LABORATORY MANUAL FLUID MECHANICS LAB

 
Figure: Bernoulli’s Principle applied to a pipe of varying cross section.

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Department of College of Electrical &
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FLUID MECHANICS LAB

Laboratory Manual

Department of Mechanical Engineering (DME), College of

Electrical and Mechanical Engineering (CEME), National
University of Sciences and Technology (NUST)

 
Copyright © 2020 CEME Publishing. All rights reserved.
No part of this publication may be reproduced, stored in a retrieval system, distributed,
or transmitted, in any form or by any means without the prior written permission of author.
For permission and licensing requests, contact DME, CEME.
 i 
 

LABORATORY ACADEMIC HONOR CODE

SECTION 1. STATEMENT OF PURPOSE

The faculty and administration of the College of E&ME believes the fundamental objective
of the Institute is to provide the students with a high-quality education while developing
in them a sense of ethics and social responsibility. We believe that trust is an integral part
of the learning process and that self-discipline is necessary in this pursuit. We also
believe that any instance of dishonesty hurts the entire community. It is with this in mind
that we have set forth a student Honor Code at Fluid Mechanics Lab.

SECTION 2. OBJECTIVES

An Academic Honor Code at this laboratory aims to cultivate a community based on

trust, academic integrity, and honor. It specifically aims to accomplish the following:

 Ensure that students understand that academic dishonesty is a violation of the

profound trust of the entire academic community;
 Ensure that students understand that the responsibility for upholding academic
honesty at this laboratory lies with them;
 Prevent any students from gaining an unfair advantage over other students through
academic misconduct;
 Clarify what constitutes academic misconduct among students at this laboratory
and what is expected of them by the Institute, the faculty, and their peers;
 Cultivate an environment where academic dishonesty is not tolerated among the
students;
 Secure a centralized system of education and awareness of the Honor Code;

SECTION 3. STUDENT RESPONSIBILITIES

Students are expected to act according to the highest ethical standards. The immediate
objective of an Academic Honor Code is to prevent any student from gaining an unfair
advantage over other students through academic misconduct. Such acts include but are not
be limited to the following:
 Unauthorized Access: Possessing, using, or exchanging improperly acquired
written or verbal information in the preparation of a laboratory report, examination,
or other academic assignment.
 Unauthorized Collaboration: Unauthorized interaction with another Student or
Students in the fulfillment of academic requirements.
 Plagiarism: Submission of material that is wholly or substantially identical to that
created or published by another person or persons, without adequate credit
notations indicating the authorship.
 False Claims of Performance: False claims for work that has been submitted by an
another student.
 Grade Alteration: Alteration of any academic grade or rating so as to obtain

 
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unearned academic credit.

 Deliberate Falsification: Deliberate falsification of a written or verbal statement of
fact to a Laboratory Engineer, so as to obtain unearned academic credit.
 Distortion: Any act that distorts or could distort grades or other academic records.

While these acts constitute assured instances of academic misconduct, other acts of
academic misconduct may be defined by the Laboratory Engineer. Students must sign the
Academic Honor Agreement affirming their commitment to uphold the Honor Code before
becoming a part of this laboratory. The Honor Agreement may reappear on exams and other
assignments to remind Students of their responsibilities under the Laboratory Academic
Honor Code.

Student Signature

Dated

 
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LIST OF SYMBOLS / ABBREVIATIONS:

psi Pounds per square inch

K Loss Coefficient

N Force (in Newtons)

C Coefficient of Discharge

Cc Coefficient of Contraction

Cv Coefficient of Velocity

Cd Coefficient of Discharge (Orifice Meter)

Re Reynolds Number

f Friction Factor

H Pressure head

Q Volumetric Flow Rate

BEP Best Efficiency Point

 
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SAFETY PRECAUTIONS:
1. Do not operate any machine unless you have been trained to do so and authorized by
the Lab OIC/Incharge.

2. Do not touch any part of the machine until you are sure that the machine is properly
shutdown.

3. Do not touch, oil, adjust, calibrate while the machine is running.

4. Wear goggles and safety gloves if required.

5. Do not wear loose clothes while working close to the machine.

6. Focus on the experiment and avoid distractions.

7. In case of any emergency switch off the power supply and report to your OIC.

8. In case of burning fire, use sand and water.

9. In case of electric fire, switch off immediately and then use only sand.

 
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OUTCOME BASED EDUCATION (OBE):

Outcome Based Education (OBE) system is based on the Washington Accord, the purpose of
which is to regulate the engineering education programs in participating educational
institutions by specifying a set of guidelines on which students can be evaluated. These
guidelines are developed for each individual program and can vary based on the program
content. The main parts of the OBE system are classified as;

i. Program Educational Objectives (PEOs)

ii. Program Learning Outcomes (PLOs)
iii. Course Learning Outcomes (CLOs)
iv. Key Performance Indicator (KPI)
v. Assessment
vi. Continual Quality Improvement (CQI)

A brief description of these terminologies is given below;

Program Educational Objectives (PEOs)

•Program educational objectives are broad statements that describe the career and professional
accomplishments that the program is preparing graduates to achieve. The assessment will
begin after at least 5 years of graduation.

Program Learning Outcomes (PLOs)

•Statement that describe what students are expected to know and able to perform or attain by
the time of graduation in terms of skills, knowledge and behavior/ attitude that the student
acquire after following the program.

Course Learning Outcomes (CLOs)

•CLOs describe the specification of what a student should learn as the result of a period of
specified and supported course.

Key Performance Indicator (KPI)

•KPI is a minimum target/ goal set for a specific assessment. It is represented either in a
normalized value (0.0 to 1.0) or in percentage (%).

Assessment
•Assessment is the formative and/ or summative determination for a specific purpose of the
student’s competence in demonstrating a specific outcome. It is also the processes that
identify, collect, use and prepare data that can be used to evaluate achievement of CLOs,
PLOs, and PEOs.
 
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Continual Quality Improvement (CQI)

•It focuses on closing the loop of an assessment process. CQI will provide suitable actions in
improving the quality of CLOs, PLOs, and PEOs according to targeted KPI.

Engineering Knowledge is divided into three domains which are evaluated in an OBE based
system, these are:
i. Cognitive Domain
ii. Psychomotor Domain.
iii. Affective Domain.

Cognitive Domain involves intellectual activities, these include the classroom discussions in
simple words, the evaluation is based on what the student knows after studying the subject.

Psychomotor Domain involves motor and psychological responses of a student, in simple

words, the evaluation is based on what the student is able to perform under supervision.

Affective Domain involves the emotional beliefs, values and attitudes of the students which
are then evaluated under controlled conditions.

Further information on OBE evaluation system will be disseminated by the respective course
instructor(s) from time to time and as deemed necessary.

 
 

TABLE OF CONTENTS
List of Experiments:
1. Introduction to the lab equipment, layout and the safety precautions.

2. Hydraulic Bench:
To understand the working of hydraulic bench and to measure the flow rate.

3. Flow through an Orifice:

(a) To determine the contraction, velocity and discharge coefficients (Cc, Cv and Cd)
for a sharp edged orifice.
(b) To determine the relationship between flow rate and head drop across the orifice
and to demonstrate that the discharge coefficient is constant over a range of flow
conditions.

4. Flow through a Venturimeter:

(a) To determine the coefficient C of a venturi meter by comparing the measured flow
rate with the ideal flow rate.
(b) To measure the pressure distribution along the meter and compare it with the
ideal pressure distribution.

5. Flow over a Weir:

(a) To determine the discharge coefficient C for rectangular and vee notch by
comparing the measured flow with the ideal flow.
(b) To determine the relationship between head H and flow rate Q over rectangular and
vee notches (weirs).

6. Impact of a Jet:
(a) To measure the force produce by a water jet when it strikes two types of vane: a
flat plate and a hemispherical cup.
(b) To compare the results with the theoretical values calculated from the moment flux
in the jet.

7. Pelton Turbine:
Determination of torque produced using a Pelton wheel.

8. Flow through a straight pipe:

(a) To demonstrate the existence of laminar and turbulent flow and to establish the
value of Reynolds number for transition from laminar to turbulent flow.
(b) For the laminar flow regime, to use Poiseuille’s equation to calculate the coefficient
of viscosity .

 
 

(c) To determine the variation of friction factor ‘f’ in the laminar and turbulent flow
regimes.

9. Losses in Pipe Bends:

(a) To determine the relationship between total head loss and flow rate for pipe bends
and other common fittings.
(b) To determine the loss coefficient K for each fitting and to compare the results
with standard data.

10. Pipe Flow Visualization in Laminar and Turbulent Regimes:

To visualize the difference between laminar and turbulent pipe flow.

11. Stability of a Floating Body:

(a) To determine how the stability of a rectangular pontoon is affected by altering the
vertical position of its center of gravity.
(b) To demonstrate how the metacentric height can be used as a measure of the
stability.
(c) To determine the height of the metacentric and compare this with the theoretical
value.

12. Determination of Hydrostatic Pressure:

To determine the hydrostatic pressure.

13. Calibration of a pressure gage:

To study and implement the calibration procedure of a pressure Gauge.

14. Free and a Forced Vortex:

To study the surface profiles and shapes of free & forced vortexes and to plot the
relation between surface profiles and speed under different conditions.

15. Wind Tunnel:

To understand the working of the wind tunnel.

 
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Introduction to the Lab

This course is a foundation to many theoretical and practical aspects that allow students to
understand the fundamental concepts of fluid mechanics. This lab familiarizes the student with
the practical aspects of topics such as hydrostatic force on a submerged body, flow through
various devices, pipe flow, and rotational flow regimes like a vortex.

LEARNING OUTCOMES:
Upon successful completion of the course, the student will demonstrate competency by being
able to:

1. Comprehend the fluid behavior for internal and external flows.

2. Analyze the flow through different devices and come up with the relevant
equations.
3. Demonstrate practical knowledge about key fluid mechanics concepts by
performing experiments.

PRACTICAL APPLICATION:
At the end of this course student will be able to understand key aspects of fluid mechanics.
They will have understanding of the various fluid flow regimes and will be able to practically
analyze the various fluid mechanics problems.

 
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EXPERIMENT # 1: INTRODUCTION TO THE LAB EQUIPMENT,

LAYOUT AND THE SAFETY PRECAUTIONS

Lab Layout:

 
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Safety Precautions:

 
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EXPERIMENT # 2: DESCRIPTION OF HYDRAULIC BENCH

Objective:

To understand the working of hydraulic bench and to measure the flow rate.

Theoretical Background:

The Hydraulic bench provides facilities for performing a number of experiments. A small
centrifugal pump, drawing water from the water sump, which lies below the pump, delivers to
apparatus placed on the top of the bench. The flow rate is controlled by the valve, and is measured
by collecting water in the weigh tank. The weigh tank is supported beneath the bench to one end
of the weigh beam. The other end of the weigh beam projects slightly from the bench support, and
carries a weight hanger, sufficient to balance the dry weight of the tank, plus a small amount of
water. An operating lever, adjusted to weigh hanger, may be set in either the standby mode or the
weighing model. In the standby mode, a drain valve at the base of the weigh tank is opened
automatically, so alloying the contents to be emptied back to the sump.

Hydraulic Bench

To find the rate of discharge, the lever is moved to the weighing mode. This allows the free end of
the weighing beam to drop to its lower stop, there by closing the drain valve. Water then starts to
accumulate steadily in the weigh tank, so there comes a time when the weighing beam rises to its
upper stop. A stop clock is started at this instant. A known weigh is then added to hanger, so
returning the beam to its lower position. The stop watch is stopped when the beam rises to its upper
stop for a second time. The lever ratio of the weighing beam is 3: 1, so the weight of the water
collected in the time interval is three times the added weight. The flow rate(Kg/Sec) can be
calculated by dividing that weight by the time measured by the stop watch.

 
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Observations and Calculations:

1. Mass flow rate bench:

Time (s) (Q = V/t)

S Weight on Hangar Mass of Water Volume
No (kg) (kg) (m3) (m3/s)

2. Volumetric flow rate bench:

S Volume (Liters) Volume (m3) Time (s) (Q = V/t)

No (m3/s)

Conclusions:

 
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Notes:

 
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EXPERIMENT # 3: FLOW THROUGH AN ORIFICE

Objective:

1. To determine the contraction, velocity and discharge coefficients (Cc, Cv and Cd) for a sharp
edged orifice.
2. To determine the relationship between flow rate and head drop across the orifice and to
demonstrate that the discharge coefficient is constant over a range of flow conditions.

Applications of orifice:

There are several reasons you might want to install a restrictive device or orifice in a piping
system.

 To create a false head for a centrifugal pump, allowing you to run the pump close to its
BEP.
 To increase the line pressure.
 To decrease the flow through a line.
 To increase the fluid velocity in a line.

Apparatus: -
Orifice meter.

 
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Theory: -

An Orifice is an opening in a vessel through which the liquid flows out.

Orifice meter is used to measure the discharge through pipe. An orifice meter, in its
simplest form consists of a plate having a sharp edge circular hole known as an orifice. This plate
is fixed inside a pipe as shown.

Vena Contracta: -
It has been observed, that the jet, after leaving the orifice, gets contracted. The
maximum contraction takes place at a section slightly on the downstream side of the orifice, where
the jet is more or less horizontal. Such a section is known as Vena Contracta as shown.
Section 1 Section 2

HYDRAULIC COEFFICIENTS: -
a) Coefficient of Contraction: -
Cc = Area of jet at Vena Contracta
Area of Orifice

b) Coefficient of Velocity: -

 
 9 
 

Cv = Actual velocity of jet at Vena Contracta

Theoretical velocity of jet

c) Coefficient of Discharge: -
Cd = Actual Discharge
Theoretical Discharge

= Actual Velocity x Actual Area .

Theoretical Velocity x Theoretical Area

= Actual Velocity x Actual area

Theoretical Velocity Theoretical area

Cd = Cv x Cc

We can predict the velocity at the orifice using the Bernoulli equation. Apply it along the
streamline joining point 1 on the surface to point 2 at the center of the orifice.

P1+ρ (u12/2) + ρgz1 = P2+ρ (u22/ 2) + ρgz2_____(1)

At the surface velocity is negligible (u1 = 0) and the pressure atmospheric (p1 = 0). At the orifice
the jet is open to the air so again the pressure is atmospheric (p = 0). The eq1 will transform to

ρgz1 = ρ (u22/ 2) + ρgz2

The density ρ will be cancelled. If we take the datum line through the orifice then z1 = h and z2
=0, putting all these values in the above equation we will get

___________(2)

This is the theoretical value of velocity. Unfortunately, it will be an over estimate of the real
velocity because friction losses have not been taken into account. To incorporate friction, we use
the coefficient of velocity to correct the theoretical velocity,

 
 10 
 

Each orifice has its own coefficient of velocity; It usually lies in the range of (0.97 - 0.99)

To calculate the discharge through the orifice we multiply the area of the jet by the velocity. The
actual area of the jet is the area of the vena contracta not the area of the orifice. We obtain this
area by using a coefficient of contraction for the orifice

So the discharge through the orifice is given by

Where Cd is the coefficient of discharge, and Cd = Cc Cv

 
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Method: -
1. Stand the apparatus on the top of the hydraulics bench and connect the bench supply hose
to the inlet pipe diffuser to about 30mm below the top of the overflow pipe.
2. Connect a hose to the overflow pipe and push the other end of the hose into the drain hole
in the bench top.
3. Position the apparatus so that the orifice is directly above the pipe leading to the bench
weighing tank.
4. Switch on the bench pump and open the flow control valve to supply water to the apparatus.
5. When the water level has risen to the top of the overflow pipe, adjust the flow control valve
to obtain a overflow pipe. This will ensure a constant water level in the tank.
6. Determination of Cc and Cv. Set the traverse mechanism so that the sharp blade will pass
through the water jet emerging from the orifice.
7. Traverse the blade or pitot tube to intersect one edge and then the opposite edge of the jet.
Record the lead screw reading at each point (the lead screw has I thread per mm and each
division on the hand nut represents 0,1mm)
8. Now set the pitot tube in the center of the water jet. From the manometers on the side of
the tank, read the pitot head  hp and the head  h across the orifice.
9. Measure the flow rate through the orifice by quantity of water in the bench weighing tank.
10. Record the diameter d of the orifice (this is given on the apparatus)
11. Carefully reduce the flow rate to the tank so that the head h is reduced by about 10%
Adjust the inlet pipe to keep the diffuser about 30mm below the water.
12. When the water in the tank has settled to a constant level, read the exact value of head and
measure the flow rate through the orifice.
Repeat (11) and (12) until you have about 8 sets of readings over a range of flow rates.

 
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Observations:

Diameter of the orifice (d) = mm = m

Area of orifice (A orifice ) = d2 / 4 = m

Tank piezometer reading (∆h) = mm m

Coefficient of contraction:

Lead screw reading on left side of the jet ( L1) = mm

Lead screw reading on right side of the jet (L2) = mm

Difference = diameter of jet (L1 – L2) = mm

Or (L1 – L2-dia meter of pitot tube) = mm

Coefficient of contraction:

Coefficient of contraction( Cc ) = (dc / d) 2 =

Cc =
Coefficient of Velocity:

As from equation 2 we have

U2 = (2gh) ½
So we will take the readings of velocity in terms of water head.
U2 actual = ( 2g∆hp ) ½
U2 theoretical = ( 2g∆h ) ½
Coefficient of velocity = Cv = (U2 actual / U2 theoretical ) = ( 2g∆hp ) ½ / ( 2g∆h ) ½
By simplifying the above equation, we get
________
Cv =√ (∆hp / ∆h)

Pitot tube reading = ∆hp = m

__________
Coefficient of Velocity = Cv = √ (∆hp / ∆h)
Cv

Coefficient of Discharge:

Mass of water collected = M Kg

Volume of water collected = V = M/ ρ = M / 1000 m3
Time taken = t sec
Volume Flow rate = Q=V/t= m3 / s

 
 13 
 

From the equation Q = Cd A orifice √ 2g∆h

Where Cd = ( Q ACT / Q TH)
Then by rearranging the above equation we get

Cd = Q .
A orifice √ 2g∆h
Variation of Flow Rate with Head:

M V T ∆h Q x 10-4 √∆h Cd
(Kg) (m3) (s) (m) (m3 / s) m½

Avg Cd =

Actual Coefficient of discharge = Cd ACT =

Theoretical coefficient of Discharge = Cd TH = Cv x Cc

% Error = ( Cd TH - Cd ACT / Cd TH ) x 100

Now write a brief summary of what you have learnt from the experiment. When writing
your conclusions, it may help you to think about the following questions:

i. Do your results show that Bernoulli’s equation can be applied with reasonable accuracy?
ii. Is the approach velocity really negligible?
iii. Is Cd constant over the range of flow rate?
iv. How accurate are your results?

 
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Conclusion:

Plot √∆h against Q x 104 (m3 / s):

 
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Notes:

 
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EXPERIMENT # 4: FLOW THROUGH A VENTURI METER

Objective.

1. To determine the coefficient C of a Venture Meter by comparing the measured flow rate
with the ideal flow rate.
2. To measure the pressure distribution along the meter and compare it with the ideal pressure
distribution.

Apparatus: -
Venturi Meter.

Theory:-

A Venturi meter is an apparatus for finding out the discharge of a liquid flowing in a pipe.
A venture meter, in its simplest form, consists of the following three parts:
(a). Convergent cone (b). Throat (c). Divergent cone.

 
 17 
 

A Venturi meter

Applying Bernoulli along the streamline from point 1 to point 2 in the narrow throat of the
Venturi meter we have

By the using the continuity equation we can eliminate the velocity u2,

Substituting this into and rearranging the Bernoulli equation we get

 
 18 
 

To get the theoretical discharge this is multiplied by the area. To get the actual discharge taking
in to account the losses due to friction, we include a coefficient of discharge

This can also be expressed in terms of the manometer readings

Thus the discharge can be expressed in terms of the manometer reading::

Notice how this expression does not include any terms for the elevation or orientation (z1 or z2) of
the Venturimeter. This means that the meter can be at any convenient angle to function.

 
 19 
 

The purpose of the diffuser in a Venturi meter is to assure gradual and steady deceleration after
the throat. This is designed to ensure that the pressure rises again to something near to the original
value before the Venturi meter. The angle of the diffuser is usually between 6 and 8 degrees. Wider
than this and the flow might separate from the walls resulting in increased friction and energy and
pressure loss. If the angle is less than this the meter becomes very long and pressure losses again
become significant. The efficiency of the diffuser of increasing pressure back to the original is
rarely greater than 80%.

 
 20 
 

Method.

1. Stand the apparatus on top of the hydraulics bench. Connect the bench supply hose to the
inlet pipe and secure to with a hose clip. Connect a hose to the outlet pipe and put the other
end of the hose into the hole leading to the bench weighing tank.
2. Open the outlet valve, then switch on the bench pump and open the bench supply valve to
admit water to the apparatus.
3. Partly close the outlet valve so that water is driven into the manometer tubes. Then carefully
close both valves so that you stop the flow whilst keeping the levels of ware in the
manometers somewhere within the range of the manometer scale.
4. Level the apparatus by adjusting the leveling the screws until the manometers each read
the same value.
5. Open both valves and carefully adjust each one in turn until you obtain the maximum
differential reading (h1-h2) whilst keeping all the water levels within the range on the
manometer scale. If necessary, adjust the general level by pumping air into the reservoir or
releasing air from it
6. Record all of the manometer readings and measure the flow rate by timing the collection
of water in the bench weighing tank.
7. Partly close the outlet valve to reduce the differential reading (h1-h2) by about 10%. Adjust
the supply valve to keep all of the readings within the range on the manometer scale.
8. Repeat (8) and (9) until you have about 8 sets of readings over a range of flow rate. For
one of these conditions, again record all of the manometer reading.

 
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RESULTS AND CALCULATIONS

CALCULATION OF C

Q = Ca2 2g(h1-h2)/ 1-(a2/a1)2

Rearranged to express C we have

C = 1/a2  1-(a2 /a1)2 /2g Q/  h1 – h2

Now d1 = 26,00 mm a1 = 531 mm2 = 5,31 10 – 4 m2

(a2/a1)2 = 0.143 1- (a2/a1)2 = 0.857

C = 1039
h1-h2

TABLE 1. DIMENSIONS OF VENTURI TUBE

Diameter d2/dn a22/an (a22/a1-a22/an)

Piezometer dn (mm)
Tube No. n
A(1) 26.00 0.615 0.144 0.000
B 23.20 0.690 0.226 0.082
C 18.40 0.869 0.575 0.431
D(2) 16.00 1.00 1.000 0.856
E 16.80 0.953 0.830 0.686
F 18.47 0.867 0.565 0.421
G 20.16 0.787 0.400 0.256
H 21.84 0.730 0.289 0.145
J 23.53 0.680 0.215 0.071
K 25.24 0.633 0.168 0.024
L 26.00 0.615 0.144 0.000

 
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TABLE 2 MEASUREMENTS OF (h1 – h2) AND Q

Qty .t h1 h2 Q x 10-4 .h1-h2 √h1-h2 C

( kg ) (s) ( mm) (mm) (m3 / s) (m) m

Avg C

TABLE 3. MEASUREMENT OF PRESSURE DISTRIBUTION ALONG VENTURI

METER

Piezometer Q = m3 / s Q = m3 / s
tube No. U22/ 2g = m U22/ 2g = m

.hn .hn-h1 .hn-h1 .hn .hn-h1 .hn-h1

(mm) (m) u22/2g (mm) (m) u22/2g

A (1)
B
C
D(2)
E
F
G
H
J
K
L

Conclusions:

 
 23 
 

Plot. hn-h1 against distance in (mm)

u22/2g

 
 24 
 

Plot the variation of √h1-h2 with Q

 
 25 
 

Plot the variation of C with Q

 
 26 
 

Notes:

 
 27 
 

EXPERIMENT # 5: FLOW OVER WEIRS

Objectives:

1. To determine the relationship between head H and flow rate Q over rectangular and vee
notches (weirs)
2. To determine the discharge coefficient C for each notch by comparing the measured flow with
the ideal flow.

Apparatus: -

Theory: -

a. Flow Over Notches and Weirs: -

A notch is an opening in the side of a tank or reservoir which extends above the surface of the
liquid. It is usually a device for measuring discharge. A weir is a notch on a larger scale - usually
found in rivers. It may be sharp crested but also may have a substantial width in the direction of
flow - it is used as both a flow measuring device and a device to raise water levels.

b. Weir Assumptions: -

We will assume that the velocity of the fluid approaching the weir is small so that kinetic energy
can be neglected. We will also assume that the velocity through any elemental strip depends only
on the depth below the free surface. These are acceptable assumptions for tanks with notches or
reservoirs with weirs, but for flows where the velocity approaching the weir is substantial the
kinetic energy must be taken into account (e.g. a fast moving river).

c. A General Weir Equation

To determine an expression for the theoretical flow through a notch we will consider a horizontal
strip of width b and depth h below the free surface, as shown in the figure below.

Elemental strip of flow through a notch

 
 28 
 

integrating from the free surface, , to the weir crest, gives the expression for the
total theoretical discharge

This will be different for every differently shaped weir or notch. To make further use of this
equation we need an expression relating the width of flow across the weir to the depth below the
free surface.

d. Rectangular Weir

For a rectangular weir the width does not change with depth so there is no relationship between b
and depth h. We have the equation,

A rectangular weir

Substituting this into the general weir equation gives

To calculate the actual discharge we introduce a coefficient of discharge, , which accounts for
losses at the edges of the weir and contractions in the area of flow, giving

 
 29 
 

'V' Notch Weir

For the "V" notch weir the relationship between width and depth is dependent on the angle of the
"V".

"V" notch, or triangular, weir geometry.

If the angle of the "V" is then the width, b, a depth h from the free surface is

So the discharge is

And again, the actual discharge is obtained by introducing a coefficient of discharge

 
 30 
 

Method.

1. Carefully slide the rectangular notch plate into the groove on the apparatus and check that
the rubber seal makes contact with the plate along all three edges.
2. Switch on the bench pump and open the bench supply valve. The apparatus with water until
the level reaches the bottom (crest) of the notch.
3. Using a beaker, add or remove water until the water surface is just level with the notch
crest. Use a steel rule to check that the level is correct
4. Set the hook gauge dial to zero and slide the hook up or down until the point of the hook
just coincides with the water surface. Subsequent readings of the water level will then be
relative to the true datum at crest level.
5. Set the hook gauge to a reading of 60mm. Then adjust the bench supply valve until the
water level corresponds roughly to the hook gauge setting.
6. Wait until the water level has settled to a constant value, then adjust the hook to this level
and read the exact value of head.
7. Measure the flow rate by timing the collection of water in the bench-weighing tank. Again
use the hook gauge to measure the water level and record a mean value of head.
8. Now decrease the head by about 5mm and take another set of head and flow rate reading.
Repeat this procedure until you have about 8 sets of reading over a range of heads down to
about 15mm.
9. Close the bench supply valve and fit the vee notch to the apparatus. Set the water level to
the base of the vee by adding or removing water. Check that the level is correct by
observing the notch from close to the water surface. The point of the vee and its reflection
should just coincide.
10. Repeat the procedure given in steps (5) to (9), but this time obtains reading over a range of
heads between 80mm and 30mm.
11. Switch off the bench pump. Record the witch b of the rectangular notch the semi-angle 
of the vee notch.

 
 31 
 

RESULTS AND CALCULATIONS: -

Results for Rectangular Notch: -

Width of the rectangular notch b = mm = m

For Rectangular Notch:

Cd = Q 3 (1/√2g) 1/2 H -3/2 1/B

2
RESULTS FOR RECTANGULAR NOTCH

H Qty .t Q x 10 -4 Log Q Log H

(mm) (kg) (s) (m3/s) (m3/s) (m)

CALCULATION FOR THE DISCHARGE COEFFICIENT

H -3/2 Cd = Q 3 1/√2g H -3/2 1/b

2

 
 32 
 

Results for V Notch:-

Angle θ = 30o Tan θ = 0.57735

For V- Notch: Q = C 8 √ 2 g tan θ H 5/2
15
C = Q 15 1/√2g 1/tanθ H -5/2
8
RESULTS FOR V- NOTCH

H Qty .t Q x 10 -4 Log Q Log H

(mm) (kg) (s) (m3/s) (m3/s) (m)

CALCULATION FOR THE DISCHARGE COEFFICIENT

H -5/2 C= Q 15 1/√2g 1/tanθH -5/2

8

Avg Cd

Conclusions:

 
 33 
 

Plot a graph of Q against H for Rectangular as well as Vee Notch:

 
 34 
 

Plot a graph of Log Q against Log H:

 
 35 
 

Notes:

 
 36 
 

EXPERIMENT # 6: IMPACT OF A JET

Introduction:

Water turbines are widely used through the world to generate power. In the type of water turbine
referred to as a Pelton wheel, one or more water jets are directed tangentially on to vanes generated
to the rim of the turbine disc. The impact of the water on the vanes generates a torque on the wheel,
causing it to rotate and to develop power. Such turbines can generate considerable output at high
efficiency. Power in excess of 100 MW, and hydraulic efficiencies greater than 70%, are not
uncommon. It may be noted that the Pelton wheel is best suited to conditions where the available
head of water is great, and the flow rate is comparatively small.

Objectives: 

1. To measure the force, produce by a water jet when it strikes two types of vane: a flat plate
and a hemispherical cup.
2. To compare the results with the theoretical values calculated from the moment flux in the
jet.

Apparatus

Fig No: 1

Method
 
1. Fit the flat plate to the apparatus.
2. Set the weighing beam to its datum position. Set the jockey weight on the beam so that
datum groove is at zero on the scale. Turn the adjusting nut above the spring until the
grooves on the tally are in line with the top plate.

 
 37 
 

3. Switch on the bench pump and open the bench supply valve.
4. Fully open the supply valve and slide the jockey weight along the beam until the jockey
return to its datum position. Record the reading on the scale corresponding to the grove on
the jockey weight.
5. Measure the flow rate by timing the collection of water.
6. Move the jockey weight inwards by 10 to 15 mm and reduce the flow rate until the beam
is approximately level position.
7. Repeat the step 6 until you have 6 sets of readings over the range of flow. For the last set,
the jockey should at about 10mm from the zero position.
8. Switch off the bench pump and fit the hemispherical cup to the apparatus using the same
method as of flat plat take another set of readings.

Switch off the bench pump and record the mass m of the jockey weight, the diameter of the nozzle
and the distance of the vanes from the outlet of the nozzle.

 
 38 
 

 
 39 
 

 
 40 
 

 
 41 
 

 
 42 
 

RESULTS AND CALCULATIONS:

TABLE # 1 RESULTS FOR A FLAT PLATE

Qty (kg) t (s) ∆x (mm) m∙ U (m/s) Uo (m/s) m∙ Uo F

(kg/s) (N) (N)

TABLE # 2 RESULTS FOR A HEMISPHERICAL CUP

Qty (kg) t (s) ∆x (mm) m∙ U (m/s) Uo (m/s) 2 m∙ Uo F
(kg/s) (N) (N)

Conclusions:

 
 43 
 

1. Plot the Force on a Vane (F) versus Momentum Flux (m∙ Uo) for a Flat Plate

 
 44 
 

2. Plot the Force on a Vane (F) versus Momentum Flux (2m∙ Uo) for a Hemispherical
Cup

 
 45 
 

Notes:

 
 46 
 

EXPERIMENT # 7: PELTON TURBINE

Objective: To determine the torque produced by a pelton turbine

The unit is designed for training and experimentation. It is used for demonstration purposes
relating to the principle of functioning of a pelton turbine. The orifice of the injection nozzle can
be altered by axial adjustment of the nozzle valve. Load can be placed on the turbine with an
adjustable, mechanical braking device.
The main parts of the pelton turbine are
1. Nozzle and flow regulating arrangement
2. Runner and buckets
3. Casing
4. Breaking jet

DESCRIPTION

3 8

6 7

 
 47 
 

1. Adjustable breaking device 2. Spring balance

3. Nozzle valve 4. Nozzle inlet
5. Turbine housing 6. Nozzle adjustment
7. Outlet through open housing 8. Pelton wheel
9. Base plate

THEORY
Hydraulic machines are defined as those machines which convert either hydraulic energy (energy
possessed by water) into mechanical energy or mechanical energy into hydraulic energy.
Turbines are defined as hydraulic machines which convert hydraulic energy into mechanical
energy. hydraulic turbines are of different types according to specification and pelton wheel is
one of the types of hydraulic turbines.

Pelton wheel turbine:

The pelton wheel turbine is a tangential flow impulse turbine. The water strikes the bucket along
the tangent of the runner. The energy available at the inlet of the turbine is only kinetic energy.
The pressure at the inlet and outlet is atmospheric. The turbine is used for high heads.
Constructional Details:
Nozzle and flow regulating arrangement:
The amount of water striking the buckets of the runner is controlled by providing a spear in the
nozzle. The spear is a conical needle which is operated either by a hand wheel or automatically
in an axial direction depending upon the size of unit. When the spear is pushed forward into the
nozzle the amount of water striking the runner is reduced. On the other hand, if the spear is
pushed back, the amount of water striking the runner increases.

Runner with buckets:

It consists of a circular disc on the periphery of which a number of buckets evenly spaced are
fixed. The shape of the buckets is of double hemispherical cup or bowl. Each bucket is divided
into two hemispherical parts by a dividing wall which is known as splitter.
Casing:
The function of the casing is to prevent the splashing of the water and to discharge water to tail
race. It also acts as safe guard against accidents. As pelton wheel is an impulse turbine, the
casing of the pelton wheel does not perform any hydraulic function.

Breaking Jet:

 
 48 
 

When the nozzle is completely closed by moving the spear in the forward direction the amount
of water striking the runner reduces to zero. But the runner due to inertia goes on revolving for a
long time. To stop a nozzle in a short time a small nozzle is provided which directs the jet of
water on the back of buckets. This jet of water is called breaking jet.

Working of Pelton wheel turbine:

The water from the reservoir flows through the penstocks at the outlet of which a nozzle is fitted.
The nozzle increases the kinetic energy of the water flowing through the penstock by converting
pressure energy into kinetic energy. At the outlet of the nozzle, the water comes out in the form
of jet and strikes on the splitter, which splits up the jet into two parts. These parts of the jet glides
over the inner surfaces and comes out at the outer edge. The buckets are shaped in such a way
that buckets rotates, runner of turbine rotates and thus hydraulic energy of water is converted into
mechanical energy on the runner of turbine which is further converted into electrical energy in a
generator/alternator.

 
 49 
 

Procedure:
1. Connect the apparatus with the hydraulic bench.
2. Switch on the hydrau8lic bench pump.
3. Open the valve slowly so that water begins to flow through the turbine.
4. Adjust the flow rate in turbine by nozzle adjuster screw.
5. Load the turbine by turning the adjustment breaking device.
6. Note down the speed of turbine in rpm with the help of tachometer. Note down the
breaking power F.

F b = F 1 – F2

7. Now the torque can be calculated by

T = Fb . r
r : radius of pulley = 25 mm

8. The mechanical power produced by the turbine can be calculated by

PM = 2πnT / 60
n : speed of the pelton wheel in rpm.

 
 50 
 

Observations:

Sr. # n Force F1 Force F2 Net force Fb Torque T Power

(rpm) (N) (N) (N) (Nm) PM
(watt)

Conclusions:

 
 51 
 

Plot torque (Nm) and power (watts) against rotational speed (rev/min)

Notes:

 
 52 
 

EXPERIMENT # 8: LAMINAR, TURBULENT FLOW AND

REYNOLD’S NUMBER

Friction Loss Along a Pipe

Objectives:

1. To demonstrate the existence of laminar and turbulent flow and to establish the value of
Reynolds number for transition from laminar to turbulent flow.
2. For the laminar flow regime, to use Poiseuille’s equation to calculate the coefficient of
viscosity .
3. To determine the variation of friction factor ‘f’ in the laminar and turbulent flow regimes.

Apparatus:

Fig No: 3

Method:

1. Connect the bench supply hose to the inlet of the apparatus and direct the outlet flexible
outlet pipe into the bench drain.
2. Open the needle valve (N) on the right of the apparatus.
3. Start the bench pump and slowly open the bench supply valve so that water flows through
the apparatus.

 
 53 
 

4. Open the bleed screws (B) at the top of the mercury U-tube, and then slowly closes the
needle valve so that the air is expelled from the piezometer tubes. Open the air valve (V)
to release the air from the water manometer. When all air bubbles have been driven out,
close the bleed screws and air valve.
5. With the needle valve (N) closed, check that the mercury levels in the U–tube are in
balance. If not repeat the process of expelling air. For the first part of the experiment obtain
readings of head loss h along the pipe using the mercury U-tube as follows.
6. Close the water manometer isolating tap (T) and fully open the needle valve.
7. Collect the flow from the outlet pipe into a measuring cylinder and measure the time t for
collection of a known quantity Q.
8. Read the heights of the two columns of mercury in the U-tube.
9. Reduce the flow rate by partially closing the needle valve to produce approximately 10%
reduction in differential U-tube reading, and then repeat the measuring process.
10. Repeat this procedure until you have about 10 sets of readings over the whole flow range.
11. Measure the water temperature from time to time during the experiment. Now obtain a
similar set of readings over a smaller range of flow, using the constant head tank and the
water manometer for measurement of head loss. To do this, proceed as follows;
12. Switch on the bench pump and adjust the bench supply valve until you obtain a steady
trickle of water down the overflow pipe.
13. Open the isolating tap (T), and then pump some air into the top of the manometer to depress
the water surfaces to a convenient level in the two limbs.
14. Check that the two sides balance at zero flow; If they do not, repeat the process of bleeding
air from the top of the manometer.
15. Starting with a differential manometer reading of about 450mm of water again take
readings of head loss and flow rate until you have about10 sets of readings over the whole
range.
16. Measure the water temperature from time to time during the experiment.
17. Record the length L and diameter D of the test pipe.

 
 54 
 

Results

Length of pipe between piezometer tapping, L = mm = m

Diameter of pipe D= mm = m
Cross-section area A= m2

Result with Mercury U-tube

Mean temperature of water = o

C
Coefficient of viscosity = Ns/m2 (from graph)
Hydraulic gradient, i = (h1 – h2)/L
Velocity, V = Qty/ t x A
Reynold’s number, Re = VD/
Where;  = 1000 Kg/m3
Plot i against V and add a scale of Re along the top of the graph. Obtained values of log i and log
V and plot a graph.

t h1 h2 i  V Re Log i Log V
Qty (oC)

Determination of critical Reynolds number

As the flow rate reduced, laminar flow first becomes established and when V has the value,
V= m/s
Re =

Calculation of viscosity from experimental results

Poiseuille’s equation i = 32 V/ gD2

 = gD2/ 32 x i / V
From fig 1. the standard value of viscosity at the mean temperature is

 
 55 
 

 = --------------------Ns/m2

Calculation of index n in turbulent regime

For the turbulent regime the slope of the line is

n=
iV

Calculation of ‘f’ as a function of Re

The relationship between friction factor f and hydraulic gradient i is given by the equation;
i = 4f/D V2/2g
f = i/4 D2g/V2
The relationship between Reynolds number Re and velocity V has been established previously in
these results for the particular temperature of the tests.
Read off values of i at few values of Vin each of the laminar and turbulent region. Calculate values
of f and Re from the expressions. Then plot a graph between friction f and Re with the following
standard equations.
Laminar: f = 16/ Re
Turbulent: 1/ f = 4log (Re f) – 0.4

Conclusions

In your laboratory, write a summary what you have learned from the experiment and answer the
following questions.
1. At what value of Re does turbulent flow change to laminar flow? How does this value
compare with the accepted value of 2000?
2. What accuracy have you achieved in measuring the coefficient of viscosity?
3. What difference in friction factor you expect if the inside surface of the pipe is very rough?

 
 56 
 

Plot f against Re for both Laminar and Turbulent Regimes

 
 57 
 

Notes:

 
 58 
 

EXPERIMENT # 9: PRESSURE LOSSES IN BENDS AND PIPES

Objectives:

1. To determine the relationship between total head loss and flow rate for pipe bends and
other common fittings.
2. To determine the loss coefficient K for each fitting and to compare the results with standard
data.
Apparatus:

Fig No:4

Method:

1. Close the globe valve K and open the gate valve D. Switch on the bench pump and open
the bench supply valve to admit water to the dark blue circuit. Allow water to flow for 2 to
3 minutes.
2. Close the gate valve D and bleed all the air into the top of the manometer tubes. Check that
all the manometers show zero pressure difference.
3. Open the gate valve and then, by carefully open the bleed screws at the top of the mercury
U-tube, fill each limb with water. Make sure that all air bubbles have been expelled, and
then close the bleed screws.
4. Close the gate valve, open the globe valve, and repeat the procedure for the light blue
circuit.

Dark Blue Circuit

5. Open fully the bench supply valve. Then close the globe valve and open fully the gate valve
to obtain the maximum flow rate through the dark blue circuit.

 
 59 
 

6. If necessary, adjust the water level in the manometers by pumping air into, or releasing air
from the bleed valves at the tops of the manometers.
7. Record the readings of the manometers in the dark blue circuit. Note the reference number
of each manometer and also record the type of fitting next to each pair of results. Also read
the levels in the mercury U-tube connected between the inlet and out let of the gate valve
D.
8. Measure the flow rate by timing the collection of water in bench weighing tank.
9. Measure the water temperature.
10. Close the gate valve to reduce the differential manometer readings by about 10%. Again
read the manometer and U-tube, and then measure the flow rate.
11. Repeat this procedure until you have about 10 sets of readings over the whole range of
flow.

Observations:

Result for dark blue circuit

Water temperatures:-------------- oC Mean temperatures: ---------------------oC

Sr. M t V V2/ Manometer readings and differential heads U-tube
No Kg s m/s 2g (mm of water) (mm of Hg)
m Elbow Bend Straight pipe Mitre bend Gate valve
m 1 2 h’ 3 4 hf 5 6 h’ h1 h2 H
1
2
3
4
5
6
7
8
9
10

 
 60 
 

Light Blue Circuit

Close the gate valve and open the globe valve. Then repeat (6) and (11) to obtain the sets of
readings for the light blue circuit.

Results for light blue circuit

Water temperature:-------------- oC Mean temperature: ---------------------oC

M t V V2 Manometer readings and differential heads (mm of water) U-tube
Sr. Kg s m/s /2g (mm of
mm Hg)
No
Expansion Contraction Bend J Bend H Bend G Globe
Valve
7 8 h 9 1 h 1 1 h 1 1 h 1 1 h h h 
’ 0 ’ 1 2 ’ 3 4 ’ 5 6 ’ 1 2 H

Conclusions:

 
 61 
 

Plot ΔH against V2/2g for each bend:

Elbow Bend:

Straight Pipe:

Mitre Bend:

 
 62 
 

Pipe Expansion:

Pipe Contraction:

Bend G:

Bend H:

 
 63 
 

Bend J:

From the slope of each graph, calculate the loss coefficient K.

K = ΔH / [V2/2g]

Compare the values of loss coefficient K obtained from the experiment to theoretical values and
write down below.

 
 64 
 

Notes:

 
 65 
 

EXPERIMENT # 10: TO VISUALIZE THE DIFFERENCE BETWEEN

LAMINAR & TURBULENT FLOW

INTRODUCTION

The Osborne Reynolds demonstration apparatus has been designed for students’ experiment on
the laminar, transition and turbulent flow. It consists of a transparent header tank and flow
visualization pipe. The header tank is provided with a diffuser and stilling materials at the bottom
to provide a constant head of water to be discharged through a bell mouth entry to the flow
visualization pipe. Flow through this pipe is regulated using a control valve at the discharge end.
The water flow rate through the pipe can be measured using the volumetric tank (or volumetric
cylinder). Velocity of the water can therefore be determined to allow the calculation of the
Reynolds number. A dye injection system installed on top of the header tank so that flow pattern
in the pipe can be visualized.

GENERAL DESCRIPTION
Unit Assembly

 
 66 
 

1. Dye reservoir 2.Dye injector

3. Stilling tank 4. Observation tube
5. Water inlet valve 6. Bell mouth
7. Water outlet valve 8. Overflow tube

The Osborne Reynolds Demonstration apparatus is equipped with a visualization tube for students
to observe the flow condition. The rocks inside the stilling tank are to calm the inflow water so
that there will not be any turbulence to interfere with the experiment. The water inlet/outlet valve
and dye injector are utilized to generate the required flow.

THEORY

The Reynolds number is widely used dimensionless parameters in fluid mechanics.

Reynolds number formula . R = VL
v

R = Reynolds number
V = Fluid velocity, (m/s)
L = Characteristic length or diameter (m)
v = Kinematic viscosity (m2/s)

Reynolds number R is independent of pressure

Pipe Flow Conditions

For water flowing in pipe or circular conduits, L is the diameter of the pipe. For Reynolds number
less than 2300, the pipe flow will be laminar. For Reynolds number = 2300 the pipe flow will be
considered a transitional flow. Turbulent occur when Reynolds number is above 2300. The
viscosity of the fluid also determines the characteristic of the flow becoming laminar or turbulent.
Fluid with higher viscosity is easier to achieve a turbulent flow condition. The viscosity of fluid is
also dependant on the temperature.

Laminar Flow
Laminar flow denoted a steady flow condition where all streamlines follow parallel paths, there
being no interaction (mixing) between shear planes. Under this condition the dye observed will
remain as a solid, straight and easily identifiable component of flow.

 
 67 
 

Transitional Flow
Transitional flow is a mixture of laminar and turbulent flow with turbulence in the center of the
pipe, and laminar flow near the edges. Each of these flows behaves in different manners in terms
of their frictional energy loss while flowing, and have different equations that predict their
behavior.

Turbulent Flow
Turbulent flow denotes and unsteady flow condition where streamlines interact causing shear
plane collapse and mixing of the fluid. In this condition the dye observed will become disperse in
the water and mix with the water. The observed dye will not be identifiable at this points.

 
 68 
 

Procedure

1. Lower the dye injector until it is seen in the glass tube.

2. Open the inlet valve and allow water to enter stilling tank.
3. Ensure a small overflow spillage through the over flow tube to maintain a constant level.
4. Allow water to settle for a few minutes.
5. Open the flow control valve fractionally to let water flow through the visualizing tube.
6. Slowly adjust the dye control needle valve until a slow flow with dye injection is achieved.
7. Regulate the water inlet and outlet valve until an identifiable dye line is achieved.
8. Measure the flow rate using volumetric method i-e collect the water from the outlet having
die in it in a volumetric tank and calculate the time with a stop watch.
9. Repeat the experiment by regulating water inlet and outlet valve to produce different flows.

Table

Sr. # Discharge Time (sec) Flow rate Q Flow Rate Q Reynolds

(Liter) (LPS) (m3/sec) Number

Conclusion:

 
 69 
 

Notes:

 
 70 
 

EXPERIMENT # 11: STABILITY OF FLOATING BODY

Objectives

1. To determine how the stability of a rectangular pontoon is affected by altering the vertical
position of its center of gravity.
2. To demonstrate how the metacentric height can be used as a measure of the stability.
3. To determine the height of the metacenter and compare this with the theoretical value.

Theory: -

Whenever a body is placed over a liquid, either it sinks down or float on the liquid. If we
analyze the phenomenon of floatation, we find that the body, placed over a liquid, is subjected to
the following two forces: -
1. Gravitational Force 2. Up thrust of the liquid.
Since the two forces are opposite to each other, therefore we have to study the comparative effect
of these forces. A little consideration will show, that if the gravitational force is more than the up
thrust of the liquid, the body will sink down. But if the gravitational force is less than the up thrust
of the liquid, the body will float. This may be best understood by the Archimedes’ principle as
discussed below.
a). Archimedes’ Principle: -
Whenever a body is immersed wholly or partially in a fluid, it is buoyed up
(i.e lifted up) by a force equal to the weight of the liquid displaced by the body.

b). Buoyancy: - The tendency of a fluid to uplift a submerged body, because of the upward thrust
of the fluid, is known as the force of buoyancy or simply buoyancy. It is always equal to the weight
of the fluid displaced by the body.

c). Centre of Buoyancy: - It is the point through which the force of buoyancy is supposed to act.
It is always the centre of gravity of the volume of the liquid displaced.

d). Metacenter: -
Whenever a body, floating in a liquid, is given a small angular displacement, it
starts oscillating about some point. This point, about which the body starts oscillating, is called
metacentre.

e). Metacentric Height: -

The distance between the centre of gravity of a floating body and
metacenter is called metacentric height.

 
 71 
 

As a matter of fact, the metacentric height of the floating body is a direct measure of its stability.
Or in other words, more the metacentric height of a floating body, more it will be stable. In the
modern design offices, the metacentric height of a floating body or a ship accurately calculated to
check its stability. Some values of metacentric height are given below:
Merchant Ships = up to 1 m
Sailing ships = up to 1.5 m
Battle ships = up to 2.0 m
River Craft = up to 3.5 m

Conditions of equilibrium of Floating Body:

A body is said to be in equilibrium, when it remains in a steady state,
while floating in a liquid. Following are the three conditions of equilibrium of a floating body.
 Stable equilibrium
 Unstable equilibrium
 Neutral equilibrium

Stable Equilibrium: -
A body is said to be in stable equilibrium, if it returns back to its original
position, when given a small angular displacement. This happens when metacenter ( M ) is higher
than the centre of gravity ( G ).

Unstable Equilibrium: -
A body is said to be in an unstable equilibrium, if it does not return back to
its original position and heels farther away, when given a small angular displacement. This
happens when the metacenter (M) is lower than the centre of gravity (G).

Neutral Equilibrium: -
A body is said to be in a neutral equilibrium, if it occupies a new position
and remains at rest in the new position, when given a small angular displacement. This happens
when metacenter (M) coincides with the centre of gravity (G).

 
 72 
 

Method

1. Record the weights, W of the complete pontoon, w of the jockey and Wy of the adjustable
weight on the mast.
2. Measure the overall length L and width D of the pontoon.
3. Set the adjustable weight about half way up the mast and measure its height Y1 from the
base of the pontoon.
4. Determine the height y of the center of the gravity from the base of pontoon by “up-ending”
it and balancing the mast on the edge of a steel rule. Loop the plumb the plumb line over
the scale so that the plumb bob is kept approximately in its normal position. When the
pontoon is hanging vertically, mark the balance point with pencil.
5. Measure the height of the balance point from the base of pontoon. This represents the height
y of the center of gravity.
6. Fill the plastic container with water to a depth of about 70mm and float the pontoon in it.
Set the jockey weight exactly half way across the pontoon and check the reading of the
plumb line on the scale. If necessary, set the reading to zero by adjusting the pin at the top
of the mast.
7. Set the adjustable weight to its lowest position on the mast and record its height from the
base of the pontoon.
8. Set the jockey weight to 5 different position on each side of the pontoon, for each position,
record the distance X1 from the center of the pontoon and measure the angle of tilt 
9. Repeat the reading for three or four other height of the adjustable weight, raising it each
time by about 50mm. The pontoon will become decreasingly stable as you move the
adjustable weight up the mast, so the number the tilt angle reading you can take will be
limited by the width of the scale.

 
 73 
 

Results and calculations

Weight of total floating assembly W = Kgf

Jockey weight w = Kgf
Adjustable weight Wy = Kgf
Length of pontoon L= mm = m
Breadth of pontoon D= mm = m
Enter your other results in table.

Calculations
Second moment of water plain area,
1
I = --------- LD3
12
1

12
I= m4
Volume of water displaced,
Weight W
V = --------------------
Specific weight of water
Theoretical value of BM,
BM = I / V
Depth of immersion (2X Yb) = V/ LD
Height of center of buoyancy B above base, Yb = mm

Determination of height of G

Height of adjustable weight of above base Y1 = mm

Measured height of G above base Y= mm
The ratio of the adjustable weigh Wy to the total weight W is 1:
Y = Y1 + A
Where A is a constant. Substituting for Y and Y1
= ------------- + A
A = ---------------- mm
Hence calculate values of Y in table

 
 74 
 

Table: measured angles of tilt

Position of jockey weight X1 (mm)

Height of Height -75 -60 -45 -30 -15 0 15 30 45 60 75 Angle
Adjustable Of G Of
Weight Y1 Y Tilt
(mm) (mm) 

Table: calculated values of GM and BM from experimental results

Height of G X1/  GM BG BM
Y (mm/degree) (mm/radian) =w/W.X1/ =Y-Yb =BG+GM
(mm) (mm) (mm) (mm)

Conclusion:

 
 75 
 

Plot Angle of Tilt against Displacement:

Plot BG against GM:

 
 76 
 

Notes:

 
 77 
 

EXPERIMENT # 12: Center of Pressure and Hydrostatic Force on a submerged body

Objectives:

• To understand the hydrostatic pressure distribution

• To verify the location of center of pressure

Apparatus:

The apparatus is designed in a way that only the moment due to hydrostatic pressure distribution
on the vertical end of water vessel should be included. The water vessel is designed as a ring
segment with constant cross-section. The top and bottom faces are concentric circular arcs centered
on the pivot so that the resultant hydrostatic force at every point passes through the pivot axis and
does not contribute to the moment.

 
 78 
 

 
 79 
 

 
 80 
 

 
 81 
 

 
 82 
 

Conclusions:

 
 83 
 

Compare your experimental results with the results obtained from theory:

Notes:

 
 84 
 

EXPERIMENT # 13: Calibration of a Pressure Gauge

Objectives:

 To study dead weight calibration.

INTRODUCTION

A dead weight tester apparatus uses known traceable weights to apply pressure to a fluid for
checking the accuracy of readings from a pressure gauge. A dead weight tester (DWT) is a
calibration standard method that uses a piston cylinder on which a load is placed to make an
equilibrium with an applied pressure underneath the piston. Deadweight testers are so called
primary standards which means that the pressure measured by a deadweight tester is defined
through other quantities: length, mass and time. Typically deadweight testers are used in
calibration laboratories to calibrate pressure transfer standards like electronic pressure measuring
devices.

GENERAL DESCRIPTION

The mechanism of the gauge is shown in the figure below. A tube, having a thin wall of oval cross
section, is bent to a circular arc encompassing about 270 degrees. It is rigidly held at one end,
where the pressure is admitted to the tube, and is free to move at the other end, which is sealed.
When pressure is admitted, the tube tends to straighten, and the movement at the free end operates
a mechanical system which moves a pointer round the graduated scale – the movement of the
pointer being proportional to the pressure applied. The sensitivity of the gauge depends on the
material and dimensions of the Bourdon tube; gauges with a very wide selection of pressure ranges
are commercially available.

 
 85 
 

FORMULA

The formula on which the design of a DWT is based basically is expressed as follows:

p = F/A [Pa]

where:

p : reference pressure [Pa]

F : force applied on piston [N]
A : effective area [m2]

 
 86 
 

PART IDENTIFICATION

Diameter of piston = 18mm

Mass of piston = 0.5kg

 
 87 
 

Procedure

1. Remove the piston from unit.

2. Close valve V1 and open valve V2.
3. Fill cylinder with oil.
4. Now close valve V2.
5. Put piston back in position with V1 and V2 in close position.
6. Read out pressure value on gauge and compare it with theoretical results.
7. Repeat the experiment by adding weights.

Observations

Sr. # Applied Applied Area Theoretical Practical

Load Load (m2) Pressure Pressure
(kg) (N) (N/m2) (N/m2)
1
2
3
4
5
6
7
8
9

Conclusion:

 
 88 
 

Calculate the calibration factor of your pressure gauge:

Notes:

 
 89 
 

EXPERIMENT # 14: FREE AND FORCED VORTEX

Free Vortex

Objectives:
1. To study on surface profile and speed.
2. To find a relation between surface profile and speed.

Procedure:
1. Perform the general start-up procedures.
2. Select an orifice with diameter 24mm and place it on the base of cylinder tank.
3. Close the output valve and adjust the valve to let the water flows into the sink from two pipes
with 12.5 mm diameter. The water can flow out through the orifice.
4. Switch on the pump and open the valve slowly until the tank limit. Maintain the water level
by controlling the valve.
5. When the water level is stable, collect the vortex profile by measuring the vortex diameter
for several plane.
6. Push down the profile measuring gauge until the sharp point touch the water surface.
7. Record the measured height, h (from the top of the profile measuring gauge to the bridge.
Obtain the value of a (mm) - distance from the bridge to the surface of the water level (bottom
level of the cutout).
8. Use the pitot tube to measure the velocity by sinking it into the water at the depth of 5mm
from the water surface. Measure the depth of the pitot tube in the water and also the height
difference of the U tube at the side of the tank.
9. Repeat Step 3-8 for another two orifice with diameter 16mm and 8mm respectively.
10. Plot the coordinates of vortex profile for all diameter of orifice in the same graph and
calculate the gradient of graph as shown below:
X= ∙
Which X is the pressure head / depth of the pitot tube.
11. Plot the velocity which study from the pitot tube reading, H versus the radius of the profile.
V = (2gH)0.5
Theoretically, the velocity can be calculated by using the following equation:
K
V 
r

 
 90 
 

Diameter at Measured Pitot Tube Pressure

Centre, D Height, h Head Head /
(mm) (mm) Difference, Depth of the
H (mm) pitot tube, X
(mm)

Forced Vortex

Objectives:
1. To study on surface profile and angular velocity.
2. To find a relation between surface profile and total head.

Procedures:
1. Perform the general start-up procedures.
2. Place a closed pump with two pedals on the foot of the bed.
3. Close the output valve and adjust the valve to let the water flows into the sink
from two pipes with 9.0 mm diameter. The water can flow out through another
two pipes with 12.5mm diameter.
4. Make sure that the water flow with the siphon effect by raising the hose to a
standard before letting the water to the sink.
5. Measure the angular speed of the pedals by counting the number of circles in a
certain times.
6. Push down the surface probe until the sharp point touch the water surface.
7. Record the vertical scale reading.
8. Repeat Step 4-7 for another two volumetric flow rate.
9. Plot the coordinates of vortex profile for different angular velocity.
10. Plot the calculated profile vortex in the same graph as they relate as
h = h0 + r2

Compare both experimental and calculated profile.

Distance from ho (mm)

Centre (mm) 1st
2nd 3rd
(___LPM) (___LPM) (___LPM)

 
 91 
 

0
30
70
110
No of revolutions
in 60s
Angular Velocity
(rad/s)

SUMMARY OF THEORY

1.1 Free Cylindrical Vortex

When a liquid is flowing out of a tank through a hole at the bottom of the tank, free vortex
is formed with the number of oscillation depending on the distortion that created the flow.
The liquid is moving spirally towards center following current, energy per unit mass is
assumed to be constant when energy loss by viscosity is neglected. If, while the mass of
water is rotating, the central exit hole is plugged, the flow of water in the vertical plane
ceases and the motion becomes one of simple rotation in the horizontal plane. This is
known as free cylindrical vortex.

Bernoulli’s theorem can be used because the movement is along the flow axis,
p V2
  z  constant
g 2 g

For horizontal plane, the relation becomes

p V2
  constant
g 2 g

Integration of the above relation with r gives

1 dp V dV
 0 (1)
g dr g dr

Next, consider a pair of stream line being divided with distance r and is in same horizontal
plane and are linked by a fluid tube wide A . The centrifugal force of the tube is balanced
by the pressure difference between both ends, that is
V 2 dp
g  A  r    r  A
gr dr

 
 92 
 

gV 2 dp
 (2)
gr dr

Combine (1) and (2) to produce

V 2 V dV
 0
gr g dr
dV V
 0
dr r

Integrate above relation to obtain

ln r  ln V  constant
vr  K (constant)
K
V  (3)
r

In free cylinder vortex, velocity is inversely proportional to distance from spiral axis.
Bernoulli’s theorem is used to determine surface profile as follow:
V2
 z  C (constant) (4)
2g

Substitute (3) into (4)

K2
zC
2 gr 2
K2
Cz (5)
2gr 2

That is, equation for hyperbolic curve yx 2  A that is symmetry to axis of rotation and is
horizontal to z = C

1.2 Free Vortex

Movement in free vortex is different with free cylindrical vortex because free vortex
contains radial velocity towards center. Equation for such situation can be generated by
considering the water passes through round segments towards its diameter, where energy
passing any tube and is kept constant until

 
 93 
 

p V2
  z  constant
g 2 g

If A and V is surface area and velocity of a particular position, and A1 , V1 are surface area
and velocity at distance r from center circle,
AV  A1V1  constant

By taking A  Kr ,
r1V1
V
r

If z is constant,
2 2
p r1 V1
 C
g 2 gr 2
2
p r V2
 C  1 12 (6)
g 2gr
Also,
2
p1 V1
 C
g 2 g

2 2 2
p  p1 V1 r V
  1 12
g 2 g 2 gr
p  p1 V1  r1 
2 2

 1   (7)
g 2g  r 2 
Free vortex can be said as combination of cylinder vortex and radial flow. Velocity is
inversely proportional to radius in every case. Angle between flow axis and radius vector
at any point is constant and these axis form the spiral pattern.

1.3 Forced Vortex

As we know, angular velocity is constant,

V  r

Increase in radial pressure is given by

dp V2
   2 r
dr r

 
 94 
 
p2 r2
p1
dp   2  rdr
r1

1
p 2  p1   2 (r2 2  r1 2 ) (8)
2

By taking p1  p0 , when r1  0 , and p 2  p when r2  r ,

p  p0 w 2 2
 r
g 2g

Because p
g  h , so
2
h  ho  r2
2g
2
h  h0  r2 (9)
2g

This is a parabolic equation.

Surface profile for forced vortex can be represented by equation:

2r 2
z
2g

Distribution of total head can be represented by equation:

2r 2
H
g
Where:
Z = Surface profile
 = Angular velocity
r = Radius
g = Gravity
H = Total Head
Angular velocity can be calculated by:

2π x revolution
Ω
time s

Where: Z = Surface profile, Ω = Angular velocity

r = Radius, g = Gravity

 
 95 
 

Conclusions:

Notes:

 
 96 
 

EXPERIMENT # 15: Wind Tunnel

Objectives

1. To study the operation of the wind tunnel.

2. To find the velocity of air in the test section of the wind tunnel using Pitot tube.

Apparatus:

Wind Tunnel Specifications:

Overall Length = 4.4 meters

Height = 2.0m
Width=0.9m
Test section airspeed = 50 m/s (max)
Test section dimensions = 230 mm x230 mm x480 mm

AF-81 Wind Tunnel is basically designed for study of aerodynamics in subsonic region. Typically
Subsonic (or low-speed) aerodynamics studies fluid motion in flows which are much lower than
the speed of sound everywhere in the flow.

A purpose built contraction is designed to allow uniform velocities in the test section of the wind
tunnel and velocities up to 50 m/s are attainable in the wind tunnel. A mechanical damper assembly
is installed in the wind tunnel which provides continuous variable control of the air velocity.

In solving a flow problem, one decision is to be made, whether to incorporate the effects of
compressibility or not. Compressibility is a description of the amount of change of density in the
flow. When the effects of compressibility on the flow are small i.e. at low velocities, the density
is assumed to be constant. The problem is then treated as an incompressible low-speed
aerodynamics or a subsonic flow problem. If study of the flow is characterized by large velocities,
the density is not constant anymore and varies according to the velocity, the problem is then called
a compressible flow problem and effects of compressibility on the flow have to be incorporated in

 
 97 
 

the solution. In air, compressibility effects are usually ignored when the Mach number of the flow
does not exceed 0.3. Flows involving Mach number greater than 0.3 should be solved by
incorporating compressibility effects.

Test Section of the Wind Tunnel:

1. In the test section, the air velocity can be measured by a Pitot Static Tube, and the pressure
variation can be measured along various models/aero foils.
2. To prevent unnecessary vibrations in the test section the fan assembly is mounted in its
own support and fitted with anti-vibration mounts.

Calculation of Velocity:

Air Velocity in the test section can be calculated from the Bernoulli’s equation.

Total Pressure = Static Pressure + Dynamic Pressure

Mathematically;

⇒ 

Static pressure is negative because of the air flowing above the Pitot static tube creates a negative
pressure on the surface of the Pitot static tube,

Air velocity can be derived from the velocity pressure relation which comes out to be:

⇒ 
Since;

and;

 
 98 
 

Substituting and solving for V in the above mentioned equation yields;

V /
⇒ 
Here;

P1 = atmospheric pressure (mbar)

P2 = Pressure difference on the manometer (mbar)
R = Specific Gas Constant (287.1 J/Kg 0K)
T = Temperature (Kelvin)

Observations:

S No Temperature P1 (mbar) P2 (mbar) Velocity (m/s)

(Kelvin)

 
 99 
 

Conclusions:

Notes: