQ
where ΔH is the head above the V-notch weir.
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CVG2116 LABORATORY MANUAL Winter 2010
5. Using a control volume that includes the water between the uniform flow
sections where the depths were measured, find the force on the gate
using the momentum equation. Be sure to include the hydrostatic forces
on the water at the two ends of the control volume.
3.5 Report
1. Comment on the pressure distribution for the two conditions and compare
the plot obtained from the stagnation pressure head to the hydrostatic
pressure head.
2. Discuss why the pressure distribution shown in your plot differs from the
pressure distribution when the gate is closed. Explain how the gate
opening affects the pressure distribution on the gate.
3. Compare the values of the forces calculated by the two methods.
4. Comment upon the advantages and disadvantages of the two methods.
5. Discuss possible practical applications in calculating forces on structures.
6. List possible sources of errors involved with respect to each method when
determining the force on the gate, as well the sources of error generally
noticed while conducting this experiment.
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CVG2116 LABORATORY MANUAL Winter 2010
FORCE ON A SLUICE GATE
Condition #1: 1) Water surface level in V-notch reservoir, H: ____________
2) Depth of water upstream, Y1: ____________
3) Depth of water downstream, Y2: __________
4) Manometer readings for piezometer taps in the gate, h:
24) ______________
23) ______________
22) ______________
21) ______________
20) ______________
5) Height of the gate opening, δ: _____________
Condition #2: 5) Water surface level in V-notch reservoir, H : ____________
6) Depth of water upstream, Y1: ____________
7) Depth of water downstream, Y2: __________
8) Manometer readings for piezometer taps in the gate, h:
24) _______________
23) _______________
22) _______________
21) _______________
20) _______________
5) Height of the gate opening, δ: _______________
In general: 1) Zero reading of channel bed manometer, h0:___________
2) Measure channel width, w: ________________
3) Height of the taps above gate bottom, zi:
24) 26.67cm_______
23) 13.97cm_______
22) 6.35cm________
21) 3.81cm________
20) 1.27cm_________
4) Zero reading for V-notch weir, H0: 24.2cm______
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CVG2116 LABORATORY MANUAL Winter 2010
4.0 IMPULSE TURBINE
4.1 Introduction
Different types of turbomachinery add or extract energy from flowing fluid.
Despite the many varieties and uses of turbo-machines, fundamental engineering
concerns are related to the calculation of the power input, power output, and
operating efficiency for different operating conditions of flow rate, Q, and
operating speed, n.
In this experiment, measurements for a model impulse turbine, including flow
rate, available water power, output or brake power, and the rotational speed, will
be made. From these measurements the operating characteristics of the turbine
will then be found. These are curves which show the relationships among the
considered variables.
The impulse turbine operates at atmospheric pressure by the force of a high-
speed jet acting on vanes mounted on a wheel. The type of impulse water turbine
used in this experiment is called the Pelton turbine and is essentially a
development of the water wheel. Pelton turbines are used where the head is high
and the flow rate is relatively low.
The jet of an impulse turbine is produced by a needle valve which controls the
flow rate. In prototype turbines, the opening of the valve is adjusted automatically
by speed control devices as the load on the turbine varies. The load on the
turbine is the electrical generator which must rotate at constant speed while
generating electrical current.
Quantities of interest are the following:
1. Flow rate through the turbine, Q.
2. Operating speed, n, usually expressed in rpm (rotations per minute).
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CVG2116 LABORATORY MANUAL Winter 2010
3. Head at the needle valve, H. This head represents the energy available to
the turbine. Available power or power input is expressed as:
inP HQγ= (4.1)
4. Power output or brake power. This is the power transmitted to the shaft by
the turbine. In a test setup it is usually measured by a Prony brake which
is a device used to create and measure the torque on a rotating shaft.
Then the power output can be expressed as,
outP Tω= (4.2)
Where, T is the torque.
ω is the angular speed in rad/s.
5. Efficiency, η
out
in
PP
η = (4.3)
4.2 Objective
The main goal of this experiment is to determine the output characteristics of a
Pelton turbine and evaluate its performance under different operating conditions.
4.3 Experimental Procedure
1. Runs should be taken at 3 different head settings, as obtained by
adjusting the needle valve.
2. For each run, at least 5 different loading conditions should be applied
using the Prony brake (at non-zero rotational speeds).
3. The required measurements are:
a. Pressure head reading on the pressure gauge (H)
b. Discharge over the V-notch weir (Q)
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CVG2116 LABORATORY MANUAL Winter 2010
c. Force on Prony brake indicated by the mercury column (F)
d. Shaft speed measured by the tachometer (n)
4.4 Calculations
1. Use the accompanying calibration curve to correct the pressure gauge
readings for losses in the nozzle.
2. Calculate the power input, power output, and efficiency for each reading.
To obtain the torque, use the given expression,
(4.4) T Fd=
where, d is the torque arm (16.04 cm or 6.315 in).
3. Plot power output and efficiency vs. speed for each head.
4. Plot efficiency vs. power output for each head.
4.5 Report
1. Discuss your results.
2. How do you think model performance (i.e., efficiency) would compare with
prototype performance?
3. Why might a turbine model be less efficient then the prototype?
4. Do the minor losses make any sense in the model?
5. Why does the power decrease as ω increases after the peak is reached?
6. Which of the two graphs in step #3 (of the calculations) has an advantage
over the other in terms of modeling, and why?
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CVG2116 LABORATORY MANUAL Winter 2010
IMPULSE TURBINE
1st head at needle valve: ________
Break #1 Break #2 Break #3 Break #4 Break #5 Brake Force [lbf]
Discharge [cfm]
Shaft speed [rpm]
2nd head at needle valve: ________ Break #1 Break #2 Break #3 Break #4 Break #5 Brake Force [lbf]
Discharge [cfm]
Shaft speed [rpm]
3rd head at needle valve: ________ Break #1 Break #2 Break #3 Break #4 Break #5 Brake Force [lbf]
Discharge [cfm]
Shaft speed [rpm]
Arm brake length: ____________
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CVG2116 LABORATORY MANUAL Winter 2010
CALIBRATION CURVE FOR WATER HEAD GAUGE(IMPULSE TURBINE)
0
10
20
30
40
50
60
70
80
90
100
0 5 10 15 20 25 30 35 40
Pressure, P [PSI]
Feet
of W
ater
(Pre
ssur
e H
ead)
, H [f
t]
Observed Reading True Reading
Example:Observed: 43 ftCorrected: 36.3 ft
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CVG2116 LABORATORY MANUAL Winter 2010
5.0 PIPE FLOW HEADLOSS
5.1 Introduction
Energy must be supplied to fluid flowing in a pipe to overcome the resistance
caused by friction with the pipe walls. At present, the most widely accepted way
of determining this energy loss in pipeflow is the Darcy-Weisbach equation which
is expressed as,
2
2fL vh fD g
= (5.1)
In this equation hf is the head lost to flow resistance, f is the Darcy-Weisbach
coefficient, L is the pipe length, D is the diameter, v is the average velocity, while
g is the gravitational constant.
The Darcy-Weisbach coefficient (or friction factor) is usually assumed to be a
function of the Reynolds number, Re vD vDρ μ ν= ⇒ , and the pipe roughness
height, e or ks, where ρ is the density, μ is the dynamic viscosity and ν is the
kinematic viscosity of the fluid Other factors, such as roughness spacing and
shape, may also affect the value of f; however, these effects have not been well
defined and may be negligible in many cases.
The Moody diagram (refer to the Fluid Mechanics textbook) relates f to the
Reynolds number and the relative roughness (e/D or ks/D) in the most convenient
way. Two commonly used formulas for certain types of flow are shown below,
Laminar flow:
64Re
f = (Hagen-Poiseuille equation) (5.2)
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CVG2116 LABORATORY MANUAL Winter 2010
Turbulent smooth Pipe flow:
1 40.316Re
f = (Blasius equation) (5.3)
5.2 Objective
The objective of this experiment is to measure the head loss in pipes of different
diameters and at different flow rates, as well as to compute experimental values
of the Darcy-Weisbach coefficient, f, and then compare them with theoretical or
accepted values.
5.3 Experimental Procedure
1. After checking with the lab instructor that the apparatus is ready, open the
manometer valves for the first pipe. Be sure the other manometer valves
are closed.
2. Slowly open the discharge valve of the pipe until the maximum flow
possible is established in the pipe. The maximum flow will be determined
by the maximum height of the manometer, or by the fully open valve
position. Allow a few minutes after setting the valve to ensure steady
conditions.
3. Read the water level in the left and right manometers and determine the
flow rate using the level gauge on the volumetric tank at the outlet.
4. Take 4 additional readings at lower flow rates, repeating the manometer
readings and the volumetric rate measurements.
5. Repeat steps 1 through 4 for the other pipes.
6. Record the average temperature of the water during the experiment.
Note: Pipe internal diameters are: 7.6mm, 14.5mm, 20.6mm and 26.8 mm,
volumetric tank area is 0.207 m2 and the distance between the manometer
taps, L, is 2.44 m.
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CVG2116 LABORATORY MANUAL Winter 2010
5.4 Calculations
1. Perform the calculations, listing them in a neat tabular format.
2. Calculate Q in m3/s and v in m/s for each flow condition.
3. Calculate f from the Darcy-Weisbach formula.
4. Find the Reynolds number using the viscosity coefficient corresponding to
the measured temperature.
5. Plot the experimental data for f vs. Re on log-log paper.
6. Show the Hagen- Poiseuille and Blasius equations on the plot.
5.5 Report
1. Discuss your results.
2. Compare your results with the Moody diagram. Indicate any reason for
lack of agreement.
3. What are the physical reasons for different regions on the Moody diagram:
laminar, transition and fully rough (turbulent) flow regions?
4. What natural processes would affect pipe roughness?
Note: The transition zone is very unstable and may extend beyond the region
indicated on the Moody diagram.
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CVG2116 LABORATORY MANUAL Winter 2010
PIPE FLOW HEAD LOSS
Pipe (Internal) Diameter: 26.8mm
Level indicator in tank (h2-h1) or (Δh) [cm]
Time (t) [s]
Left manometer reading (mL) [cm]
Right manometer reading (mR) [cm]
Q1 Q2 Q3 Q4 Q5
Pipe (Internal) Diameter: 20.6mm
Level indicator in tank (h2-h1) or (Δh) [cm]
Time (t) [s]
Left manometer reading (mL) [cm]
Right manometer reading (mR) [cm]
Q1 Q2 Q3 Q4 Q5
Pipe (Internal) Diameter: 14.5mm
Level indicator in tank (h2-h1) or (Δh) [cm]
Time (t) [s]
Left manometer reading (mL) [cm]
Right manometer reading (mR) [cm]
Q1 Q2 Q3 Q4 Q5
Pipe (Internal) Diameter: 7.6mm
Level indicator in tank (h2-h1) or (Δh) [cm]
Time (t) [s]
Left manometer reading (mL) [cm]
Right manometer reading (mR) [cm]
Q1 Q2 Q3 Q4 Q5
Water Temperature: Tank dimensions (Area):
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CVG2116 LABORATORY MANUAL Winter 2010
6.0 FORCED VORTEX
6.1 Introduction
Analysis of fluid flow is often accomplished by simplifying assumptions with
respect to the kinematics of the flow, by assuming simplified patterns of fluid
motion as represented by streamlines. Vortex motion is a basic flow pattern; it is
defined as motion in circular paths.
There are two types of vortices distinguished in the dynamics of the motion and
the resulting velocity distributions. These are forced and free vortices. The forced
vortex is caused by external forces on the fluid such as the impeller of a pump,
whereas the free vortex naturally occurs in the flow and can be observed in a
drain or in the atmosphere in the form of a tornado.
An equation for the forced vortex can be derived (refer to the textbook) by
applying Newton's law to a fluid element and assuming there are no shear
stresses acting on the fluid (i.e., no relative motion between adjacent particles).
The resulting equation can be expressed between two points:
( )2
2 22 1 2 12
h h r rg
ω− = − (6.1)
where, h is the piezometric head.
ω is the rotation in rad/s.
r is the radius.
In this experiment, a forced vortex is created by a rotating plate fitted with blades;
this is very similar to the action of the impeller of a pump.
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CVG2116 LABORATORY MANUAL Winter 2010
6.2 Objective
The objective of this experiment is to study the piezometric head variation in a
forced vortex at different rates of rotation.
6.3 Experimental Procedure
1. Record the initial level in the piezometer tubes. Check whether the same
reading is obtained at both ends of the tube bank. If not, the leveling
screws should be adjusted so that the readings are the same.
2. Turn on the transformer switch.
3. Set the dial at 20. Allow enough time for the levels in the tubes to become
steady. Record the levels on the piezometers.
4. Determine the rotational speed with the tachometer.
5. Repeat steps 5 and 6 for the remainder dial settings. For the highest dial
setting, ensure that none of the piezometer levels are off scale.
6. Set the dial to zero and turn the switch off.
7. Record the distances from the axis of rotation to the piezometer tapping
points.
6.4 Calculations
1. For each run, plot the piezometric head reading against the radial
distance. Draw a smooth curve through the data points, extending it to r =
0 (i.e. y-axis).
2. For each run, plot on graph paper the difference in piezometric head
between each measured value and the value at r = 0, against r2. Draw a
straight line through the points for each run.
3. Find the slope of each line and compare it to its theoretical value from the
given equation:
2
2
0 2p pz z
gω
γ γ⎛ ⎞
+ − + =⎜ ⎟⎝ ⎠
r (6.2)
where, p zγ+ is the piezometric head;
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CVG2116 LABORATORY MANUAL Winter 2010
0
p zγ
⎛+⎜
⎝ ⎠
⎞⎟ is the piezometric head at r = 0.
Note: The gear ratio is 1:7.
6.5 Report
1. Provide the comparisons indicated in step 3 of the calculations and
discuss them.
2. Discuss briefly the practical applications of the forced vortex.
3. Compare the equation of the forced vortex [Eq. (6.2)] to the Bernoulli
equation in terms of:
a. Assumptions
b. Flow characteristics and streamlines
c. External pressure forces
d. Derivation
Combining both equations yields an important law of conservation. Are the
two equations the same?
4. Compare the theoretical with experimental values of the angular speed, ω,
obtained from step 3 of the calculations.
5. Comment on the possible sources of error (e.g., variance from ideal vortex
motion).
Note: The sampling ports are below the drive disk.
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CVG2116 LABORATORY MANUAL Winter 2010
FORCE VORTEX
Initial level of piezometer tubes Tube
1 Tube
2 Tube
3 Tube
4 Tube
5 Tube
6 Tube
7 Tube
8 Tube
9 Tube
10 Head pressure [in]
Piezometer pressure head for a given motor speed Tube
1 Tube
2 Tube
3 Tube
4 Tube
5 Tube
6 Tube
7 Tube
8 Tube
9 Tube
10 Speed [rpm]
Head pressure [in] Dial 20
Head pressure [in] Dial 30
Head pressure [in] Dial 40
Head pressure [in] Dial 50
Head pressure [in] Dial MAX:60
Distance of pressure taps from tank centerline Tube
1 Tube
2 Tube
3 Tube
4 Tube
5 Tube
6 Tube
7 Tube
8 Tube
9 Tube
10 Distance [in]
Gear ratio: 1:7
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CVG2116 LABORATORY MANUAL Winter 2010
C. REFERENCES
Beatriz, M.P. (2006). Guide for Writing Laboratory Reports, Department of Civil Engineering, University of Ottawa, Ottawa, Canada, September 2003 (rev. August 2006).
Daugherty, R.L. and Franzini, J.B. (1979). Fluid Mechanics with Engineering Applications, 7th Edition, McGraw-Hill Inc, New York, N.Y.
Streeter, V.L. and Wylie, E.B. (1985). Fluid Mechanics, 8th Edition, Mcgraw-Hill College, New York, N.Y.
Vennard, J.K. and Street, R.L. (1982). Elementary Fluid Mechanics, 6th Edition, John Wiley & Sons Inc, New York, N.Y.
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