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JNEC CIVIL/FM-I/AUG 2010

MAHATMA GANDHI MISSION’S

JAWAHARLAL NEHRU ENGINEERING COLLEGE,

AURANGABAD. (M.S.)

DEPARTMENT OF CIVIL ENGINEERING

FLUID MECHANICS LABORATORY

MANUAL

Prepared By Approved By

Mr. L. K. Kokate Prof. B. M. Patil

Lab Incharge H.O.D. CIVIL


’FLUID MECHANICS -I’ EXPERIMENTS

SUBJECT: - Fluid Mechanics-I

CLASS: - Second Year Civil Engineering

LIST OF EXPERIMENTS

Sr. No. Name of Experiment Page No.

From To

I Study of pressure measuring devices.

II Determination of meta centric height.

III Calibration of Bernoulli’s equation.

IV Calibration of Venturimeter.

V Determination of Hydraulic coefficient for orifices.

VI Determination of coefficient of discharge for mouthpiece.

VII Calibration of Rectangular notch.

VIII Calibration of Triangular Notch.

IX Study of electrical analogy method for plotting of flow nets.

Time Allotted for each Practical Session = 02 Hrs.


EXPERIMENT NO: II - To Determine the Metacentric Height of a Cargo / War Ship

AIM: - To Determine the Metacentric Height of a Cargo / War Ship

INTRODUCTION:-

Metacenter is defined as, the point about which the body starts oscillating when it is tilted (inclined) by a

small angle.

Metacenter may also be defined as, the point at which the line of action of force of buoyancy will meet the

normal axis of the body when the body is given a small angular displacement.

Metacentric Height is defined as, the distance between the Metacenter of a floating body & center of gravity.

DESCRIPTION:-

To Determine the Metacentric Height of a Cargo / War Ship


is defined as, the point about which the body starts oscillating when it is tilted (inclined) by a

may also be defined as, the point at which the line of action of force of buoyancy will meet the

ody is given a small angular displacement.

is defined as, the distance between the Metacenter of a floating body & center of gravity.


is defined as, the point about which the body starts oscillating when it is tilted (inclined) by a

may also be defined as, the point at which the line of action of force of buoyancy will meet the

is defined as, the distance between the Metacenter of a floating body & center of gravity.

The ship

model is

approximately 37

cm size square in

plan and is about

23 cm high. The

model is floated on

water. The ship is

tilted by moving a

small weight at the

level of the deck

of the ship. To

note down the tilt

of the ship, a

plumb is provided

which records the

tilt on a graduated

arc of a circle. An

arrangement is

made to load the


ship as a War ship or Cargo ship.

PROCEDURE:-

Sr.

No. For Cargo Ship For War Ship

1 Place suitable symmetrical weights at the

bottom of the ship and load it as a Cargo Ship.

Place suitable symmetrical weights at the deck

level of the ship and load it as a War Ship.

2 Float the ship on the water. Float the ship on the water.

3 Adjust the balancing weights on both the sides

of the ship so that the Plumb indicates zero

reading on the graduated arc.

Adjust the balancing weights on both the sides

of the ship so that the Plumb indicates zero

reading on the graduated arc.

4 Keep the Moving (Hanging) Load/Weight at a

distance of 3.5 cm off the centre on left side.

Keep the Moving (Hanging) Load/Weight at a

distance of 3.5 cm off the centre on left side.

5 Note down the tilt of the ship in degrees. Note down the tilt of the ship in degrees.

6 Go on shifting the Hanging Load towards left &

note down the distance of the centre, & tilt of

the ship.

Go on shifting the Hanging Load towards left

& note down the distance of the centre, & tilt

of the ship.

7 Repeat the procedure by shifting the load on the

right hand side of the centre.

Repeat the procedure by shifting the load on

the right hand side of the centre.

OBSERVATION

W1 = Weight of the ship including balancing weight in grams.

W2 = Total weight added to make it as a Cargo / War Ship.

W3 = Weight of the Hanging Load in grams.


OBSERVATION TABLE:-

SPECIMEN CALCULATIONS:-

W = (w1 + w2) in grams.

MG1 or MG2 = Metacentric Heights in centimeters.

= W1 x X / W x tan θ0

Average MG = MG1 + MG2 / 2

RESULTS:-

• Metacentric Height of a Cargo Ship (MG c) = …………..cms.

• Metacentric Height of a War Ship (MGw) = …………..cms.

CONCLUSION:-

Sr.

No.

Distance off

the centre to

the left ‘X’ in

cms

Tilt of the

Ship ‘θ’ in

degrees

Metacentric

Height=MG1 in

cms.

Distance off

the centre to

the left ‘X’

in cms

Tilt of the

Ship ‘θ’ in

degrees

Metacentric

Height=MG2 in

cms

Average

MG in

cms

1

2

3

4


As the angle of tilt (θ0) increases, Metacentric Height (MG or GM) also

……………increases / decreases.

EXPERIMENT NO: III - to Verify Bernoulli’s Theorem

AIM-: To verify the Bernoulli’s theorem.

Apparatus-: Bernoulli’s Set – Up, Stop Watch, & Meter Scale.

Theory-: 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). The energy per unit weight of the fluid is Pressure Energy.

Therefore,

Pressure Energy = P / ρg

Kinetic Energy = V2 / 2g &

Datum Energy = Z

The applications of Bernoulli’s theorem are-:

1) Venturi Meter

2) Orifice Meter

3) Pilot Tube


Description-:

The equipment is designed as a self sufficient unit; it has a sump tank, measuring tank, & 0.5 HP monoblock pump for

water circulation. The apparatus consists of Supply Tank & Delivery Tank, which are

channel. The channel tapers for a length of 25 cm & then piezo

– centre for measurement of pressure head.

Procedure-:

1. Keep the bypass valve open & start the pump & slo

2. The water shall 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

5. Change the discharge & repeat the procedure.

6. Do the necessary calculations using the readings noted down before.


water circulation. The apparatus consists of Supply Tank & Delivery Tank, which are connected to a Perspex flow

channel. The channel tapers for a length of 25 cm & then piezo-meter tubes are fixed at a distance of 5 cm , centre

Keep the bypass valve open & start the pump & slowly start closing the valve.

The water shall start flowing through the flow channel. The level in the piezometer tubes shall start rising.

Open the valve at the delivery tank side, & adjust the head in piezometer tubes to a steady position.

ads at all the points and also discharge with the help of Diversion Pan in the measuring tank.

Change the discharge & repeat the procedure.

Do the necessary calculations using the readings noted down before.


connected to a Perspex flow

meter tubes are fixed at a distance of 5 cm , centre – to

The water shall start flowing through the flow channel. The level in the piezometer tubes shall start rising.

Open the valve at the delivery tank side, & adjust the head in piezometer tubes to a steady position.

in the measuring tank.


Specifications-:

Tube

No.

1 2 3 4 5 6 7 8 9 10 11 12 13 14

C/S

Area

3.6 3.2 2.8 2.4 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8

Observation Table-:

Result-:

1) At discharge ………..liters / second,

Total head is ………..centimeters.

2) At discharge ………..liters / second,

Total head is ………..centimeters.


EXPERIMENT NO: IV - FLOW THROUGH VENTURIMETER

AIM:

To determine the co-efficient (K) of the Venturimeter.

DESCRIPTION:

Venturimeter is a device, used to measure the discharge of any liquid flowing through a pipe line. The

pressure difference between the inlet and the throat of the Venturimeter is recorded using a mercury differential

manometer, and the time is recorded for a measured discharge. Venturimeters are used to measure the flow rate of

fluid in a pipe. It consists of a short length of pipe tapering to a narrow throat in the middle and then diverging

gradually due to the reduced area and hence there is a pressure drop. By measuring the pressure drop with a

manometer, the flow rate can be calculated by applying Bernoulli’s equation.

The meters are fitted in the piping system with sufficiently long pipe lengths (greater than 10 mm diameter)

upstream of the meters. Each pipe has the respective Venturimeter with quick action cocks for pressure tappings.

These pressure tappings are connected to a common middle chamber, which in turn is connected to a differential

manometer. Each pipe line is provided with a flow control water is collected in an M.S. collecting tank of cross

sectional are 0.4 m x 0.4 m provided with gauge scale fitting and drain valve.

PROCEDURE:

1. The diameters of the inlet and throat are recorded and the internal plan

dimensions of the collecting tank are measured.

2. Keeping the outlet valve closed, the inlet valve is opened fully.

3. The outlet vale is opened slightly and the manometric heads in both the limbs (h1 and h2) are noted.

4. The outlet valve of the collecting tank is closed tightly and the time‘t’ required for ‘H’ rise of water

in the collecting tank is observed using a stop watch.

5. The above procedure is repeated by gradually increasing the flow and observing the required

readings.

6. The observations are tabulated and the co-efficient of the Venturimeter is computed.


FORMULAE USED:

Constant of Venturimeter, K =

Where, a1 = area of inlet

a2 = area of throat

h = Venturi head in terms of flowing liquid =

h1 = Manometric head in one limb of the manometer

h2 = Manometric head in other limb of the manometer

Sm = Specific gravity of following liquid

S1 = Specific gravity of following liquid

g = Acceleration due to gravity

Actual Discharge (Qa) =


OBSERVATIONS AND RESULT:

Diameter of inlet, d1 = …….mm

Diameter of inlet, d2 = …….mm

Internal plan dimensions of collecting tank

Length, l =…….mm

Breadth, b =…….mm

Sr.

No

.

Manometric Readings (mm)

of Water

Venturi

head in

terms of

flowing

fluid

(h) mm

�ℎ

Time for

‘H’=100mm rise ‘t’

Sec.

Actual

Discharge

(mm3/sec)

Coefficient of

Venturimeter

H h2 Difference

X=(h1-h2)

Trials Avg.

1 2

01

02

03

Mean Value of Cd = …….


MODEL CALCULATIONS : (Reading No. )

Area of inlet of Venturimeter a1 = πd1

2 /4 (mm2)

Area of throat of Venturimeter a2 = πd2

2 /4

(mm

2)

Internal plan area of collecting tank = l x b (mm2)

Actual discharge, Qa = ��

� (mm

3/s)

Coefficient of Meter, (K) = Qa / C. �ℎ

GRAPH:

Qa vs. �ℎ ----- �ℎ on X-axis

RESULT:

Average Co-efficient of the Venturimeter, Cd = …………

------------------------------------------------------------------------------------


EXPERIMENT NO: VII CALIBRATION OF RECTANGULAR

NOTCHES

Objectives

To Determine the coefficient of discharge of the given Rectangular notch for different rates of flow.

Equipment required

The given notch fitted on an open channel of the experiment setup, hook

gauge to measure the water level over the notch and measuring tank with stop

watch to measure the actual flow rate.

Principle

In open channel flows, weirs are commonly used to either regulate or to measure the volumetric flow rate.

They are of particular use in large scale situations such as irrigation schemes, canals and rivers. For small

scale applications, weirs are often referred to as notches and are sharp edged and manufactured from

thin plate material. The basic principle is that discharge is directly related to the water depth above the

crotch (bottom) of the notch. This distance is called head over the notch. Due to the minimal installation

costs flow rate measurement with a notch is very less expensive. The rectangular notch is the most

commonly used thin plate weir. The flow pattern over a notch or weir is complex and there is no analytical

Solution to the relationship between discharge and head so that a semi-empirical Approach has to be used.

The expression for discharge over a rectangular notch is given by,

where,

L = width of the notch, (m)

h= head of water over the notch, (m)

g= acceleration due to gravity (m/s2)

Water is allowed to pass through the given notch at different flow rates. Ac-

tual discharge through the channel can be determined using the collecting tank

and stopwatch setup.


Where,

a = area of the collecting tank. (m2)

H = height difference of the water column in the piezometer, (m)

t = time taken to rise H meters, (sec)

The coefficient of discharge CD is defined as the ratio of actual discharge

obtained experimentally to the theoretical discharge. i.e.

Calibration is the validation of specific measurement techniques and equipment.

It is the comparison between measurements of known magnitude made

with one device and another measurement made in as similar way as possible

with a second device. In order to use any device for measurement it is necessary

to empirically calibrate them. That is, here in this case pass a known discharge

through the notch and note the reading in order to provide a standard for measuring

other quantities in a different location. Provided the standard mechanics

of construction are followed no further calibration is required for a similar second

device with same geometry.

The calibration equation is stated as,

Qac = K hn

where ,

K and n are constants depending on the geometry of the notch. Taking

logarithm on both sides we get,

logQac = log k+n log h

which is the equation of a straight line,

where ,

log k is the y intercept and n is its slope.

The graph logQac Vs. logh is to be plotted to find k and n.


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 sometime 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. Draw the necessary graphs and calibrate the the notch.

Observations and calculations

Length of the rectangular notch = —m

Angle of the triangular notch = —deg

Collecting tank area = — m2


For a rectangular notch Q = K H(3/2)

K = Cd .(2/3). (2g)(1/2)

.L @ B = ___ m

Sr.

No.

Hook Guage

Reading H

Measuring Tank

Reading R Vol. Qact. Qth Cd. log H

log

Qact

C.B

W.

S

Diff.

H'

(cm)

. (m) I.R.

F.R

.

Diff.

R'

(cm) (m) V=AXR (m3)

V/T

(m3/s

ec)

(2/3).√ (2g).L.H(3/2)

(m3/sec) Qact/Qth

1

2

3

4

5

6

7

For first reading:

Qact = ___ m3/sec

Qtheo = ___ m3/sec

Cd = Q/ Qtheo ___

K = ___

Should be n =~ (3/2 )

→→ if we take the log for the two sides of equation :

log Q = log K + n log H ,

where n : the power of H = ___ ( the slope.) from table .

log k = ___ from graph → k = ___ → Cd = ___ .

Results and Inference

The given notches are calibrated with the calibration equation

where

k=__,

n=__ for rectangular notch.

The average coefficient of discharge of the given notches are,

Rectangular notch, CDR =

The required characteristics are plotted.

______________________________________________________________________________________


EXPERIMENT NO: VIII CALIBRATION OF TRIANGULAR

NOTCHES

Objectives

To Determine the coefficient of discharge of the given Triangular notch for different rates of flow.

Equipment required

The given notch fitted on an open channel of the experiment setup, hook

gauge to measure the water level over the notch and measuring tank with stop

watch to measure the actual flow rate.

Principle

In open channel flows, weirs are commonly used to either regulate or to measure

the volumetric flow rate. They are of particular use in large scale situations

such as irrigation schemes, canals and rivers. For small scale applications, weirs

are often referred to as notches and are sharp edged and manufactured from

thin plate material. The basic principle is that discharge is directly related to the

water depth above the crotch (bottom) of the notch. This distance is called head

over the notch. Due to the minimal installation costs flow rate measurement

with a notch is very less expensive.

The V notch or triangular notch design causes small changes in discharge to have a

large change in depth allowing more accurate head measurement than with a

rectangular notch. The flow pattern over a notch or weir is complex and there is no analytical

solution to the relationship between discharge and head so that a semi-empirical

approach has to be used.

The expression for discharge over a triangular notch is given by,

where,

L = width of the notch, (m)

θ= angle of the notch, (deg)

h= head of water over the notch, (m)

g= acceleration due to gravity (m/s2)


Water is allowed to pass through the given notch at different flow rates.

Actual discharge through the channel can be determined using the collecting tank

and stopwatch setup.

Where,

a = area of the collecting tank. (m2)

H = height difference of the water column in the piezometer, (m)

t = time taken to rise H meters, (sec)

The coefficient of discharge CD is defined as the ratio of actual discharge

obtained experimentally to the theoretical discharge. i.e.

Calibration is the validation of specific measurement techniques and equipment.

It is the comparison between measurements of known magnitude made

with one device and another measurement made in as similar way as possible

with a second device. In order to use any device for measurement it is necessary

to empirically calibrate them. That is, here in this case pass a known discharge

through the notch and note the reading in order to provide a standard for measuring

other quantities in a different location. Provided the standard mechanics

of construction are followed no further calibration is required for a similar second

device with same geometry.

The calibration equation is stated as,

Qac = K hn

where ,

K and n are constants depending on the geometry of the notch. Taking

logarithm on both sides we get,

logQac = log k+n log h

which is the equation of a straight line,

where ,

log k is the y intercept and n is its slope.

The graph logQac Vs. logh is to be plotted to find k and n.


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 sometime 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. Draw the necessary graphs and calibrate the the notch.

Observations and calculations

Length of the rectangular notch = —m

Angle of the triangular notch = —deg

Collecting tank area = — m2


For a triangular notch Q = K H(3/2)

K = Cd .(8/15). (2g)(1/2)

.tan(Ѳ/2) @ B = ___ m

Sr. No.

Hook Guage

Reading H

Measuring Tank

Reading R Vol. Qact. Qth Cd.

log

H

log

Qact

C.B W.S

Diff.

H'

(cm).

(m

) I.R.

F.

R.

Diff. R'

(cm) (m)

V=AXR

(m3)

V/T

(m3/sec)

(8/15). (2g)(1/2).tan(Ѳ/2)

H(5/2)

(m3/sec)

Qact

/Qth

1

2

3

4

5

6

7

For first reading:

Qact = ___ m3/sec

Qtheo = ___ m3/sec

Cd = Q/ Qtheo ___

K = ___

Should be n =~ (3/2 )

→→ if we take the log for the two sides of equation :

log Q = log K + n log H ,

where n : the power of H = ___ ( the slope.) from table .

log k = ___ from graph → k = ___ → Cd = ___ .


Results and Inference

The given notches are calibrated with the calibration equation

where

k=__,

n=__ for triangular notch.

The average coefficient of discharge of the given notches are,

Triangular notch, CdR =

The required characteristics are plotted.

_____________________________________________________________________________________