GOVERNMENT POLYTECHNIC

MUZAFFARPUR

LAB MANUAL OF FLUID MECHANICS AND

MACHINERY LAB

SUBJECT CODE - 1625407

Government Polytechnic Muzaffarpur

Name of the Lab: Fluid Mechanics and Machinery

Lab

Subject Code: 1625407

List of Experiments

Exp. No. Experiment Page No.

1 To verify the Bernoulli’s theorem. 1-2

2 To determine the coefficient of discharge of

Venturimeter.

3-4

3 To determine the coefficient of discharge,

contraction & velocity of an Orifice.

5-7

4 To determine the friction factor for the pipes.

(Major Losses).

8-9

5 To conduct the performance test and to plot the

operating characteristics of Pelton wheel

turbine.

10-13

6 To conduct performance test on a Single stage

Centrifugal pump test rig.

14-16

7 To determine the overall efficiency of a

Reciprocating Pump.

17-20

1

EXPERIMENT NO. – 1

AIM:

To verify the Bernoulli’s theorem.

APPARATUS USED:

A supply tank of water, a tapered inclined pipe fitted with no. of piezometer tubes point,

measuring tank, scale, and stop watch.

THEORY:

Bernoulli’s theorem states that when there is a continues connection between the particle of

flowing mass liquid, the total energy of any sector of flow will remain same provided there is

no reduction or addition at any point.

FORMULA USED:

PROCEDURE:

1. Open the inlet valve slowly and allow the water to flow from the supply tank.

2. Now adjust the flow to get a constant head in the supply tank to make flow in and out

flow equal.

3. Under this condition the pressure head will become constant in the piezometer tubes.

4. Note down the quantity of water collected in the measuring tank for a given interval

of time.

5. Compute the area of cross-section under the piezometer tube.

6. Compute the area of cross-section under the tube.

7. Change the inlet and outlet supply and note the reading.

8. Take at least three readings as described in the above steps. 9.

OBSERVATION TABLE:

1 2 3 4 5 6 7 8 9 10 11 Reading of piezometric tubes

Area of cross Section under the foot of each point

Velocity of water under foot of each point

V2/2g

p/ρ

V2/2g + p/ρ

2

PRECAUTIONS:

1. When fluid is flowing, there is a fluctuation in the height of piezometer tubes, note

the mean position carefully.

2. Carefully keep some level of fluid in inlet and outlet supply tank.

RESULT:

3

EXPERIMENT NO. – 2 AIM:

To determine the coefficient of discharge of Venturimeter.

APPARATUS USED:

Venturimeter, installed on different diameter pipes, arrangement of varying flow rate, U- tube

manometer, collecting tube tank, vernier calliper tube etc.

FORMULA USED:

Where

A = Cross section area of inlet

a = Cross section area of outlet

Δh = Head difference in manometer

Q = Discharge

Cd = Coefficient of discharge

g = Acceleration due to gravity

THEORY:

Venturimeter are depending on Bernoulli’s equation. Venturimeter is a device used for

measuring the rate of fluid flowing through a pipe. The consist of three part in short

1. Converging area part

2. Throat

3. Diverging part

4

PROCEDURE:

1. Set the manometer pressure to the atmospheric pressure by opening the upper

valve.

2. Now start the supply at water controlled by the stop valve.

3. One of the valves of any one of the pipe open and close all other of three.

4. Take the discharge reading for the particular flow.

5. Take the reading for the pressure head on from the u-tube manometer for

corresponding reading of discharge.

6. Now take three readings for this pipe and calculate the Cd for that instrument

using formula.

7. Now close the valve and open valve of other diameter pipe and take the three

reading for this.

8. Similarly take the reading for all other diameter pipe and calculate Cd for each.

OBSERVATIONS:

Diameter of Venturimeter =

Area of cross section =

Venturimeter =

Area of collecting tank=

Discharge Manometer reading

Initial

(cm.)

Final

(cm)

Difference Time

(sec)

Discharge H1 H2 H2-

H1

Δh=13.6(H2-

H1) Cd=

𝑸√𝑨𝟐−𝒂𝟐

𝑨.𝒂√𝟐𝒈∆𝒉

PRECAUTIONS:

1. Keep the other valve closed while taking reading through one pipe.

2. The initial error in the manometer should be subtracted final reading.

3. The parallax error should be avoided.

4. Maintain a constant discharge for each reading.

5. The parallax error should be avoided while taking reading the manometer.

RESULTS:

5

EXPERIMENT NO. – 3

AIM:

To determine the coefficient of discharge, contraction & velocity of an Orifice.

APPARATUS USED:

Supply tank with overflow arrangement, Orifice plate of different diameter, hook gauge,

collecting tank, piezometric tube.

FORMULA USED:

Cd =

𝑄𝑎𝑐𝑡𝑢𝑎𝑙

𝑄𝑡ℎ𝑒𝑜𝑟𝑎𝑡𝑖𝑐𝑎𝑙

Q theoretical = Theoretical velocity × theoretical area = √2gh. a

Cd =

Q

√2gh.a

Cv = actual velocity of jet at vena contracta

theoretical velocity

Coefficient of contraction = area of jet at vena contracta

area of orifice

Cc = ac

a

THEORY:

A mouthpiece is a short length of pipe which is two or three times its diameter in length. If

there pipe is filled externally to the orifices, the mouthpiece is called external cylindrical

mouthpiece and discharge through orifice increase is a small opening of any cross section on

the side of bottom of the tank, through which the fluid is flowing orifice coefficient of

6

velocity is defined as the ratio of two actual discharge to orifice ratio of the actual velocity of

the jet at vena-contracta to the coefficient of theoretical velocity of the jet coefficient of

contraction of defined as ratio of the actual velocity of jet at vena- contracta.

VENA- CONTRACTA:

The fluid out is in form of jet goes on contracting form orifice up to dispute of about ½ the

orifice dia. After that expand this least relation.

COEFFICIENT OF VELOCITY:

It is a ratio of actual velocity jet at vena-contracta to theoretical velocity.

Coefficient of contraction:

Coefficient of contraction = Area of jet at vena contracta

Area of orifice

COEFFICIENT OF DISCHARGE:

Cd =

𝑄𝑎𝑐𝑡𝑢𝑎𝑙

𝑄𝑡ℎ𝑒𝑜𝑟𝑎𝑡𝑖𝑐𝑎𝑙

PROCEDURE:

1. Set the mouthpiece of orifice of which the Cc, Cu, Cd are to be determined.

2. Note the initial height of water in the steady flow tank and the height of datum from the

bottom of orifice and mouthpiece. These remains constant for a particular mouthpiece or

orifice.

3. By using the stop valve, set a particular flow in tank and tank height of water in tank.

4. Take the reading of discharge on this particular flow.

5. Using hook gauge, find the volume of Xo Y for mouthpiece.

6. Take three readings using hook gauge for one particular orifice.

7. Using the formula get value of Cd, Cv, and Cc for a particular orifice and mouthpiece.

OBSERVATION: x' + y' are reading on horizontal/vertical scale

ao h=µa o x’ y’ X=x’-x oy Y=y’-yo Cv=x/2gh Average

h = Reading on piezometer

ao = Reading on piezometer at level on centre of mouthpiece

yo = Reading on vertical scale at exit of orifice

xo = Reading on horizontal scale at exit of orifice

7

Sr. No. X ZP FR volume time Q=V Cd=Q/2gh Average

PRECAUTIONS:

1. Take the reading of discharge accurately.

2. Take value of h without any parallax error.

3. Set the orifice and mouthpiece.

4. Height of water in the steady flow.

5. Take reading from hook gauge carefully.

RESULT:

8

EXPERIMENT NO. – 4 AIM:

To determine the friction factor for the pipes. (Major Losses).

APPARATUS USED:

A flow circuit of G. I. pipes of different diameter viz. 15 mm, 25mm, 32 mm dia, U-tube

differential manometer, collecting tank.

FRICTION FACTOR IN PIPES OR MAJOR LOSSES:

A pipe is a closed conduit through which fluid flows under the pressure. When in the pipe,

fluid flows, some of potential energy is lost to overcome hydraulic resistance which is

classified as:-

1. The viscous friction effect associated with fluid flow.

2. The local resistance which result from flow disturbances caused by

3. Sudden expansion and contraction in pipe

4. Obstruction in the form of valves, elbows and other pipe fittings.

5. Curves and bend in the pipe.

6. Entrance and exit losses.

The viscous friction loss or major loss in head potential energy due to friction is given by

hf = 𝟒𝐟𝐥𝐯𝟐

𝟐𝐠𝐝

Hence the major head loss is friction loss

hf = 𝟒𝐟𝐥𝐯𝟐

𝟐𝐠𝐝 -----------Darcy Equation

Losses in pipes during flow

9

Where,

hf =Major head loss

l = Length of pipe

4f = Friction factor

v = Inlet velocity

g = Acceleration due to gravity

d = Diameter of pipe

PROCEDURE:

1. Note down the relevant dimensions as diameter and length of pipe between the

pressure tapping, area of collecting tank etc.

2. Pressure tapping of a pipe is kept open while for other pipe is closed.

3. The flow rate was adjusted to its maximum value. By maintaining suitable amount of

steady flow in the pipe.

4. The discharge flowing in the circuit is recorded together with the water level in the

left and right limbs of manometer tube.

5. The flow rate is reduced in stages by means of flow control valve and the discharge &

reading of manometer are recorded.

6. This procedure is repeated by closing the pressure tapping of this pipe, together with

other pipes and for opening of another pipe.

OBSERVATION:

Diameter of pipe D =

Length of pipe between pressure tapping L =

Area of collecting tank =

Sr.

No.

Manometer Reading Discharge measurement

F =

2gD5

8LQ2hf

Left

limb

H1

Right

limb

H2

Difference

of head in

terms of

water hf =

13.6 (H2-

H1)

Initial

cm.

Final

cm.

Time

sec

Discharge

Q

(cm3/sec)

PRECAUTIONS:

1. When fluid is flowing, there is a fluctuation in the height of piezometer tubes, note the

mean position carefully.

2. There in some water in collecting tank.

3. Carefully keep some level of fluid in inlet and outlet supply tank.

RESULT:

10

EXPERIMENT NO. – 5 AIM:

To conduct the performance test and to plot the operating characteristics of Pelton wheel

turbine.

APPARATUS:

Pelton wheel test rig, Tachometer.

THEORY:

Pelton turbine is a impulse turbine. Which uses water available at high heads (pressure) for

generation of electricity. All the available potential energy of the water is converted into

kinetic energy by a nozzle arrangement. The water leaves the nozzle as a jet and strikes the

buckets of the Pelton wheel runner. These buckets are in the shape of double cups, joined at

the middle portion in a knife edge. The jet strikes the knife edge of the bucket with the least

resistance and shock and glides along the path of the cup, deflecting through an angle of 160°

to 170°.This deflection of the water causes a change in momentum of the water jet and hence

an impulse force is supplied to the buckets. As a result, the runner attached to the bucket

moves, rotating the shaft. The specific speed of Pelton wheel varies from 10 to 100.

In the test rig the Pelton wheel is supplied with water under the high pressure by a centrifugal

pump. The water flows through the venturimeter to the Pelton wheel. A gate valve is used to

control the flow rate to the turbine. The venturimeter with pressure gauges is connected to

determine the flow rate in the pipe. The nozzle opening can be decreased or increased by

opening the spear wheel at entrance side of the turbine.

The turbine is loaded by applying the dead weights on the brake drum. Placing the weights on

the weight hanger. The inlet head is read from the pressure gauge. The speed of the turbine is

measured with the help of tachometer.

EXPERIMENTAL PROCEDURE:

1. Prime the pump with water and start the pump.

2. Gradually open the delivery valve of the pump.

3. Adjust the nozzle at the half of the opening by operating the needle valve by using the

spear wheel.

4. The head should be made constant by operating the delivery valve and the head shows

be maintained at constant value.

5. Measure the turbine rpm with the tachometer.

6. Note the pressure gauge reading at the turbine inlet.

7. Observe the readings of h 1 and h 2 corresponding the fluid level in the two

manometer links which are connected to venturimeter.

8. Adjust the load on the break drum and note down the speed of the turbine, using the

tachometer and spring balance reading.

9. Add additional weights and repeat the experiment for other loads.

10. For constant speed tests, the main valve has to be adjusted to reduce or increase the

inlet head to the turbine for varying loads spring balance reading.

11

11. Add additional weights and repeat the experiment for other loads.

12. For constant speed tests, the main valve has to be adjusted to reduce or increase the

inlet head to the turbine for varying loads.

SCHEMATIC DIAGRAM OF PELTON WHEEL TURBINE:

Fig. Cut- Sectional view of pelton wheel turbine

12

S.No Gate

opening

Pressure

gauge

(kg/cm 2 )

Vacuum

pressure

mm of

Hg

Manometer

reading

Speed of

rotation

Spring

balance

P i

KW

P o

KW

η%

h1

cm

h2

cm

T1

kg

T2

kg

1

2

3

4

5

Electrical output

Load (kw) Voltage (V) Current (I) (A) Speed(N)rpm

CALCULATIONS:

Input power (Pi) = (ρ × g × Q × h) W

Flow rate of water Q = Cd 𝒂𝟏×𝒂𝟐×√𝟐𝒈𝑯

√𝒂𝟏−𝒂𝟐

d 1 = diameter Of venture inlet = 65mm

d 2 = diameter. Of venture throat= 39mm

Cd = coefficient of discharge of venturimeter = 0.9

Where

a 1 = area of inlet of the venturimeter.

a 2 = area of the venturimeter throat.

H = h1 - h2 [𝑠1

𝑠2− 1]

h = Total head of water (m)

h = suction head (hs) + delivery Head (h d) + Datum Head

Where

h d = delivery head = P d /ρ

hs = suction head = 𝑷𝒔×𝟏𝟑𝟔𝟎𝟎

𝛒

Output power (Po) = 𝟐𝛑×𝑵×𝑻

𝟔𝟎

T = (T1 - T2) × g × dia. Of break drum

dia. Of break drum = 0.15m

N = speed in tacho meter

Efficiency of the turbine ηm %= Po /Pi

13

Electrical efficiency = ηe % = Po / Pi

Po = electrical output = V × I

GRAPHS:

1. Speed vs. efficiency

2. Speed vs. power input

3. Speed vs. power output.

RESULT: The efficiency of pelton wheel is _________%.

14

EXPERIMENT NO. – 6

AIM:

To conduct performance test on a Single stage Centrifugal pump test rig.

INTRODUCTION:

A pump may be defined as mechanical device when interposed in a pipe line, converts the

mechanical energy supplied to it from an external source into hydraulic energy, thus resulting

in the flow of liquid from lower potential to higher potential.

The pumps are of major concern to most engineers and technicians. The types of pumps vary

in principle and design. The selection of the pump for any particular application is to be done

by understanding their characteristics. The most commonly used pumps for domestic,

agricultural and industrial are Centrifugal, axial flow, reciprocating, air jet, and diaphram and

turbine pumps. Most of these pumps fall into the main class namely Rotodynamic,

Reciprocating (positive displacement) and Fluid operated pumps.

THEORY:

The principle of operation of a single stage centrifugal pump is covered under Rotodynamic

pump category. In this pump, the liquid is made to rotate in a closed volute chamber. Thus

creating the centrifugal action, which gradually builds the pressure gradient towards outlet

resulting in a continuous flow.

These pumps are of simple construction can be directly coupled to electric motor and more

suitable for handling clear, semi viscous, as well as turbid liquids. The hydraulic head per

stage at low flow rates is limited and hence not suitable for high heads, in case of single stage

centrifugal pumps. But as the pump in this case in a multi stage construction the pressure

gradually builds up in successive stages almost equally in each stage. Thus achieving

considerably higher heads. The multi stage centrifugal pump test rig allows the students to

understand and study the various characteristics and pressure build up pattern in individual

stages.

DESCRIPTION:

The single stage Centrifugal pump test rig mainly consists of:

a) Single stage Centrifugal pump

b) AC Drive motor of suitable capacity coupled to pump by stepped pulley arrangement.

c) SS sump tank and measuring tank with a piezometer

d) G. I. Pipe connections with necessary control valve etc… mounted on a neatly painted

M.S. structure. The panel board is equipped with an energy meter for measurement of power

input to the motor, a digital RPM indicator to indicate the speed of the pump/motor, a

Vacuum gauge to measure suction head, & pressure gauge for measurement of delivery head,

a starter of suitable capacity, indicating lamps and fuse etc.

CALCULATIONS:

Basic data / constants:

1 kg /cm2 = 760 mm Hg (10 m of water)

15

Density of water = 1000 kg /m3 (9810 N/ m3)

Area of collecting tank = 0.125 m2

Discharge rate “ Q ” in m3 / s

Q = (A x h) / t

Where ‘h’ is height of water collected in measuring tank for a time interval of ‘t’ sec.

Total head “ H ” in m

H = 10 (Delivery Pressure + Vacuum head)

= 10(P + Pv)

Where,

P is pressure in kg /cm2, Pv is the Vacuum in mm of Hg

P= (1.032+ pressure reading) Pv = (1.032- (suction pressure reading x 1.33 x 10-3))

Power input to motor (kW)

Data: Energy meter constant E.M.C. = 3200 Rev/kw-h

I.P = K ×3600

E.M.C. ×t×ƞmotor = KW

Where ηmotor = 0.70, (70 %)

Where ‘K’ is the number of revolutions energy meter disc = 10 rev

‘t’ is the time taken in seconds by the Energy Meter for K revolutions

(1hp = 0.736 kW)

(1 kW = 1.36 hp.)

Output Power (delivered by the pump) kW

= 𝑾× 𝑸 ×𝑯

𝟏𝟎𝟎𝟎 = KW

Where W is 9810 N/m3,

Q is Discharge

% η pump = Out power x 100

input power

Speed

N

(rpm)

Delivery

pressure p

(kgf/cm2)

Suction

pressure

Pv

mm of Hg

Time taken

for 10

Impulse of

energy

meter (te) s

Water level rise in tank

R

Discharge

time

t (s) mm m

16

Speed of

pump

N

(rpm)

Head

H

m of water

Discharge

Q

(m3/s)

Power input

to pump

Pin

(kW)

Power

developed by

pump Pp

(kW)

Overall

efficiency

Ƞo

(%)

CALCULATIONS:

Basic data / constants:

1kg/cm2 = 760 mm Hg (10 m of water)

Density of water = 1000 kg / m3

Area of collecting tank = 0.125 m2

Discharge rate “ Q ” in m3 / s

Q = (A x h) x 100

Where ‘h’ is height of water collected in measuring tank for a time interval of ‘t’ sec.

Total head “ H ” in m

Pd=1.032 + Reading

Pv=1.032 – (Reading x 1.315 x 10-3)

H = 10 (Delivery Pressure + Vacuum head)

= 10 (Pd + Pv)

Where Pd is pressure in kg / cm2 , Pv is the Vacuum in mm of Hg

17

EXPERIMENT NO-7

AIM:

To determine the overall efficiency of a Reciprocating Pump.

INTRODUCTION:

Reciprocating pump is a positive displacement plunger pump. It is often used where

relatively small quantity of water is to be handled and delivery pressure is quite large.

Reciprocating pumps are widely used as Automobile Service Stations, Chemical Industries,

or as metering and dosing pumps.

The apparatus consists of a two cylinder, double acting reciprocating pump mounted over the

sump tank. The pump is driven by DC motor. An energy meter measures electrical input to

motor. Measuring tank is provided to measure discharge of the pump. The pressure and

vacuum gauges provided to measure the delivery pressure and suction vacuum respectively.

SPECIFICATIONS:-

1. Reciprocating pump - stroke length 16 mm, piston dia 22 mm. 2 piston, with air

vessel on discharge side, suction 15 mm discharge 15 mm.

2. DC motor, 1 HP 1440 RPM.

3. Measuring tank – 300 X 400 X 300 mm height provided with gauge tube and

funnel for diverting the flow into measuring tank or sump tank.

4. Sump tank – 600 X 500 X 300 mm height.

i. Pressure gauge 0 - 2 1 Kg/cm2 for discharge pressure,

ii. Vacuum gauge 0 -760 mm Hg for suction vacuum,

iii. Energy meter for motor input measurement.

PROCEDURE:

1. Fill up sufficient water in sump tank.

2. Open the gate valve in the discharge pipe of the pump fully.

3. Check nut bolts & the driving belt for proper tightening.

4. Connect the electric supply and switch on the supply.

5. Slightly close the discharge valve. Note down pump speed, delivery

6. Pressure, suction vacuum, time for 10imps of energy meter & for flow

measurement close the measuring tanks drain valve, take time for 10 lits.

7. Repeat the procedure for different gate valve closing. Take care that discharge

pressure does not rise above 8 Kg/cm2.

8. Change the speed and take readings for different gate valve openings.

OBSERVATIONS:-

Piston Dia (m) “D” = 0.022 m

Suction Stroke (m) “l” = 0.016 m

Volume per Stroke(m3) “Vs” = 1.2164 * 10-5

18

Volume of water collected (m3) = 10 m

3

Frictional Losses (m) = 2 m

Fig. Reciprocating Pump

OBSERVATION TABLE:

Sr NO

Pump

speed

“Np”

Qth

Time to

collect

water

“ t ” sec

Qact

Vacuum

Gauge “

Ps” (mm

hg)

Suction

Head Hs

Pressure

Gauge “

Pd”

Delivery

Head

“Hd”

Total

Head

“Ht”

1

2

3

4

5

19

Output Power of

pump “Pw”

Time for 10 imp.

"te" sec

Input Power Ip

Taking motor

efficiency 80%

(ISP)

Effeciency “η%”

1

2

3

4

5

CALCULATIONS

1. Volume per stroke =

2. Theoretical Discharge,

Qth =

3. Actual Discharge,

Qact= 0.01/t

4. Suction Head,

Hs =

Where,

Sp, gravity of mercury = 13.6

Ps = Vaccum/Suction Pressure in mm of Hg

5. Delivery head,

Hd = Pd/w

6. Total head where

Ht = Hs + Hd + 2 mtr

Where, Frictional losses = 2 mtr.

7. Output power of pump

PW =W ×Qa×Ht

1000 Kw

Where,

W = Specific weight of water = 9810 N/m3

Qact = Discharge m3/sec.

Ht = Total head m

8. Input power to pump-Let time required for 10 indication mean pulse of energy meter be “te” sec. then,

IP = 10 × 3600

te × 1600 Kw

Where,

Energy meter constant is 1600 imp/Kwh.

20

9. Taking motor efficiency 80 %, we have input shaft

Power S.P. = I.P. x 0.80

10. Overall efficiency of pump =

Result -:

From Observations:

1. Maximum Efficiency = ή = ……………………..%

2. I.H.P = ………

3. Total Head = …….

4. B.H.P. (output) = ………….