Laboratory Manual

DEPARTMENT OF CIVIL ENGINEERING

UNIVERSITY OF OTTAWA

Mahmoud Al-Riffai and Ioan Nistor

CVG2116

INTRODUCTORY FLUID MECHANICS LABORATORY

LABORATORY MANUAL

1. PITOT TUBE TRAVERSE

3. FORCE ON A SLUICE GATE

5. PIPE FLOW HEADLOSS

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

ii


1


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".

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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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):

3


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

4.5 Theory

Winter 2010

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!

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.

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

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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Fig 1.

Experiment 1 - Pitot Tube Traverse Fig 4.

Experiment 4 – Impulse Turbine

Fig 2.

Experiment 2 – Bernoulli’s Equation Fig 5.

Experiment 5 – Pipe Flow Headloss

Fig 3.

Experiment 3 – Force on a Sluice

Gate

Fig 6.

Experiment 6 – Forced Vortex

8


1.0 PITOT TUBE TRAVERSE


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, v

0

, in all parts of the flow, an increment of volume,

Δ

V , will flow out of the pipe in a time increment,

Δ t , and is equal to:

Δ = Δ

(1.1)

The velocity, v

0

, is the velocity normal to the cross-sectional area, A , of the pipe.

The flow rate, Q , can be expressed as:

Q

= dV dt

= lim t 0

Δ

V

Δ t

= v

0

A (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 crosssectional area, A .

9


Q

= v d

A

∫

A (1.3)

In this expression v n

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, v

=

Q

A

(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, p stagnation

/

γ

, and the static pressure head, p static

/

γ

, at a point. The difference between the two pressure heads is the velocity head, v n

2

/2g , as shown in the expression below, v n

2

2 g

= p stagnation

γ

− p static

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.

10


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. 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.

, wallto-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.

11



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.

12


PITOT TUBE TRAVERSE

Cross-section of the channel:

1/3 2/3

3/4

Depth

1/2

1/4

Width W : _________

Depth D : _________

Pitot tube diameter: 4mm

N.B. Flow going through the sheet

Left wall

Width

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: _______________

13



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,

γ p z v

2

+ + = constant (2.1)

2 g where, p/

γ

is pressure head. z is elevation head. v

2

/2g is velocity head.

The first two heads are combined to give the piezometric head, h , as shown below, h

=

γ p

+ z (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”).

14


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.

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 ( h

A

to h

L

). 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.

15



Table 2.1: Dimensions of the apparatus (see Figure 7 below)

Station

Diameter,

φ

(mm)

Area

(mm

2

)

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

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 + v

2

/2g ( i.e.

total pressure head, H ) against the distance along the conduit. Draw curves through these points.

3. Calculate total head, H

A

, at tube A from the following expression:

H

A

= h

A

+ v

2

2

A g

(2.3)

4. For each of the four runs, compute h/H

A

. Plot these values ( h/H

A

) 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.

16

CVG21 16 LABORATORY MANUAL Winter 2010

All dimensions in ‘mm’

Direction of Flow

A B C D E F G H J K L

20 12 14 15 15 15 15 15 15 20

Fig 7.

Dimensions of Venturi meter and positions of piezometer tubes.

2.5 Report

Discuss your results, referring in particular to the following points:

1. Existence of an energy loss and how this is shown by the data.

2. Discussion of the components of the Bernoulli equation ( p/

γ

, v

2

/2g , and z ) and how they vary along the length of the Venturi section. Indicate the points of maximum velocity and minimum pressure.

3. Discuss the uniformity of the flow through the Venturi section and any deviation from this assumption.

17


Piezometric head for a given flow rate: h

A

[mm] h

B

[mm] h

C

[mm]

BERNOULLI’S EQUATION h

D

[mm] h

E

[mm] h

F

[mm] h

G

[mm]

Q

3

Time:

Mass:

Q

4

Time:

Mass:

Q

1

Time:

Mass:

Q

2

Time:

Mass: h

H

[mm] h

J

[mm] h

K

[mm] h

L

[mm]

18


3.0 FORCE ON A SLUICE GATE


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.

F n

=

A

∫

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.

19


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,

∑

JG

F

= ρ

( JJG JJG

2

− v

1

)

(3.2) where,

∑

F is the vector sum of the external forces.

JJG v

1 and

JJG v

2 are the inflow and outflow velocity vectors within the control volume, respectively.

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.

20


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, Y

1

, using a metallic ruler. Ensure that the measurement is recorded as close to the gate as possible.

5. Measure the depth of the water, Y

2

, 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.


1. Find both the stagnation and hydrostatic pressure heads at each tapping point on the gate.

21


γ p

⎞

⎟ stag h z (stagnation pressure head)

γ p

⎞

⎠ hydr

=

Y

1

− z (hydrostatic pressure head)

(3.3)

(3.4)

where, h is the measured piezometric head for any manometer; z is the elevation of the tapping point above channel bottom;

Y

1

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).

F n

= γ

A

∫

γ p dA (3.5)

4. Use the standard V-notch weir formula to find the flow rate, Q ,

Q

=

1.365

Δ

H

2.5

( SI units ) (3.6) where

Δ

H is the head above the V-notch weir.

22


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.

23


FORCE ON A SLUICE GATE

Condition #1:

1) Water surface level in V-notch reservoir, H : ____________

2) Depth of water upstream, Y

1

: ____________

3) Depth of water downstream, Y

2

: __________

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, Y

1

: ____________

7) Depth of water downstream, Y

2

: __________

8) Manometer readings for piezometer taps in the gate, h :

24) _______________

23) _______________

22) _______________

21) _______________

In general:

20) _______________

5) Height of the gate opening,

δ

: _______________

1) Zero reading of channel bed manometer, h

0

:___________

2) Measure channel width, w : ________________

3) Height of the taps above gate bottom, z i

:

24) 26.67cm_______

23) 13.97cm_______

22) 6.35cm________

21) 3.81cm________

20) 1.27cm_________

4) Zero reading for V-notch weir, H

0

: 24.2cm______

24



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 highspeed 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, , usually expressed in rpm (rotations per minute).

25


3. Head at the needle valve, H . This head represents the energy available to the turbine. Available power or power input is expressed as:

P in

= γ

HQ (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,

P out

=

T

ω

(4.2)

Where,

η

T is the torque.

ω

is the angular speed in rad/s.

η =

P out

P in

(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.

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 )

26

CVG2116 LABORATORY MANUAL Winter 2010 c. Force on Prony brake indicated by the mercury column ( F ) d. Shaft speed measured by the tachometer ( n )


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,

T

=

Fd (4.4)

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?

27


IMPULSE TURBINE

1 st

head at needle valve: ________

Break #1 Break #2 Break #3 Break #4 Break #5

Brake Force

[lbf]

Discharge

[cfm]

Shaft speed

[rpm]

2 nd



Brake Force

[lbf]

Discharge

[cfm]

Shaft speed

[rpm]

3 rd



Brake Force

[lbf]

Discharge

[cfm]

Shaft speed

[rpm]

Arm brake length: ____________

28

CVG2116 LABORATORY MANUAL

CALIBRATION CURVE FOR WATER HEAD GAUGE

(IMPULSE TURBINE)

100

Winter 2010

90

80

70

60

50

20

10

40

30

0

0

Example:

Observed: 43 ft

Corrected: 36.3 ft

5 10 15 20

Pressure, P [PSI]

25

Observed Reading

29

30

True Reading

35 40


5.0 PIPE FLOW HEADLOSS


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, h f

= f

L v

2

(5.1)

In this equation h f

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

= ρ vD

μ ⇒ vD

ν

, and the pipe roughness height, e or k s

, 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 k s

/D ) in the most convenient way. Two commonly used formulas for certain types of flow are shown below,

Laminar flow: f

=

64

Re

(5.2)

30


Turbulent smooth Pipe flow: f

=

0.316

Re 1 4

(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.

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 m

2

and the distance between the manometer taps, L , is 2.44 m.

31



1. Perform the calculations, listing them in a neat tabular format.

2. Calculate in m

3

/s and v in m/s for each flow condition.

3. Calculate 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.

32


PIPE FLOW HEAD LOSS

Pipe (Internal) Diameter: 26.8mm

Level indicator in tank

(h

2

-h

1

) or (

Δ h) [cm]

Time (t)

[s]

Left manometer reading (m

L

) [cm]

Q

1

Q

2

Q

3

Q

4

Q

5



(h

2

-h

1

) or (

Δ h) [cm]

Time (t)

[s]

Q

1

Q

2

Q

3

Q

4


L

) [cm]

Right manometer reading (m

R

) [cm]


R

) [cm]

Q

5

Q

1



(h

2

-h

1

) or (

Δ h) [cm]

Time (t)

[s]

Q

2

Q

3

Q

Q

4

2

Q

3

Q

5



(h

2

-h

1

) or (

Δ h) [cm]

Time (t)

[s]

Q

1

Q

4

Q

5

Water Temperature:


L reading (m

L

) [cm]

Left manometer

) [cm]

Tank dimensions (Area):


R

) [cm]


R

) [cm]

33



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: h

2

− h

1

=

ω 2

2 g

( r

2

2 − r

1

2

)

(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.

34


6.2 Objective

The objective of this experiment is to study the piezometric head variation in a forced vortex at different rates of rotation.

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.


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 r

2

. 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:

γ p z

⎛

⎝

γ p

+ z

⎞

⎟

0

=

ω

2

2 g r

2 (6.2) where,

γ p

+ z is the piezometric head;

35


Note: The gear ratio is 1:7.

⎛

⎝

γ p

+ z

⎞

⎠

0 is the piezometric head at r = 0.

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.

36


FORCE VORTEX

Initial level of piezometer tubes

1 2 3

Tube

4

Tube

5

Tube

6

Head pressure

[in]

Piezometer pressure head for a given motor speed

1 2 3

Tube

4

Tube

5

Tube

6

Tube

7

Tube

7

Tube

8

Tube

8

Tube

9

Tube

9

Tube

10

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

1 2 3

Tube

4

Tube

5

Distance

[in]

Gear ratio: 1:7

Tube

6

Tube

7

Tube

8

Tube

9

Tube

10

37


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.

38

Laboratory Manual

DEPARTMENT OF CIVIL ENGINEERING

UNIVERSITY OF OTTAWA

Mahmoud Al-Riffai and Ioan Nistor

CVG2116

INTRODUCTORY FLUID MECHANICS LABORATORY