Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Fluid Mechanics Laboratory
(CM-405)
List of experiments prescribed by RGPV, Bhopal
1. To determine the local point pressure with the help of
pitot tube..
2. Calibration of Venturimeter.
3. Calibration of Open channel Flow Measuring Devices
4. Calibration of Orifice Meter.
5. Calibration of Nozzle meter and Mouth Piece.
6. Reynolds experiment for demonstration of stream lines
& turbulent flow.
7. Determination of metacentric height.
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
EXPERIMENT NO.1
Pitot tube
Date of conduction:Date of submission:Submitted by other members:1.
2.
3.
Group no:-
Signature
Name of faculty incharge:
Name of Technical Assistant:
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Objective: -
Calibration of Pitot tube and measurement of air
velocity.
Theory: -
A Pitot tube is a pressure measurement instrument used to
measure fluid flow velocity. The Pitot tube is used to measure the local
velocity at a given point in the flow stream and not the average velocity in
the pipe or conduit. As this tube contains fluid, a pressure can be
measured; the moving fluid is brought to rest (stagnates) as there is no
outlet to allow flow to continue. This pressure is the stagnation pressure
of the fluid, also known as the total pressure.
Bernoulli's equation states:
Stagnation pressure = static pressure + dynamic pressure
Which can also be written
Solving that for velocity we get:
(1)
Where:




is fluid velocity;
is stagnation or total pressure;
is static pressure;
and is fluid density.
The value for the pressure drop
the manometer:
–
or
due to
, the reading on
(2)
Where:
is the density of the fluid in the manometer

is the manometer reading
And from equations (1) and (2)

(3)
Equation (3), can be used to measure fluid velocity, but For Pitot tube
measurement, measurement error could be resulted due to certain
reasons, errors may introduce in the measurement; that the probe is not
aligned with the flow direction. At low Reynolds number, validity of
𝑉 = √2𝑔∆ℎ
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
applying Bernoulli equation should be investigated further. The geometry
of the probe sting support affects the accuracy of measurement.
Therefore, calibration of pitot tube required, which can be done using a
hot-wire anemometer. Considering the linear law
𝑉 ∝ 𝑓(∆ℎ)
The pitot tube equation;
𝑉 = 𝐾√2𝑔∆ℎ
Here, K is pitot tube coefficient and needs to determine by calibration.
A heated wire of micro-meters in diameter and mini-meters in
length is inserted in the flow field. The flow velocity can be sensed based
on the principle of convective heat transfer concerning flow over a heated
2-D circular cylinder. In anemometer, the circuitry consists of a feedback
loop of a Wheatstone bridge and a series of amplifiers which directly flow
velocity.
Pitot tube is basically for time-mean velocity measurement (very
low frequency response. It is low cost, easy to use. Hot-wire is basically
for real-time velocity fluctuations measurement (high frequency
response).
Procedure:
1. Adjust air intake with the help of a valve, fix anemometer probe at
the discharge of channel.
2. Connect manometer to the Pitot tube and piezo-meter tube.
3. Start the blower.
4. Take the flow rate reading anemometer and pressure drop in
manometer.
5. Repeat the step 3 & 4 for unknown flow rate & record the reading
in the tube and draw the graph.
6. The above procedure may also be repeated for difference in depth
of Pitot tube.
Observation Table:S. no.
1
2
3
4
Anemometer
reading, V
Manometer
reading, ∆h
Actual velocity
V
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Calculation:- Plot a graph velocity Vs head as shown and determine
the slope of the line and coefficient of velocity of Pitot
tube. Use linear regression to fit the equation.
K = slope/2g
Results: The pitot tube coefficient K =
Conclusion:-
Precautions:1.
2.
3.
4.
Do not close air regulating valve fully to avoid over loading at
blower meter.
Use only mild detergents to clean the instruments do never use
any organic solvent and strong acid or alkali.
Ground the instrument properly to avoid electric shock.
The density of fluid in manometer is one.
Suggestion
Further reading resources:
Book: Lab experiment related theory available in following
books:
Book Name
Author
Page No.
1.
Fluid mechanics
Streeter
130-132,457-458
2.
Fluid mechanics
S.G Gupta
165-180
Web resources:
1. www.wikipedia.com
2. www.tmh.co.in
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
EXPERIMENT NO.2
Calibration of Flow Measuring Devices
Date of conduction:Date of submission:Submitted by other members:1.
2.
3.
Group no:-
Signature
Name of faculty incharge:
Name of Technical Assistant:
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Objective: - To calibrate following flow measuring devices.
Venturi meter, Orifice meter and Rotameter
.
Theory:
The flow rate in a closed channel is usually measured by creating
a constriction in the cross-section of the channel and measuring the
pressure drop caused by it. The drop in the pressure across the
constriction depends on the flow rate and thus is a measure of the flow
rate.
In case of a venturi meter, the flow cross-section of the channel
rapidly decreases to a minimum at the venturi throat, and then gradually
increases to the original cross-section. The difference of pressure
between the pressure tapping 1 at the inlet to the device and the
pressure tapping 2 at vena contract of slow stream which occurs almost
at the venturi throat is measured by a U- tube mano-meter.
In case of the orifice meter the vena-contract occurs at
approximately half a pipe diameter drown stream the orifice plate.
Assuming the flow to be incompressible and in-viscid between the
inlet section 1 and the vena contract section 2, and assuming the flow be
one dimensional, use of the continuity equation and the Bernoulli’s
equation leads to the flow expression as
𝑄𝑡ℎ = 𝐶𝑑 (
= 𝐶𝑑 (
𝐴1 𝐴2
√𝐴21 −𝐴22 )
𝐴2
√1−𝛽 2 )
√2𝑔 (𝜌𝑚 − 𝜌) 𝛥ℎ /𝜌
√2𝑔 (𝜌𝑚 − 𝜌) 𝛥ℎ /𝜌
Where
A1 – The area at inlet side in cm2
A2 – The area at throat in cm2
∆h – Head difference in the manometer,
g – Acceleration due to gravity (9.81m/sec²)
Coefficient of discharge
𝑪𝒅 =
Calibration of flowmeters-
𝑸𝒂
𝑸𝒕𝒉
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Equations derived above relating flow rate to the differential
pressure cannot be applied directly in practical applications. All the
flowmeters need calibration a priori where a known quantity of fluid is
passed through the flowmeter and the differential pressure across the
flowmeter related to the actual mass flowrate through a discharge
coefficient given as the ratio of actual to theoretical mass flowrate. Two
methods of knowing the actual mass flowrate are- measurement of time
for collection of a finite volume of fluid and measurement of mass
collected in a certain amount of time.
Description of Equipment:SPECIFICATIONS OF VENTURI METER:
Pipe Dia
Throat Dia
Distance of upstream pressure tap from the throat
Distance of upstream pressure tap from the throat
:
:
:
:
25 mm ID
12 mm
___mm
___mm
:
:
:
:
:
25 mm ID
12.7 mm
___mm
___mm
24x24x40
SPECIFICATIONS OF ORIFICE METER:
Pipe Dia
Orifice Dia
Distance of upstream pressure tap from the throat
Distance of upstream pressure tap from the throat
Size of collecting tank
Procedure:
1. Make a neat sketch of the experimental set-up and note/measure
the necessary dimension on it.
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
2. Clean the storage tank fill with fresh water.
3. Open the bypass line and close the delivery line.
4. Keeping the valves to the venturi meter and the orifice meter
closed, open the discharge line.
5. Slowly open the supply to the venturi meter. After the steady state
is reached, read the manometer reading and determine the flow
rate volumetrically. Also read the Rota meter reading. Repeat the
experiment for higher flow rates, by increasing the supply slowly.
6. Lose supply to the venturi meter and slowly open supply to the
orifice meter. Repeat the experiment as done In the case of venturi
meter.
7. Repeat the procedure for at least ten mass flow rates for both
venturimeter and orifice meter.
Observation Table:Sl.
No
Time for
10cm
rise
of
water
level (s )
t1 t2 tm
Actual
dischar
ge
Qa.cm3/
s
for coefficient of discharge
Differential
head in cm. of
mercury
h1
h2
Differential
head
in
cm.
of
water
Theoretical
discharge
Qth, cm3/s
Coefficient
of
discharge
Cd
h1-h2
=hHg
Calibration Table
Sl.
No
HHg in
Hw in
Qa in
cm
cm
cm3/s
Log Qa
Log
HHg
Actual
discharge
Qa =KHHgn
HHg in
cm
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Calculation:1. Calculate actual discharge through flow meter
𝑎ℎ 𝑐𝑚3
𝑄𝑎 =
𝑡
𝑡
Where
a – Area of measuring tank in cm2
h – Height differences in piezo meter in cm
t – Time to collect water for a height difference of h cm, measured in
seconds
And Now calculate coefficient of discharge for each run
𝑸𝒂
𝑪𝒅 =
𝑸𝒕𝒉
2. Calculations for Calibration curve
The equation
Qa = Cd x Qth can be written as
𝑛
𝑄𝑎 = 𝐾. 𝐻𝐻𝑔
𝑐𝑚3 ⁄𝑠
Where
𝑘 = 𝐶𝑑 (
𝐴1 𝐴2
√𝐴21 −𝐴22 )
√2𝑔 (𝜌𝑚 − 𝜌)/𝜌)
𝑛
Use linear regression to fit the equation 𝑄𝑎 = 𝐾. 𝐻𝐻𝑔
and show on
calibration curve, logQa vs logHHg and determine the slope of the line
and coefficient.
Results: -
Conclusion:-
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Precautions:1.
2.
3.
4.
Do not close air regulating valve fully to avoid over loading at
blower meter.
Use only mild detergents to clean the instruments do never use
any organic solvent and strong acid or alkali.
Ground the instrument properly to avoid electric shock.
The density of fluid in manometer is one.
Suggestions:-
Further reading resources:
Book: Lab experiment related theory available in following
books:
Book Name
Author
Page No.
1.
Fluid mechanics
Streeter
205-208,472-475
2.
Fluid mechanics
S.G Gupta
180-185
Web resources:
1. www.wikipedia.com
2. www.engineersedge.com
3.
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
EXPERIMENT NO.3
Calibration of Open channel Flow Measuring Devices
Date of conduction:Date of submission:Submitted by other members:1.
2.
3.
Group no:-
Signature
Name of faculty incharge:
Name of Technical Assistant:
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Calibration of V notch and Rectangular notch
Objectives:(i)
To determine the coefficient of discharge (Cd) of the given
notch for different rates of flow
(ii)
To calibrate the notch (by determining the constants K and
n, assuming the actual discharge Qa = K.H)
Theory: - Flow rate through open channels is measured by weirs and
notches. A weir is an obstruction placed in open channel over which the
flow occurs. The weir is generally in the form of a vertical wall with a
sharp edge at the top, running all the way across the cross section of the
open channel. When the liquid flows over the weir, the height of the
liquid above the top of the sharp edge bears a relationship with discharge
across it.
A notch is a sharp-edge device which permits the liquid to go
through it, the liquid being exposed to the atmospheric pressure.
Notches may be rectangular, triangular, circular or trapezoidal in
shape. A triangular notch is also called a V-notch.
Volume flow rate across a notch is given by
𝐻
1
𝑄𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 = 𝑏 √2𝑔 ∫0 ℎ3 𝑑ℎ
Where,
H: height of the liquid over the notch while crossing the tip of the notch.
h: is the depth of the liquid at a horizontal strip below the liquid level.
b: width of the strip at the level.
1. RECTANGULAR NOTCH
2
Total theoretical discharge = 𝑄𝑡ℎ𝑒𝑜𝑟𝑒𝑡𝑖𝑐𝑎𝑙 = 𝑏. √2𝑔. 𝐻2/3
3
However, in actual case the area of cross-section of flow is less than the
area of flow across the notch, and there are frictional losses due to the
presence of solid boundaries and eddy formation, the actual flow rate can
be approximated as
𝑄 𝑎𝑐𝑡𝑢𝑎𝑙 = 2/3 𝐶𝑑 𝑏 √2𝑔 𝐻3/2
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Where, the correction factor Cd is called coefficient of discharge which
depends on the geometry of notch and Reynolds number of flow.
2. V-NOTCH or TRIANGULAR NOTCH
For a V-notch with an included angle θ, liquid flowing through it with the
level H above the base point.
The breadth of element
This gives,
Total discharge
𝑏 = 2(𝐻 − ℎ) tan 𝜃/2
𝑄𝑡ℎ =
8
𝜃
5/2
. 𝑡𝑎𝑛 ( 2) √2𝑔 𝐻
15
3. TRAPEZOIDAL NOTCH
Discharge over trapezoidal notch = discharge over rectangular
portion + discharge over rectangular portion
2
8
𝜃
3/2
𝑄𝑡ℎ = ( 𝐿 +
. 𝑡𝑎𝑛 ( 2) . 𝐻) √2𝑔 𝐻𝑤
3
15
Description of Equipment:a) The given rectangular and triangular notches fitted on the open channel of
the experimental setup. The channel has steadying arrangement with baffles
and provision for fixing interchangeable notch plates. The steadying zone is
filled with 25mm or 40mm ballets to get steady flow.
b) Hook gauge is fixed on the notch tank’s top edge, which should be kept in
horizontal position with the help of spirit level. It is used to measure the
depth of water
c) Measuring tank Size 20 x 59 x 14.5 (LWH) meters with overflow
arrangement, gauge glass, scale arrangement and a drain valve to measure
the actual discharge.
SPECIFICATION of NOTCHES
1. Rectangular notch
2. Triangular of V-Notch
3. Trapezoidal Notch
:
:
:
5 cms width x 4 cms H
Angle of Notch 900, Hieght 4.7 cms
Angle of Notch 450, Hieght 3.0 cms
Procedure:
1. Make a neat sketch of the experimental set-up and note/measure
the necessary dimension on it.
2. Clean the storage tank fill with fresh water.
3. Open the bypass line and close the delivery line.
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
4. Keeping the valves to the Notches open the discharge line.
5. Allow the Water to flow over the notch at different rates ranging
from zero to the maximum possible level and the corresponding
head over notch shown in the hook gauge are noted.
6. Now close the supply. Note the width and height of the
rectangular notch. Slowly open the supply to the channel to
which the rectangular notch is attached. After the steady state is
reached, measure the height of the liquid over the tip of the notch.
7. Collect the water in tank for definite time interval and measure
the level of water inside tank.
8. Repeat the step 7 for different flow rates, till the entire range of
the flow rate is covered.
9. Note the included angle of the V-notch and perform the
experiment as done in the steps 7 and 8 for the rectangular
notch, noting each time the height of the liquid above the tip of
the V- notch.
Observation Table:Sl.
hook gauge reading
No
Initial Final Depth
h
h
∆h
for coefficient of discharge
Time for 10
cms raise of
water in sec.
t1
t2
Theoretical
discharge
Qth
Actual
discharge
Qa
Mean
tm
Calibration Table
Sl.
No
Hw in
Qa in
cm
cm3/s
Qth
Log
Actual discharge
HHg
Qa =KHHgn
Cofficient
of
discharge
Cd=
Qa/Qth
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Calculation:1. Calculate actual discharge through flow meter
𝑎ℎ 𝑐𝑚3
𝑄𝑎 =
𝑡𝑚
𝑡
Where
a – Area of measuring tank in cm2
h – Height differences in piezo meter in cm
t – Time to collect water for a height difference of h cm, measured in
seconds
And Now calculate coefficient of discharge for each run
𝑸𝒂
𝑪𝒅 =
𝑸𝒕𝒉
2. Calculations for Calibration curve
The equation
Qa = Cd x Qth can be written as
𝑛
𝑄𝑎 = 𝐾. 𝐻𝐻𝑔
𝑐𝑚3 ⁄𝑠
Where
2
8
𝑘 = 𝐶𝑑 ((3 𝐿 + 15 . 𝑡𝑎𝑛 (𝜃2). 𝐻) √2𝑔)
𝑛
Use linear regression to fit the equation 𝑄𝑎 = 𝐾. 𝐻𝐻𝑔
and show on
calibration curve, logQa vs logHHg and determine the slope of the line
and coefficient.
Results: -
Conclusion:-
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Precautions:1.
2.
3.
4.
Do not close air regulating valve fully to avoid over loading at
blower meter.
Use only mild detergents to clean the instruments do never use
any organic solvent and strong acid or alkali.
Ground the instrument properly to avoid electric shock.
The density of fluid in manometer is one.
Suggestions:-
Further reading resources:
Book: Lab experiment related theory available in following
books:
Book Name
Author
Page No.
1.
Fluid mechanics
Streeter
467-470,230-251
2.
Fluid mechanics
S.G Gupta
165-180
3. Fluid mechanics Modi and seth 700-703
Web resources:
1. www.wikipedia.com
2. www.engineersedge.com
3.www.tmh.in
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
EXPERIMENT NO.4
Losses due to pipe fittings
Date of conduction:Date of submission:Submitted by other members:4.
5.
6.
Group no:-
Signature
Name of faculty incharge:
Name of Technical Assistant:
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Objective:(i)
To determine the loss of head in the fitting at the various water
flow rates.
(ii)
To determine the loss coefficient for the pipe fittings.
Theory:-
Loss of head due to change in cross section, bends, elbows,
valves and fittings of all types fall into the category of minor loss in
pipeline. In long pipe lines the friction losses all much longer than this
minor losses and hence the fleeter and often neglected. But in shorter
pipelines their consideration is necessary for the correct estimate of
losses.
The minor loss in contraction can be express.
𝑉12
2𝑔
The minor loss due to enlargement can be expressed as.
ℎ𝐿 = 𝐾𝐿
(𝑉1 − 𝑉2 )
ℎ𝐿 = 𝐾𝐿
2𝑔
2
Where,
h1 = minor loss or head loss
K1 = Loss coefficient
V1 = Velocity of fluid in pipe of small diameter
V2 = Velocity of fluid in pipe of larger diameter
Description:The apparatus consist of a ½” bent and elbow. A sudden expansion
from ½ ” to 1” and a sudden contraction from 1” to ½ ” ball value and
gate value pressure taping are provided at inlet and outlet of these fitting
at suitable dust. A differential manometer in the lines gives pressure
gauge due to fittings supply to the pipeline is made through centrifugal
pump which deliver water from sump tank. The flow of water in pipeline
is made through centrifugal pump which deliver water from is regulated
by means of central valve and by pass valve discharge is measured with
the beep of measuring tank and stop watch.
Utilities Required:
1.
Power supply: single phase 220 volts, 50 Hz, 5 AMP. With earth
2.
Water supply
3.
Drain
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
STANDARD DATA:
A
→ Area of measuring tank = 98.059 × 10-3m2
S
→ Specific gravity of Hg= 13.6
g
→ Acceleration due to gravity = 9.81 m/sec2
d
→ Diameter of small pipe = 0.016 m.
d2
→ Diameter of large pipe = 0.028 m.
a1
→ Area of cross section of small diameter pipe = 2.0106 × 10-4m2.
A2
→ Area of cross section of large diameter pipe = 6.1575 × 10-4m2.
Δh = 12.6 × h
Procedure:
A)
STARTING PROCEDURE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
Clean the apparatus and make all tanks from dust.
Close the drain.
Fill sump tank ¾ with clean water and ensure that no foreign
particles an there.
Close all flow controls valves given on the water line and open bypass valve.
Check the valve of Hg in manometer tube. It showed be to half. It
is used then fills it.
Close all pressure tapes of manometer connected to different pipe
fitting.
Ensure that ON/OFF switch given on the panel is at OFF position.
Now switch on the main power supply.
Switch on the pump.
Operate the flow control valve to regulate flow of water in the
desired test section.
Open the pressure taps of manometer of related test section very
slowly to avoid the blow of water on manometer fluid.
Now open the air release valve provided on the manometer. Slowly
to release the air to manometer.
When there is no air in the manometer close the air release valves.
Adjust water flow rate in the manometer close the air release
valves.
Record the manometer reading.
Measure the flow of water, discharge through desired test section
using stop watch and the measuring tank.
Repeat same procedure for different flow rates of water, operating
control valve and by pass valve.
When experiment is over for one desired test section, open the bypass valve fully. The close the flow control valve of running test
section and open the control valve of desired test section.
Repeat same procedure for selected test section and so on.
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
B) CLOSING PROCEDURE:
1. When experiment is over close all manometers tops first.
2. Switch off pump.
3. Switch off power supply.
Calculation:1. Loss of head (for contraction):
ℎ𝑐 = 𝐾𝐿
𝑉12
2𝑔
2. Loss coefficient (for contraction and bend):
𝐾𝐿 = ℎ𝐿
2𝑔
𝑉12
𝑎𝑛𝑑 ℎ𝐿 = 12.6ℎ
Loss of head (for expansion):
𝐾𝐿 = ℎ𝐿
2𝑔
(𝑉1 − 𝑉2 )2
𝑎𝑛𝑑 ℎ𝐿 = 12.6ℎ
3. Change in kinetic energy:
e = V12 – V22 / 2g.
4. Discharge.
Q = v / t, V = A × R cm3.
Observation Table:S. no.
Pressure diff., h (cm)
Rise of water level in
measurement tank, R
(cm)
Time taken for R,
t sec
Calculation table
S. no.
Discharge,
Q
Velocity, V1
Velocity, V2
ℎ𝐿 = 12.6ℎ
Loss
coefficient, KL
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Results: -
Conclusion:-
Precautions:1. Do not run the pump at low voltage i.e. less than 180 volts.
2. Never fully close the delivery line and by pass line valves
simultaneously.
3. Always keep apparatus free from dust.
4. To prevent the clogging of moving parts. Run pump at least once in
fortnight.
5. Frequently grease the rotating parts. Once in three months.
6. Always use clean water.
7. If apparatus use for more than one month drawn the apparatus
completely and fill pump with cutting drill.
Trouble shootings:
1.
2.
If pump cuts join open the back cover of pump and rotate the shaft
manually.
If pump cuts heat up switch off the main power off 15 min and
avoid closing the flow control valve and by pass valve
simultaneously during operation.
Suggestions:-
Further reading resources:
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Book: Lab experiment related theory available in following
books:
Book Name
Author
Page No.
1.
Fluid mechanics
Indrajeet
6.2-6.50
2.
Fluid mechanics
S.G Gupta
165-180
Web resources:
1. www.wikipedia.com
2. www.engineersedge.com
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
EXPERIMENT NO.5
Reynolds Experiment
Date of conduction:Date of submission:Submitted by other members:1.
2.
3.
Group no:-
Signature
Name of faculty incharge:
Name of Technical Assistant:
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Objective:-
To perform the Reynolds experiment for determination of
different regimes of flow
Theory:-
The flow of real fluids can basically occur under two very
different regimes namely laminar and turbulent flow. The laminar flow is
characterized by fluid particles moving in the form of lamina sliding over
each other, such that at any instant the velocity at all the points in
particular lamina is the same. The lamina near the flow boundary move
at a slower rate as compared to those near the center of the flow passage.
This type of flow occurs in viscous fluids, fluids moving at slow velocity
and fluids flowing through narrow passages.
The turbulent flow is characterized by constant agitation and
intermixing of fluid particles such that their velocity changes from point
to point and even at the same point from time to time. This
type of flow occurs in low density Fluids flow through wide passage and
in high velocity flows.
Reynolds number is defined as, the ratio of inertia force to the
viscous force .Where viscous force is shear stress multiplied area and
inertia force is mass multiplied acceleration.
𝑉𝐷𝜌
𝑉𝐷
𝑅𝑒 =
=
(𝑣 = µ𝜌 )
µ
𝑣
Where
Re-Reynolds number
V - Velocity of flow
D - Characteristic length=diameter in case of pipe flow
Ρ - Mass density of fluid =1000
µ - dynamic viscosity of fluid = 0.55x 103
v - Kinematic viscosity of fluid
Reynolds observed that in case of flow through pipe for values of
Re<2000 the flow is laminar while offer Re>40000 it is turbulent and for
2000<Re<4000 it is transition flow.
Description:A stop watch, a graduated cylinder, and Reynolds apparatus which
consists of water tank having a glass tube leading out of it. The glass
tube has a bell mouth at entrance and a regulating valve at outlet, a dye
container with an arrangement for injecting a fine filament of dye at the
entrance of the glass tube. Potassium permanganate (to give brightly
reddish color streak) thermometer and measuring tank.
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Procedure:
Start the experiment by pressing start button with default values of
temperature of water and time taken and diameter of pipe. Then pass the
experiment with few cycles and note the observation.
Observation1:
1) Start the experiment and allow the water to flow in to the tank of the
apparatus. Water level in the pyrometer is slightly rising along with rise
in tank. Control valve of the glass tube should be slightly opened for
removing air bubbles.
2) After the tank is filled outlet valve of the glass tube and inlet valve of the
tank should be closed, so that water should be at rest.
Observation2:
1) Keeping the velocity of flow is very small and inlet of the die injector is
slightly opened, so that the die stream moves at a straight line
throughout the tube showing the flow is laminar.
2) Again measure the discharge and increase the velocity of flow.
Observation3:
1) Note the observations till the die stream in the glass tube breaks up and
gets diffused in water.
2) Repeat the experiment by decreasing the rate of flow and by changing the
temperature and diameter of pipe.
Observation Table:Inner diameter of glass tube, D =
Cross - sectional area of glass tube, 𝐴 =
Mean temperature of water – t - =
Kinematic viscosity of water-ν- =
S.No
Discharge
‘q’ in (liters)
Time taken for
Discharge ‘t’ in
(sec)
Discharge
‘Q’ in
(cm3/sec)
Calculation:1) Discharge –
𝑄 = 𝐴ℎ⁄𝑡
𝜋
2) Velocity of flow – 𝑉 = 𝑄. 4 𝐷²
𝜋
4
𝐷²
Velocity
‘V’
(cm/sec)
Reynold’s
Number
‘Re’
Type of
flow
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Results: 1. Reynolds number –Re = VD/ ν
2. Regime of flow =
Conclusion:-
Suggestions:-
Further reading resources:
Book: Lab experiment related theory available in following
books:
Book Name
Author
Page No.
1.
Fluid mechanics
Streeter
228-274
2.
Fluid mechanics
S.G Gupta
263-308
Web resources:
1. www.wikipedia.com
2. www.tmh.in
EXPERIMENT NO.6
Bernoulli’s Theorem Apparatus
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Date of conduction:Date of submission:Submitted by other members:1.
2.
3.
Group no:-
Signature
Name of faculty incharge:
Name of Technical Assistant:
Objective: -
To verify the Bernoulli’s theorem experimentally i.e.
conservation of mechanical energy
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Theory:- Bernoulli’s equation states as follows:
“In an ideal, incompressible fluid flow when the flow is steady and
continuous, the sum of pressure energy, kinetic energy and
potential energy is constant along a stream line”.
Mathematically,
p
V2

 z  Cons tan t
w
2g
For two sections
2
2
p1 V1
p
V

 z1  2  2  z 2
w
2g
w
2g
This is called Bernoulli’s equation.
Assumptions: It may be mentioned that the following assumptions are
made in the derivation of Bernoulli’s equation.
1.
2.
3.
4.
The liquid is ideal and incompressible.
The flow is steady and continuous.
The flow is along the streamline, i.e. it is one-dimensional.
The velocity is uniform over the section and is equal to the mean
velocity.
5. The only forces acting on the fluid are the gravity forces and the
pressure forces.
Rate of flow or Actual Discharge (Q):
The water flowing through the section of a pipe or a channel under the
steady state conditions is collected in a collecting tank for a known time
t. The rise of water level in the collecting tank is noted down. The actual
discharge is
Q 
area of the collecting Tank x rise of water level in the collecting Tank
time (t )
Description:The experimental set up consists of a horizontal Perspex duct of smooth
variable cross-section of convergent and divergent type. The section is 40
mm x 40 mm at the entrance and exit and 40 mm x 20 mm at middle.
The total length of duct is 90 cm. The piezometric pressure P at the
locations of pressure tapping is measured by means of 11 piezometer
tubes installed at an equal distance 7.5 cm along the length of conduit.
The duct is connected with supply tanks at its entrance and exit end
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
with means of varying the flow rate. A collecting tank is used to find the
actual discharge.
Data: area of collecting tank, A= 0.1 m2
Procedure:
1. Clean the apparatus and make all tanks free from dust
2. Close the drain valve provided.
3. Fill sump tank ¾ with clean water and ensure that no foreign particles are
there.
4. Close all control valves given on the water line and open by-pass valve.
5. Ensure that ON/Off switch given on the panel is at OFF position.
6. Now switch on the main power supply.
7. Switch ON the pump.
8. Operate the flow control valve to regulate the flow of water.
9. Measure the height of water level in tubes.
10. Measure the flow rate using measuring tank and stop watch
11. Repeat steps the same procedure for different flow rates of water operating
control valves and By-pass valve.
12. When experiment over switch OFF pump.
13. Switch off power supply to panel.
Observation Table:S.
N
o
Discharge
Discharge Diameter
Measurement Q, cm3/sec
of
passage
Rise of
Time
mm.
water level
sec
(h2-h1)
Area of
c/s of
passage
A, cm2
V2 / 2g
cm
Calculation:1. Compute the area of cross section ‘a’ at a given section
𝑎 = 𝜋 𝑑 2 ⁄4
2. Calculate Discharge:
3. Velocity of flow: V=Q/a
4. Velocity head= V2 / 2g
𝑄=𝐴
(ℎ2 −ℎ1 )
𝑡
P/w + Z
cm
P/w+ Z +
V2/2g
cm
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Results: -
Conclusion:-
Precautions:1. Apparatus should be in leveled conditions.
2. Reading must be taken in steady or nearby steady conditions and
it should be noted that water level in the inlet supply tank should
reach the overflow condition.
3. There should not be any air bubble in the piezometer and in the
Perspex duct.
4. By closing the regulating valve, open the control valve slightly such
that the water level in the inlet supply tank reaches the overflow
conditions. At this stage check that pressure head in each
piezometer tube is equal. If not adjust the piezometers to bring it
equals.
.
Suggestions:-
Further reading resources:
Book: Lab experiment related theory available in following
books:
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
1.
2.
Book Name
Fluid mechanics
Fluid mechanics
Author
Streeter
modi and seth
Web resources:
1. www.wikipedia.com
2. www.engineersedge.com
3 www.tmh.in
Page No.
208-210
293-300
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
EXPERIMENT NO.7
Meta-centric Height
Date of conduction:Date of submission:Submitted by other members:1.
2.
3.
Group no:-
Signature
Name of faculty incharge:
Name of Technical Assistant:
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Objective:- Determination of meta-centric height.
Theory:Buoyancy: When a body is immersed in a fluid either wholly of partially,
it is buoyed or lifted up by a force, which is equal to the weight of fluid
displaced by the body.
Centre of Buoyancy: The point of application of the force of buoyancy
on the body is known as the centre of buoyancy. It is always the centre of
gravity of the volume of fluid displaced.
Meta-centre: Figure shows a body floating in a liquid in a state of
equilibrium. When it is given a small angular displacement, it starts
oscillating about some point M. The point, about which the body
oscillates, is called meta-centre.
The meta-centre may also be defined as a point of intersection of
the axis of body passing through centre of gravity G and original centre
of buoyancy B and a vertical line passing through the centre of buoyancy
B1 of the tilled position of the body.
Meta-centric height: The distance between the centre of gravity of a
floating body and the meta-centre is called meta-centric height.
For stable equilibrium, the position of meta-centre M remains higher
than centre of gravity of the body G.
For unstable equilibrium, the position of meta-centre M remains lower
than G.
For neutral equilibrium, the position of meta-centre M coincides with G.
Determination of Meta-centric Height: A known weight W1 is shifted
by a distance Z across the axis of tilt. The change in momentum due to
this shift is W1 Z. Let the angle of tilt be θ. The change in moment due to
this tilt is equal to (Wc + W1) GM tanθ.
W1 Z
Wc  W1  tan 
Wc = weight of the vessel
W1 = weight of unbalanced mass
Z = distance of the unbalanced mass from the centre of the cross bar.
GM 
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Description:The experimental set up consists of a pontoon (flat bottomed vessel)
which is allowed of float in a M.S. tank having a transparent side.
Removable steel strips are placed in the model for the purpose of
changing the weight of the vessel. By means of a pendulum (consisting of
a weight suspended to a longer pointer), the angle of tilt θ can be
measured on a graduated arc. For tilting the ship model a cross bar with
two movable hangers is fixed on the model. Pendulum and graduated arc
are suitably fixed at the centre of the cross bar.
Procedure:
1. Note down the relevant dimensions as area of collecting tank, mass
density of water etc.
2. Note down the water level in the tank when pontoon is not in the
tank.
3. Pontoon is allowed to float in the tank. Note down the reading of
water level in the tank. Mass of pontoon can be obtained by the
help of Archimedes’s principle.
4. Position of unbalanced mass, weight of unbalanced mass and the
angle of heel can be noted down. Calculated the meta-centric
height of the pontoon.
5. The procedure is repeated for other positions and value of
unbalanced mass.
6. Also the above procedure is repeated while changing the weight of
the pontoon by changing the number of strips in the pontoon.
Observation Table:Water level without pontoon, Y1 (cm) =
S.No.
Reading on
tank with
pontoon Y2
cm
Mass of
pontoon
Wc=(Y2Y1)Aw
gm
Unbalanced
mass W1
gm
Angle of
heel θ
degree
Distance of
unbalanced
mass Z, cm
Metacentric
Height
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT
Calculation:-
Results: The metacentric height of a flat bottom pontoon =
Conclusion:-
Precautions:1.
2.
3.
Apparatus should be in leveled conditions.
Reading must be taken in steady condition of water.
Unbalanced mass should be measured by taking care that water
disturbance should be minimum.
Suggestions:-
Further reading resources:
Book: Lab experiment related theory available in following
books:
Book Name
Author
Page No.
1.
Fluid mechanics
Streeter
65-70
2.
Fluid mechanics
Indrajeet
4.2-4.7
Web resources:
1. www.wikipedia.com
2. www.engineersedge.com
Fluid Mechanics Laboratory
Lab code- ME-405
MECH. ENGG. DEPARTMENT