Motihari College of Engineering,
Motihari
Department of Mechanical Engineering
FLUID MECHANICS
LAB. MANUAL
FOR
BEU, B. Tech. – 4th semester
(Mechanical Engineering)
NAME:…………………………………………………………………………………..……………
ROLL NUMBER: - ………………………………… BATCH:-…………………………..
ENROLLMENT NO. :- …………………………… YEAR: - …………………………...…
BRANCH: - MECHANICAL ENGINEERING SEMESTER: -IV
Department of Mechanical Engineering
FLUID MECHANICS
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Motihari College of Engineering,
Motihari
Department of Mechanical Engineering
CERTIFICATE
THIS IS TO CERTIFY THAT
MR. / MRS. / MS. ________________________________________________
ROLL NO. _____________BRANCH
MECHANICAL
ENGINEERING
SEMESTER IVth HAS SATISFACTORY COMPLETED THE COURSE IN
THE SUBJECT OF FLUID MECHANICS WITHIN THE FOUR WALLS OF
MOTIHARI COLLEGE OF ENGINEERING, MOTIHARI .
DATE OF SUBMISSION: - ________________
________________
STAFF IN CHARGE
FLUID MECHANICS
______________________
HEAD OF DEPARTMENT
2
1
To understand pressure measurement
procedure and related
instrument/devices.
2
To determine the Metacentric height of a
floating body.
3
Verification of Bernoulli’s Theorem.
4
To measure the velocity of flow using
pitot tube.
5
Determine co-efficient of discharge Cd
using venturimeter
6
Determine co-efficient of discharge Cd
using orifice meter
7
To determine co-efficient of discharge
Cd of tri-angular(V-notch) & rectangular
notch.
8
To determine the different types of flow
patterns by Reynolds’s experiment
9
To determine the friction factor for
different pipe.
10
Study of determination of losses in pipe
friction.
11
To determine the viscosity of fluid by
viscometer(Redwood Apparatus)
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REMARKS
SIGNATURE
TITLE
DATE
PAGE
SR. NO
INDEX
EXPERIMENT: 01
AIM:- TO UNDERSTAND
RELATED INSTRUMENT.
PRESSURE
MEASUREMENT
PROCEDURE
AND
Pressure measurements can be divided into three different categories:
1. Absolute pressure
2. Gage pressure
3. Differential pressure.
1. ABSOLUTE PRESSURE
Absolute pressure refers to the absolute value of the force per-unit-area exerted on a surface by a
fluid. Therefore the absolute pressure is the difference between the pressure at a given point in a
fluid and the absolute zero of pressure or a perfect vacuum.
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APPLICATION OF ABSOLUTE PRESSURE MEASUREMENT
A typical application for absolute pressure sensors is the so called barometer, a device where the
current ambient pressure is measured and its variation used to predict changing weather. Another
application would be a device called altimeter (or altitude meter) which measures the
atmospheric pressure and converts it into an altitude reading typically referenced to mean sea
level. It uses the effect that atmospheric pressure reduced with height and can therefore be used
for this purpose.
In industry e.g. applications with low pressure ranges that need a measurement of vacuum,
require absolute pressure sensors for high accuracy. For example, in packaging industry, a
vacuum of a defined quality must be generated, so that a maximum shelf life can be safely
ensured. The residual amount of oxygen in the packaging (i.e. the residual pressure relative to
vacuum) is directly proportional to the shelf-life of the packaged food.
2. GAUGE PRESSURE
Gage pressure is the measurement of the difference between the absolute pressure and the local
atmospheric pressure. Local atmospheric pressure can vary depending on ambient temperature,
altitude and local weather conditions. A gage pressure by convention is always positive.
A negative' gage pressure is defined as vacuum. Vacuum is the measurement of the amount by
which the local atmospheric pressure exceeds the absolute pressure. A perfect vacuum is zero
absolute pressure. Figure 1 shows the relationship between absolute, gage pressure and vacuum.
3. DIFFERENTIAL PRESSURE
Differential pressure (DP or ∆p) is the difference between two applied pressures. For example,
the pressure at point “A” equals 100psi and the pressure at point “B” equals 60psi. The
differential pressure is 40psi (100psi – 60psi).
INDUSTRIAL APPLICATIONS FOR DIFFERENTIAL PRESSURE GAUGES
Differential pressure gauges are often found in industrial process systems and yet, they are easily
overlooked or misunderstood. In fact, a differential pressure gauge can often times provide
multiple solutions to everyday problems. Typical application of differential pressure gauge are in
Refineries, petrochemical or chemical plants include filter monitoring, liquid level measurement
and flow measurement.
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 FILTER MONITORING
Filtration is a vital part of an efficient operation in industrial process systems. A differential
pressure gauge can be used to detect a contaminated or clogged filter. As the filter collects
foreign materials, the pressure before the filter builds up. The Differential pressure gauge
measures the pressure before and after the filter. The more the filter gets clogged with particles,
the more the differential pressure increases. Once the differential pressure reaches a maximum
value, then the operator knows that the filter needs to be changed.
Figure: filter measuring setup
In addition to the three types of pressure measurement, there are different types of fluid systems
and fluid pressures.
 LIQUID LEVEL MONITORING
Sealed tanks often have an atmospheric pressure gas blanket on top of the contained liquid. The
pressure of the gas blanket adds to the hydrostatic pressure created by the water column of the
content. This makes it difficult to get an accurate level measurement using a conventional
pressure gauge. A differential pressure gauge measures the difference in gas pressure from the
total pressure, thus translating into a true liquid level reading. Differential pressure gauges can
also be used on production and injection wells to measure the difference between reservoir
pressure and bottom-hole pressure, or between injection pressure and average reservoir pressure.
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Figure: liquid level monitoring setup
 FLOW MONITORING
Differential pressure gauges are also used to measure the flow of a liquid inside a pipe. Utilizing
an orifice plate, venturi, or flow nozzle to reduce the diameter inside a pipe; the differential
pressure gauge measures the pressure before and after the orifice. The pressure drop across the
orifice is then mechanically translated by the differential pressure gauge into the flow rate.
Differential pressure gauges are an uncomplicated solution for a visual indicator when measuring
process flow.
Figure: flow monitoring
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MEASURING DEVICES FREQUENTLY USED IN MECHANICAL ENGINEERING
1. LIQUID COLUMN GAUGE (U-TUBE MANOMETER)
Technically a manometer is any device used to measure pressure. However, the word manometer
is commonly used to mean a pressure sensor which detects pressure change by means of liquid in
a tube. The U-tube manometer is somewhat self-descriptive. In its basic form it consists of a
clear glass or plastic tube shaped into the form of a 'U'. The tube is partially filled with a liquid,
such as water, alcohol, or mercury (although for safety reasons mercury is no longer commonly
used). The lower the density of
the liquid, the higher the sensitivity of the manometer. The diagram opposite shows a basic Utube manometer. Both ends of the tube are open, and atmospheric pressure acts equally on the
liquid through each end. Therefore the height of the liquid on each side of the U (in each limb) is
equal.
Now we show the U-tube manometer with an unknown pressure Punknown applied to one limb.
The other limb of the tube is left as it was, that is, atmospheric pressure Patm is maintained at its
open end. The unknown pressure acts on the liquid in the tube, forcing it down the limb it is
applied to. Because the liquid is incompressible, it rises up the other limb. Hence the height of
the liquid on either side of the tube is no longer equal. The difference between the height of the
liquid in each limb, h, is proportional to the
difference between the unknown pressure and atmospheric pressure. In a U-tube manometer, the
difference between the unknown pressure and atmospheric pressure is the gauge pressure. In a
U-tube manometer
where,
ρ is the density of the liquid in the tube, in kg-m-3
g is the acceleration due to gravity, that is, 9.81 m.s-2
h is difference between the heights of the liquid in each limb, in m
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Figure: U- tube manometer
APPLICATION OF U-TUBE MANOMETER
The U-tube manometer is not in wide use in industry, although it is sometimes used to calibrate
other instruments. It is mainly used in laboratories for experimental work and demonstration
purposes. It can be used to measure the pressure of flowing liquids as well as gases, but cannot
be used remotely. If pressures fluctuate rapidly its response may be poor and reading difficult.
2. INCLINED MANOMETER:
Pressure sensor more sensitive than the U-tube manometer. Hence it is more suitable for use with
smaller pressure measurements or where greater accuracy is required. This diagram shows its
basic design. One limb of the inclined tube manometer forms into a reservoir. The other limb of
the manometer is inclined at a known angle θ. The inclined limb is made from a transparent
material such as glass or plastic. The reservoir is usually made of plastic, but does not need to be
transparent. The surface area of the fluid in the reservoir A1 is much larger than the surface area
of the fluid in the inclined limb A2. Both limbs are open ended and so subject to atmospheric
pressure. If an unknown pressure Punknown is applied to the reservoir limb, the change in height
h1 will be relatively small compared to the change in height in the inclined limb h2.
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Figure: inclined manometer
The gauge pressure is given by the equation
Pgauge = Punknown - Patm = ρgd(A2/A1+sinθ)
Where,
r is the density of the liquid in the tube, in kg m–3
g is the acceleration due to gravity, that is, 9.81 m.s–2
d is the distance the liquid has moved along the inclined limb, in m
A2 is the cross-sectional area of the reservoir, in m²
A1 is the cross-sectional area of the liquid in the inclined limb
θ is the angle of the inclined limb from the horizontal.
Because A1 is much larger than A2, the ratio A1/A2 can be considered negligible. Therefore
Pgauge = Punknown - Patm = ρgdsinθ
APPLICATION OF INCLINED U-TUBE MANOMETER
The accuracy of inclined tube manometers relies less on the skill of the reader than U-tube
manometers. They are more sensitive, but unless the inclined limb is relatively long they cannot
be used over as wide a range of pressures. Inclined tube manometers are used where higher
sensitivity than a U-tube manometer is required. It cannot be read remotely, and it is usually used
with gases.
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3. BOURDON GAUGE
The Bourdon pressure gauge uses the principle that a flattened tube tends to change to a more
circular cross-section when pressurized. Although this change in cross-section may be hardly
noticeable, the displacement of the material of the tube is magnified by forming the tube into a C
shape or even a helix, such that the entire tube tends to straighten out or uncoil, elastically, as it
is pressurized.
Figure 3 (left) Bourdon gauge (right) Mechanism of the Bourdon gauge
In practice, a flattened thin-wall, closed-end tube is connected at the hollow end to a fixed pipe
containing the fluid pressure to be measured. As the pressure increases, the closed end moves in
an arc, and this motion is converted into the rotation of a (segment of a) gear by a connecting
link which is usually adjustable. A small diameter pinion gear is on the pointer shaft, so the
motion is magnified further by the gear ratio. The positioning of the indicator card behind the
pointer, the initial pointer shaft position, the linkage length and initial position, all provide means
to calibrate the pointer to indicate the desired range of pressure for variations in the behavior of
the Bourdon tube itself.
APPLICATION OF BOURDON GAUGE:
They are suitable for use with both liquids and gases, are used in a wide variety of applications,
both industrial and domestic. Applications range from tyre pressure gauges, measuring the
pressure in pneumatically controlled tools and machines, to pipeline pressure in chemical plants
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4. ELECTRONIC PRESSURE SENSORS
A pressure sensor measures pressure, typically of gases or liquids. A pressure sensor usually
acts as a transducer; it generates an electronic signal as a function of the pressure imposed.
Although there are various types of pressure transducers, one of the most common is the straingage base transducer. The conversion of pressure into an electrical signal is achieved by the
physical deformation of strain gages which are bonded into the diaphragm of the pressure
transducer. Pressure applied to the pressure transducer produces a deflection of the diaphragm
which introduces strain to the gages. The strain will produce an electrical resistance change
proportional to the pressure.
Figure 4 (left) Cut-away of an electronic pressure sensor (right) pressure sensor
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EXPERIMENT: 02
AIM: -TO DETERMINE THE METACENTRIC HEIGHT OF A FLOATING BODY.
INTRODUCTION:
When a body is immersed in a fluid, an upward force is exerted by the fluid on the body. The
upward force is equal to the weight of the fluid displaced by the body and is called the force of
buoyancy.
A. Centre of Buoyancy: Point through which force of buoyancy is supposed to act. This will
be the centre of gravity of the fluid displaced. This is because the buoyancy acts
vertically and is equal to the weight of the fluid displaced.
B. Meta centre: It is the point at which a body starts oscillating when a body is tilted by a
small angle.
C. Meta-centric height: The distance between the meta-centre of a floating body and the
centre of gravity of the body is called meta-centric height.
EXPERIMENTAL METHOD TO FIND OUT META-CENTRIC HEIGHT:
Let
W=Weight of the vessel including w1
G= Centre of gravity of the vessel
B= Centre of the buoyancy of the vessel
The moment due to change of G:
= 𝐺𝐺1 ∗ 𝑊
= 𝐺𝑀 tan 𝜃 ∗ 𝑊
The moment due to movement of W1:
=W1*x
For the body to be in equilibrium,
𝑊 ∗ 𝐺𝑀 tan 𝜃 = 𝑊1 ∗ 𝑥
Therefore,
𝐺𝑀 =
FLUID MECHANICS
𝑊1 ∗ 𝑥
𝑊 ∗ tan 𝜃
13
Figure: Meta- Centric height
EXPERIMENTAL PROCEDURE:
Specifications: W = ___________kg , w= _____________ kg
1. Fill up the tank with water.
2. Keep the ship floating over water.
3. Check the plumb for zero reading.
4. Displace the weight of the deck.
5. Measure the displacement and the tilted angle.
6. Repeat the steps for displacement of the weight.
OBSERVATION TABLE:
Sr.
no.
Left
x (m)
Right
Θ
x (m)
θ
1.
2.
3.
4.
5.
Faculty Signature
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CALCULATIONS:
RESULT:
Sr.
No.
Meta- centric Height
Left
Right
1.
2.
3.
4.
5.
The average meta-centric height is __________________ m.
CONCLUSION:
 The meta-centric height of the floating body is ______________ m by experimental
method.
 By Graphical method, meta-centric height is_______________ m.
Faculty Signature
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EXPERIMENT: 03
AIM: - VERIFICATION OF BERNOULLI’S THEOREM.
INTRODUCTION:
 When an incompressible fluid is flowing through a closed conduit, may be subjected to
various forces, which causes change of velocity, acceleration or energies involved.
 The major forces involved are pressure and body forces.
 According to Bernoulli’s theorem, if c/s area decrease than velocity increase and pressure
will decrease and vice-versa.
 Bernoulli’s Theorem states that, in steady, ideal flow of an in compressible fluid, the total
energy at any point of the fluid is constant. The total energy consists of Pressure Energy,
Kinetic Energy, & Potential Energy (Datum Energy).
 Therefore,




Pressure Energy = P / ρg
Kinetic Energy = V2 / 2g
Datum Energy = Z
Where P = pressure, V= velocity, ρ= density of fluid, g=9.81𝒎/𝒔𝟐
 The applications of Bernoulli’s theorem are:
 Venturi Meter
 Orifice Meter
 Pilot Tube
EXPERIMENTAL PROCEDURE:
1. Keep the bypass valve open & start the pump & slowly start closing the valve.
2. The water will start flowing through the flow channel. The level in the piezometer tubes
shall start rising.
3. Open the valve at the delivery tank side, & adjust the head in piezometer tubes to a steady
position.
4. Measure the heads at all the points and also discharge with the help of measuring tank in
the measuring tank.
5. Change the discharge & repeat the procedure.
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Figure: Bernoulli’s apparatus
PRECAUTIONS:
1. Note down the head readings after the level has been stabilized.
2. After noting the discharge, drain the measuring tank.
3. After completion of experiment, drain all the water from equipment.
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OBSERVATION TABLE:
Heads ‘h’ in m
Discharge
time for 5
litter
of
warer flow
Sr.No.
Tappings
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1
2
Table for area at different c/s and corresponding datum:
Tapping
Area m2
h* m
Sr. No.
Inlet
1
2
3
4
5
6
7
8
9
10
11
12
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13
14
Outlet
CALCULATION:
Area of flow channel, A = ________________ m2 (from table)
1. Discharge: Q = 0.01 m3 / s
2. Velocity of water , v = Q/A m/s
Therefore, Velocity head = v2/2g in m
3. Pressure head
H = P/ ρg = h + h*
Where h piezometer reading and
h* from table
4. Now, datum line is same at inlet and outlet hence, Z1=Z2=Z3
Therefore for each tapings the summation of pressure, velocity and potential head remain
constant that we have to prove from calculation.
Note: practically the value of total head goes on reducing slightly toward outlet, due to various
factors which are not considered, e.g. friction, turbulence etc.
Faculty Signature
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Faculty Signature
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CONCLUSION:
1. As value of total energy at each tapings is fairly constant.
2. As the velocity of flow increases, pressure head drops.
3. Bernoulli’s equation,
P / ρg + V2 / 2g + Z = constant is thus verified.
Faculty Signature
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EXPERIMENT: 04
AIM: -TO MEASURE THE VELOCITY OF FLOW USING PITOT TUBE.
INTRODUCTION:
A Pitot tubes are used in a variety of applications for measuring fluid velocity. This is a
convenient, inexpensive method for measuring velocity at a point in a flowing fluid. Pitot tubes
(also called pitot-static tubes) are used, for example, to make airflow measurements in HVAC
applications and for aircraft airspeed measurements.
APPARATUS:
1. A pitot tube
2. A small rectangular channel (or a pipe) with water flowing through it.
THEORY AND EQUATION:
A pitot tube is a small open tube bent at right angle and is places in the flow such that one
leg is vertical and other leg is horizontal(fig.). It is used to measure the velocity of flow at
any point in a pipe or channel. It works on the principle that if the velocity of flow at any
point becomes zero, the pressure there is increased due to conversion of kinetic energy
into pressure energy. The velocity of flow (V) is determined by measuring the rise of
liquid (h) in the tube form the equation:
𝑽𝟐
h=𝟐𝒈
or
V=√𝟐𝒈𝒉
In actual practice, the velocity head is multiplied by a constant k the value of which depends
upon the quality of the tube.
Figure- Pitot tube
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𝑉2
k×h=2𝑔
(The value of k is determined by actually measuring the velocity and velocity head ‘h’)
PROCEDURE:
1. Place the Pitot tube in the moving water properly.
2. Note down the reading of ‘h’
3. Repeat the experiment by placing the Pitot tube at different depths, finD the mean value
of ‘h’ and hence determine the velocity.
4. To find the value of ‘k’ , measure the actual velocity of flow(v) with the help of a
“current meter” and use the following relation :
𝑽𝟐
k 𝟐𝒈
=V
2
mean
2g
The value of ‘k’ varies from 0.9 to 0.99.
PRECAUTION:
1. Note down the reading accurately.
2. A pitot tube should be used preferably in pipes or channels with shallow water
moving at high velocity.
OBSERVATION TABLE:
Table: pitot tube/ current meter
S.NO. Velocity head reading ‘h’ Current meter reading
1.
2.
3.
4.
Mean value, ‘h’=…...........................
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Mean value, current meter=………………………….
Now, mean velocity head, h= V
2
mean
2g
Vmean =…………………..
Again, mean velocity as obtained from current meter reading
V=…………………….
Coefficient of the meter,
Vmean
K=
𝑽𝟐
………………….
CONCLUSION:
1. Velocity of flow by Pitot tube is………………………….
2. Velocity of flow by current meter is ………………….
3. Coefficient of meter is ………………………………………..
Faculty Signature
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EXPERIMENT: 05
AIM: TO DETERMINE CO-EFFICIENT OF DISCHAR Cd USING VENTURIMETER.
APPARATUS:Venturimeters are widely used for determination of flow of fluid. While using the venture their
calibration is important. The equipment enables to determine the co- efficient of discharge of
venturimeters.
Figure: Venturimeter
SPECIFICATIONS:
1. Supply pipe of Ø 21mm (3/4’’) connected to inlet manifold.
2. Venturimeter size inlet Ø 21.5 mm and throat Ø 15mm
3. Differential mercury manometer tappings provided at inlet and throat of venturimeter.
Manometer size 50cm height. Measuring tank size-300mm x 300mm height.
EXPERIMENTAL PROCEDURE:1. Check all the clamps for tightness
2. Open the gate valve and start the flow.
3. Open the outlet valve of the venturimeter and close the valve of orifice meter.
4. First open air cocks then open the venturimeter cocks, remove all the air bubbles and
close the air cocks slowly and simultaneously so that mercury does not run away into
water.
5. Close the gate valve of measuring tank and measure the time for 10 liters water discharge
and also the manometer difference.
6. Repeat the procedure by changing the discharge.
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PRECAUTIONS:1. Operate manometer valve gently while removal of air bubble so that mercury in
manometer does not run away with water.
2. Do not close the outlet valve completely.
3. Drain all the water after completion of experiment.
OBSERVATION TABLE FOR VENTURIMETER:Sr. No.
Manometer diff. h (m)
Time for 10 liter water discharge t (sec.)
CALCULATIONS:1. Actual discharge, QA= 0.01/t
2. Let ‘H’ be the water head across manometer in Meter.
H= Manometer difference * (sp. Gravity of Mercury-sp. Gravity of water)
Or
H= Manometer difference x (13.6-1)
A= Cross sectional area at inlet to venturimeter =3.63 x 10-4 m2
a = Cross sectional area at throat to venturimeter= 1.76 x 10-4 m2
Theoretical Discharge,
2𝑔𝐻
𝑄𝑡ℎ = 𝐴 ∗ 𝑎 ∗ √𝐴2 −𝑎2
m3/s
Or
Qth= 0.00318 *√ h
3.
m3/ s ( h in m)
Co- efficient of discharge Cd= Qa/ Qth
Faculty Signature
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RESULT TABLE:
Sr. No.
Manometer diff. h (m)
Cd
CONCLUSION:Calibrated values of co- efficient of discharge for venturimeter is ________________
Faculty Signature
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EXPERIMENT: 06
AIM: -TO DETERMINE
ORIFICEMETER.
CO-EFFICIENT
OF
DISCHARGE
Cd
USING
APPARATUS:- Orifice meters are widely used for determination of flow of fluid. While using
the venture their calibration is important. The equipment enables to determine the co- efficient of
discharge of Orifice meter.
Figure:Orifice meter
SPECIFICATIONS:
4. Supply pipe of 21mm (3/4’’) connected to inlet manifold.
5. Orifice meter size inlet 20 mm and throat 14mm
6. Differential mercury manometer tappings provided at inlet and throat of Orifice meter.
Manometer size 50cm height. Measuring tank size-300mm x 300mm height.
EXPERIMENTAL PROCEDURE:7. Check all the clamps for tightness
8. Open the gate valve and start the flow.
9. Open the outlet valve of the Orifice meter and close the valve of Venturimeter.
10. First open air cocks then open the Orifice meter cocks, remove all the air bubbles and
close the air cocks slowly and simultaneously so that mercury does not run away into
water.
11. Close the gate valve of measuring tank and measure the time for 10 liters water discharge
and also the manometer difference.
12. Repeat the procedure by changing the discharge.
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OBSERVATION TABLE FOR ORIFICEMETER:Sr. No.
Manometer diff. h (m)
Time for 10 liter water
discharge t (sec.)
CALCULATIONS:1. Actual discharge, QA= 0.01/t m3/ s
2. Let ‘H’ be the water head across manometer in metres.
H= Manometer difference * (sp. Gravity of Mercury - sp. Gravity of water)
1. Or
H= Manometer difference x (13.6-1)
or
H= h x 12.6 m
A= Cross sectional area at inlet to Orifice meter =3.14 x 10-4 m2
a= Cross sectional area to Orifice meter
= 1.54 x 10-4 m2
Theoretical Discharge,
2𝑔𝐻
𝑄𝑡ℎ = 𝐴 ∗ 𝑎 ∗ √𝐴2 −𝑎2
Or
Qth= 0.00277 x √h m3/ s
3. Co- efficient of discharge Cd= Qa/ Qth
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30
m3/s
( h in m)
Faculty Signature
Faculty Signature
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31
RESULT TABLE:
Sr. No.
Manometer diff. h (m)
Cd
PRECAUTIONS:1. Operate manometer valve gently while removal of air bubble so that mercury in
manometer does not run away with water.
2. Do not close the outlet valve completely.
3. Drain all the water after completion of experiment.
CONCLUSION:Calibrated values of co- efficient of discharge for Orifice meter is ______________
Faculty Signature
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EXPERIMENT: 07
AIM: - TO DETERMINE CO-EFFICIENT OF DISCHARGE Cd THROUGH OPEN
CHANNEL FLOW OF TRI-ANGULAR (V- NOTCH) & RECTANGULAR NOTCH.
INTRODUCTION:
 The notch is hydraulically defined as an opening provided in the side of tank , such that
liquid level is below top edge of the opening notch are generally used for measuring the
discharge of liquid in chamber.
 Different shapes of notch generally used for rectangular, triangular, trapezoidal, etc.
 A centrifugal pump sucks the water from the sump tank, and discharge it to a small flow
channel.
 The notch is fitted at the channel.
 All the notches and weirs are inter changeable.
 The water flowing over the notch falls in collector.
 The water flowing over the notch falls in the collector.
 Water coming from collector can be directed to the sump tank or to the measuring tank
for the measurement of flow.
EXPERIMENTAL PROCEDURE:
1. Check the experimental setup for leaks. Measure the dimensions of collecting tank and
the notch.
2. Observe the initial reading of the hook gauge and make sure there is no discharge. Note
down the sill level position of the hook gauge.
3. Open the inlet valve of the supply pipe for a slightly increased discharge.
Wait for some time till the flow become steady.
4. Adjust the hook gauge to touch the new water level and note down the reading.
Difference of this hook gauge reading with initial still level reading is the head over the
notch (h).
5. Collect the water in the collecting tank and observe the time t to collect H height of
water.
6. Repeat the above procedure for different flow rates by adjusting the inlet valve opening
and tabulate the readings.
7. Complete the tabulation and find the mean value of Cd.
8. Take the readings for different flow rates.
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33
9. Repeat the same procedure for other notch also.
Figure: V-notchFigure: Rectangular -notch
OBSERVATION TABLE:
Length of the rectangular notch = ___________m
Angle of the triangular notch = __________deg
Measuring tank area A = _________m2
Sr. No.
Sill level reading
‘m’
Height on upstream
‘h’ m
Discharge time for
particular height of
measuring tank
For triangular or v-notch
For rectangular notch
Faculty Signature
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34
CALCULATION:
FOR TRIANGULAR NOTCH:
1. Actual discharge Qactual = A* particular height / time (m3/s)
2. Theoretical discharge:
𝑄𝑡ℎ =
8
𝜃
5
tan √2𝑔ℎ ⁄2
15
2
3. Co-efficient of discharge Cd = Qactual / Qth
FOR RECTANGULAR NOTCH:
1. Actual discharge Qactual = A* particular height / time (m3/s)
2. Theoretical discharge:
𝑄𝑡ℎ =
2
3
√2𝑔 𝐿 ℎ ⁄2
3
3. Co-efficient of discharge Cd = Qactual / Qth
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35
Faculty Signature
CONCLUSION
The co-efficient of discharge for V-notch is _______________.
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36
The co-efficient of discharge for Rectangular notch is _______________.
Faculty Signature
EXPERIMENT: 08
AIM:-TO DETERMINE THE DIFFERENT TYPES OF FLOW PATTERN BY
RENOLDS’S EXPERIMENT.
REYNOLDS APPARATUS
 Whenever a fluid is flowing through a pipe, the flow is either laminar or turbulent. When
fluid is flowing in parallel layers or laminar, sliding past adjacent laminar. It is called
laminar flow.
 When the fluid does not flow in parallel layers and there is intermingling of fluid
particles then the flow is said to be turbulent Existence of these two types was first
demonstrated by ‘OSBORN REYNOLDS NO- 1883.
 The apparatus consists of a constant head supply tank supplied with a water. This tank is
provided with a bell mouth outlet to which a transparent tube is fitted.
 At outlet of the tube a regulating valve is provided .A dye tank containing colored dye is
fitted above the supply tank. The water flows through pipe and dye is injected at the
center of the pipe. When the velocity of flow is low (i.e. flow is laminar) then dye
remains in the form of straight filament.
 As the velocity of water (i.e. flow of water) is increased, a state is reached when the dye
filament becomes irregular and water.
 With further increase of velocity of water through the tube, dye filament becomes more
and more irregular and ultimately the dye diffuses over the entire cross section of the
tube.
 The velocity at which the flow changes from laminar to turbulent for the case of a given
fluid at given temperature and in a given pipe is known as critical velocity.
 The state of flow between these two types of flow is known as ‘transition state’ or flow in
transition.
 The Occurrence of laminar and turbulent flow is governed by relative magnitudes of
inertia and viscous forces. Reynolds related the inertia forces to viscous forced and
arrived at a dimensionless parameter now called ‘Reynolds number’
EXPERIMENTAL PROCEDURE
1. Fill up water up to the mark.
2. Fill up Sufficient water in dry tank and put a small amount of potassium permanganate in
to water.
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37
3. Prime pump (remove the end plug & fill up water, remove all the air. Then tight the plug.
Fitted near the flow control valve.) Connect the electric supply and start pump. Adjust the
water flow. Flow to about 2 Ipm. Start the dye injection.
4. Wait for some time. A steady line of dye will be observed. Adjust dye flow, if required.
5. Slowly increase the water flow see that water level in supply tank remains constant. At
particular flow rate, dye line will be disturbed note down this flow rate. By using 1 lit
measuring flask and stop watch.
6. Further increase the flow. The disturbances of dye line will go on increasing and at
certain flow; the dye line diffuses over the entire cross section. Note down this flow.
7. Slightly increase the flow and then slowly reduce the flow. Note the flow at which
diffused dye tends to become steady. (Beginning of transition zone while reducing
velocity.)
8. Further reduce the flow and note the flow at which dye line becomes straight and steady.
9. After completion of experiment drain all the water. (Drain plug is bottom of the sump
tank) and tight the Drain plug. Also clean the dye container.
OBSERVATION TABLE:Sr. No.
Flow Type
Time/ 0.5 lit. (sec)
OBSERVATIONS:
1. Increasing Velocity
(a)
Flow at beginning of transition
(b)
Flow at beginning of turbulence
2. Decreasing Velocity
(a)
Flow at beginning of transition
(b)
Flow at beginning of laminar region.
CALCULATION:
I.D. of pipe =25 mm cross sectional area of pipe
A =4.9 x 10-4 m2
Let time required for 0.5 liter in measuring flask be ‘t’ sec.
Then, flow, Q= 0.0005/t
m3/s
Velocity,
FLUID MECHANICS
V= Q/A
m/s
38
Then Reynolds number,
Re= p VL/ µ
Re= VD/ v
Where,
P= Density of fluid= 9810 Kg/ m3
V= Velocity, m/sec
L= Characteristic linear dimension= 0.025 mtr.
D= Diameter of the pipe= 0.025 m.
v= Kinetic viscosity of fluid= 0.805 x 10-8 m2/ s
µ = 7897.05 x 10-6 N-s / m2
FLUID MECHANICS
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Faculty Signature
CONCLUSION
While increasing the velocity, laminar flow is disturbed at slightly higher velocity. But
at the time of reducing the velocity, the flow does not turn to laminar at this velocity, but
becomes laminar at still lower velocity is called lower critical velocity.
Lower critical Reynolds number flow is always laminar and above upper critical
Reynolds number flow is always turbulent. Practically upper critical Reynolds number lies
between2700 to 4000 and lower critical Reynolds number is approximately 2000. Between
Reynolds number 2000 and 4000 the transition region exists.
FLUID MECHANICS
40
Faculty Signature
EXPERIMENT: 09
AIM: TO DETERMINE THE FRICTION FACTOR FOR THE DIFFERENT PIPES.
INTRODUCTION AND THEORY
The flow of liquid through a pipe is resisted by viscous shear stresses within the liquid and the
turbulence that occurs along the internal walls of the pipe, created by the roughness of the pipe
material. This resistance is usually known as pipe friction and is measured is meters head of the
fluid, thus the term head loss is also used to express the resistance to flow.
Many factors affect the head loss in pipes, the viscosity of the fluid being handled, the size of the
pipes, the roughness of the internal surface of the pipes, the changes in elevations within the
system and the length of travel of the fluid. The resistance through various valves and fittings
will also contribute to the overall head loss.
In a well-designed system the resistance through valves and fittings will be of minorsignificance
to the overall head loss and thus are called Major losses in fluid flow.
The Darcy-Weisbach equation Weisbach first proposed the equation we now know as the DarcyWeisbach formula or Darcy-Weisbach equation:
hf = f.L. v2/ 2.g.d
Where:
hf = head loss (m)
f = Darcy friction factor
L = length of pipe work (m)
d = inner diameter of pipe work (m)
v = velocity of fluid (m/s)
g = acceleration due to gravity (m/s²)
The Darcy Friction factor used with Weisbach equation has now become the standard head loss
equation for calculating head loss in pipes where the flow is turbulent.
APPARATUS DESCRIPTION
The experimental set up consists of a large number of pipes of different diameters. The pipes
have tapping at certain distance so that a head loss can be measure with the help of a U - Tube
manometer. The flow of water through a pipeline is regulated by operating a control valve which
is provided in main supply line. Actual discharge through pipeline is calculated by collecting the
water in measuring tank and by noting the time for collection.
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41
The apparatus consist of four pipes with I.D.’s , 22.5 mm G.I. pipe, 17.5 G.I. pipe 14mm copper
and 14mm Aluminum pipe. So that loss of head can be compared for different diameters and
different materials. A flow control Valve is provided at outlet of pipes. Which enables
experiments to be conducted at different flow rates. I.e. at different Velocity’s.
Tappings are provided along the length of pipes, so that drop of head can be visualized
along the length of pipe. Each pipe is provided with valve at outlet. Which enables heads to be
controlled.
EXPERRIMENTAL PROCEDURE:1. Fill up water in the Sump tank. (This water should be free of any oil content.)
2. Open all the Outlet valves and start the pump.
3. Check for leakages by closing three of outlet valves, for each pipe, and correct the leaks,
if any.
4. Open the outlet valves of the pipe to be tested.
5. Remove all the air bubbles from manometer and connecting pipes.
6. Reduce the flow. Adjust outlet valves, so that water heads in manometer are to the
readable height.
7. Note down the heads and flow rate.
8. Now, increase the flow and accordingly adjust the outlet valve, so that water will not
overflow. Note down heads and flow.
9. Repeat the procedure for other pipes.
(Note- During measuring the heads, slight variation may occur due to Voltage changes, Valves
etc. in such Cases, average readings may be taken.)
OBSERVATION TABLE:Sr.
No.
Pipe type
Head drop h ‘m’
CALCULATIONS:1) Ø 23mm G.I. pipe:FLUID MECHANICS
42
Flow rate t sec (Time for 10
Lit. in Sec.).
𝜋
Area of pipe, 𝐴 = 𝑑 2
4
m2
=( π/4) x(0.023)2 m2
= 0.0004154 m2
Discharge, 𝑄 = 0.01/𝑡
m3/ Sec.
Velocity of water, V = Q/A m/ Sec.
Let, ‘f’ be the Coefficient of friction. Test length of pipe is 1 meter.
For 1 meter length, drop of head hf
hf = Manometre difference.
According to Darcy’s- Weishbatch equation,
hf = f.L. v2/ 2.g.d
Where, f = Coefficient of friction.
L = Length of pipe= 1 m
v = Velocity of water m/sec.
g = Gravitational acceleration= 9.81 m/s2
d = inside diameter of pipe, m
Then,
f= 2. hf . d .g / L.v2
The, Value of coefficient of friction is not constant and depends upon roughness of pipe
inside surface and Reynolds’s number. Any oil content in water also affects value of ‘f’.
(Repeat the same procedure for other pipes.)
FLUID MECHANICS
43
Faculty Signature
RESULT TABLE:
Sr.
No.
Pipe type
Friction coefficient
CONCLUSION:1. Loss of head due to friction is proportional to length of pipe and square of velocity.
2. Loss of head is inversely proportional to inside diameter of pipe.
3. Average value of ‘f’ fora)
b)
22.5 mm G.I. Pipe17.5 mm G.I. Pipe-
FLUID MECHANICS
44
c)
d)
14 mm Copper Pipe14 mm Aluminum PipeFaculty Signature
EXPERIMENT:10
AIM:- TO DETERMINE THE LOSS COEFFICIENTS FOR DIFFERENT PIPE
FITTINGS.
LOSSES IN PIPE FITTINGS APPARATUS
While installing a pipeline for conveying a fluid, it is generally not possible to install a long
pipeline of same size all over and straight for various reasons, like space restrictions, aesthetics,
location of outlet etc. Hence, the pipe size varies and it changes its direction. Also, various
fittings are required to be used. All these variations of sizes and the fittings cause the loss of fluid
head. The apparatus is designed to demonstrate the loss of head due to following fittings1.
2.
3.
4.
Pipe bend (large bend)
pipe elbow (small bend)
Sudden Expansion of the flow.
Sudden Contraction of the flow.
The set up consists of 15mm basic piping, in which the above fittings are installed. A Pressure
tapping is provided at inlet and outlet of each fitting, which is connected to a common
differential manometer. A gate valve at outlet and a bypass valve at pump discharge control the
flow of water.
SPECIFICATIONS1.
2.
3.
4.
5.
6.
7.
8.
9.
Basic piping of 15mm size.
19mm small bend- 1 Nos.
14mm large bend- 1 Nos.
Sudden expansion from ø 16mm to 27.5 mm
Sudden contraction from ø 27.5 mm to 16 mm
½ hp centrifugal pump to circulate the water through the piping.
Multiple tapping differential manometers.
Sump tank of suitable capacity.
Measuring tank - 300 mm x 300 mm x 300 mm height.
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45
EXPERIMENTAL PROCEDURE1. Fill up sufficient clean water in the sump tank.
2. Fill up mercury in the manometer.
3. Connect the electric supply. See that the flow control valve and bypass valve are fulley
open and all the manometer cocks are closed. Keep the water collecting funnel in the
sump tank side.
4. Start the pump and adjust the flow rate. Now, slowly open the manometer tapping
connection of small bend. Open both the cocks simultaneously.
5. Open air vent cocks. Remove air bubbles and slowly & simultaneously close the cocks.
Note down the manometer reading and flow rate.
6. Close the cocks and similarly, note down the readings for other fittings. Repeat the
procedure for different flow rates.
OBSERVATIONSType of fitting- Elbow.
Sr. No.
Manometer diff. m Flow rate (Time for 10 lits. Of water ) t,
of Hg
sec
Type of fitting- Bend
Sr. No.
Manometer diff. m Flow rate (Time for 10 lits. Of water ) t,
of Hg
sec
Type of fitting- Sudden contraction.
Sr. No.
FLUID MECHANICS
Manometer diff. m Flow rate (Time for 10 lits. Of water ) t,
of Hg
sec
46
Faculty Signature
Type of fitting- Sudden Expansion
Sr. No.
Ma
Flow rate (Time for 10 lits. Of
nometer diff. m of water ) t, sec
Hg
PRECAUTIONS1. Open both the manometer cocks slowly and simultaneously, otherwise the mercury will
run away from the manometer.
2. Operate the valves gently. Do not forcely rotate them.
3. Always use clean water for the experiment.
CALCULATIONS1) ELBOWElbow, there is no change in the magnitude of velocity of water, but there is change in the
direction of water, hence head loss exists.
For elbow, Mean area A= (π/4) d2 = 2.83 x 10-4 m2
Diameter of the elbow, d = 19mm = 0.019 m.
Mean velocity of flow, V = Q/A m/s.
Where, Q = 0.01 / time required for 10 lit. m3/ sec.
Loss of head at elbow,h1 = K (V2/ 2g) m of water.
Actual head loss, h1 = Manometer diff. (m) x 12.6 .
2) PIPE BEND-
FLUID MECHANICS
47
Similar to elbow, loss of head at bend is due to change in the direction of water.
But unlike the elbow, change of direction is not abrupt, hebce loss of head is less as compared to
elbow.
For bend,Mean area, A = ( π/4 ) d2 = 1.54 x 10-4 m2
Diameter of bend, d = 14mm = 0.014 mFaculty Signature
Mean velocity of flow, V = Q/ A m/ sec.
Where, Q = 0.01 / time required for 10 lit. m3 / sec.
Loss of head at bend, h1 = K ( V2 / 2g )
Actual head loss, h1 = Manometer diff. (m) x 12.6
Experimentally obtained value of K is greater than this as it includes the loss of head for the two
collars also.
3) SUDDEN CONTRACTIONAt sudden contraction, velocity of water increases which causes pressure head to drop (according
to Bernoulli’s theorem), in addition to this there is loss of head due to sudden contraction.
Hence,
Manometer reading = (Head drop due to increment of velocity) + (head loss due to sudden
contraction.)
Assuming no loss to be there due to contraction and applying Bernoulli’s theorem at inlet and
outlet of the section,
P1 / W + V12 / 2g = P0 / W +V02 / 2g
Inlet size = ø 27.5 mm = 0.0275 m.
Ai = 5.94 x 10-4 m2
Outlet size = ø 16 mm =0.016 m.
A0 = 2.01 x 10-4 m2
Vi = Q / Ai m / s.
Vo = Q / A0 m/s.
Where, Q = discharge = (0.01) / time required for 10 lit. m3 / sec.
Ai and A0 = inlet and outlet area respectively , m2.
Drop of head due to velocity increment,
hv= V02 / 2g – V12 / 2g
Actual drop, h = (manometer reading x 12.6 )
Loss of head due to sudden contraction
hc = h - hv
hc = K (V02/ 2g)
Theoretically, value of K depends upon inside diameter, curvature radius, turbulence surface
roughness and many other factors. Hence, it is better to determine the value of K experimentally.
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48
4) SUDDEN EXPANSION:At sudden expansion of flow, pressure increases due to reduction in velocity, but there is
pressure drop due to sudden expansion also. Hence, at sudden expansion one gets rise of pressure
lesser than that predicted theoretically.
Assuming no less of head and applying Bernoulli’s equation at inlet and outlet, similar to
equation used for sudden contraction,
Rise of pressure.
hv= V12 / 2g – V02 / 2g
Loss of head due to sudden expansion,
Actual, he = hv – (Manometer reading (m) x 12.6)
Theoretical,
he = K (Vi – V0) 2 / 2g
RESULT TABLE:
Sr. No.
Fitting
Friction Co efficient
CONCLUSION1. For any type of fitting, there is a loss of head, but its magnitude depends upon the type of
fitting.
2. Loss of head occurs due to change in magnitude or direction of the fluid velocity.
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49
EXPERIMENT: 11
AIM: TO DETERMINE THE VISCOSITY OF FLUID BY VISCOMETER (REDWOOD
APPARATUS)
OBJECTIVE
 To determine the kinematic viscosity and absolute viscosity of the given lubricating
oil at different temperatures using Redwood Viscometer.
APPARATUS REQUIRED:
 Redwood Viscometer
 Thermometer 0-100°c (2 Nos)
 Stop watch
 50 ml standard narrow necked flask
 Given Sample of oil
DESCRIPTION:
The redwood viscometer consist of vertical cylindrical oil cup with an orifice in the center of its
base. The orifice can be closed by a ball. A hook pointing upward serve as a guide mark for
filling the oil. The cylindrical cup is surrounded by the water bath. The water bath maintain the
temperature of the oil to be tested at constant temperature. The oil is heated by heating the water
bath by means of an immersed electric heater in the water bath, the provision is made for stirring
the water, to maintain the uniform temperature in the water bath and to place the thermometer ti
record the temperature of oil and water bath. The cylinder is 47.625mm in diameter and
88.90mm deep. The orifice is 1.70mm in diameter and 12mm in length,this viscometer is used to
determine the kinematic viscosity of the oil. From the kinematic viscosity the dynamic viscosity
is determined.
THEORY:
Viscosity is the property of fluid. It is defined as “The internal resistance offered by the fluid to
the movement of one layer of fluid over an adjacent layer. It is due to the Cohesion between the
molecules of the fluid. The fluid which obey the Newton law of Viscosity are called as
Newtonian fluid. The dynamic viscosity of fluid is defined as the shear required to produce unit
rate of
Angular deformation
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50
Figure (a): Redwood Viscometer
 After the cork at the bottom of the viscometer is removed, the time in seconds, which is
knownas the Saybolt Universal Seconds (S.U.S.), for the liquid to fill the 60 cm3 standard
flask is measured.
 This may then be converted to kinematic viscosity, by using the formula
EXPERIMENTAL PROCEDURE:
1.
2.
3.
4.
5.
6.
Clean the cylindrical oil cup and ensure the orifice tube is free from dirt.
Close the orifice with ball valve.
Place the 50 ml flask below the opening of the Orifice.
Fill the oil in the cylindrical oil cup up to the mark in the cup.
Fill the water in the water bath.
Insert the thermometers in their respective places to measure the oil and water
bathtemperatures.
7. Heat the by heating the water bath, Stirred the water bath and maintain the
uniformtemperature.
8. At particular temperature lift the bal valve and collect the oil in the 50 ml flask and
9. Note the time taken in seconds for the collecting 50 ml of oil. A stop watch is used
10. Measure the time taken. This time is called Redwood seconds.
11. Increase the temperature and repeat the procedure ‘8’ and note down the
Redwoodseconds for different temperatures.
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51
OBSERVATION TABLE:
(1) Room temperature TR = ……. °C
(2) Density of oil at room temperature = …….. gm/cm2
Sr. no
Temperature Time taken Kinematic
of oil °C
tofill 50ml
Viscosity in
‘Centi
Stokes’
Density in
gm/cc
Dynamic (or)
Absolute
viscosity ‘
Centi Poise’
1.
2.
3.
4.
5.
CALCULATION:
Kinematic Viscosity 𝜈
𝐵
= 𝐴𝑡 − 𝑡
 Where A and B are calibration constants having the values of 0.226x10-6 m2/s2 and
195x10-6 m2, respectively, ν is the kinematic viscosity in m2/s and t is the time in s. The
determination of viscosity is based on the premise that liquids with higher viscosities
would take longer to fill the flask since their resistance to deformation (and hence, flow)
would be higher. Note that the determined property is kinematic viscosity, rather than
dynamic viscosity, as the density of the liquid is an influential factor for flow due to
gravity.
Density of oil at particular temperature
ρt = ρR - 0.00065 ( T - TR )
T = Temperature at which the density is required
TR = Room Temperature
ρ
R
= Density of oil at room temperature in gm / cm3
The kinematic viscosity of the fluid is defined as the ratio of the dynamic viscosity
To density of the fluid. Its symbol is ‘v’
𝑣=
𝑤ℎ𝑒𝑟𝑒
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52
µ
𝛒
µ = dynamic viscosity
ρ = mass density of oil
µ= 𝒗 × 𝛒
Graph: Following graph has to be drawn
(1)Temperature Vs Redwood seconds
(2)Temperature Vs Kinematic Viscosity
(3)Temperature Vs Dynamic Viscosity
FLUID MECHANICS
53
CONCLUSION:
The kinematic and dynamic viscosity of given oil at different temperatures were
determined.
Sr. no
Temp. of oil
Dynamic
viscosity
Kinematic
viscosity
1.
2.
3.
4.
5.
Faculty Signature
FLUID MECHANICS
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