# FLUID MECHANICS & MACHINERY LAB MANUAL

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24 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

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SUDHARSAN ENGINEERING COLLEGE

SATHIYAMANGALAM

622 501

Department of Mechanical Engineering

FLUID MECHANICS & MACHINERY

LAB MANUAL

Prepared By

CT.Umamaheswari,

Lecturer,

Department of Mechanical Engineering,

Sudharsan Engineering College.

CE1211

FLUID MECHANICS AND MACHINERY
LABORATORY

(Common to Mechanical, Production, Aeronautical and Automobile)

LIST OF EXPERIMENTS

1.

Determination o
f the Coefficient of discharge of given Orifice meter.

2.

Determination of the Coefficient of discharge of given Venturi meter.

3.

Calculation of the rate of flow using Rotameter.

4.

Determination of friction factor for a given set of pipes.

5.

Conducting experiments
and drawing the characteristic curves of Centrifugal
pump / Submergible pump

6.

Conducting experiments and drawing the characteristic curves of reciprocating
pump.

7.

Conducting experiments and drawing the characteristic curves of Gear pump.

8.

Conducting experimen
ts and drawing the characteristic curves of Pelton wheel.

9.

Conducting experiments and drawing the characteristics curves of Francis turbine.

10.

Conducting experiments and drawing the characteristic curves of Kaplan turbine.

LIST OF EQUIPMENTS

(for a batch of 30 students)

1.

Orifice meter setup

2.

Venturi meter setup

3.

Rotameter setup

4.

Pipe Flow analysis setup

5.

Centrifugal pump/submergible pump setup

6.

Reciprocating pump setup

7.

Gear pump setup

8.

Pelton wheel setup

9.

Francis turbine setup

10.

Kaplan turbine setup

Quantity: one each.

EX.NO:

PERFORMANCE TEST ON CENTRIFUGAL PUMP

Date:

AIM:

To conduct the performance test on centrifugal pump and to draw the
characteristic curves.

APPARATUS REQUIRED:

1.

Centrifugal Pump Set
-
up.

2.

Stop Watch.

3.

Meter S
cale.

4.

Collecting tank.

FORMULAE:

1.

Actual Discharge

(Q
a
)
:

Q
a

= Ah / t in m
3
/ s

Where,

A = Area of the tank

in m of water
,

h =

Height of water rise for the given
time‘t’

in m of water,

t = Time taken
for rise of water in s

2.
Input Power (

P
i

):

P
i

= ( 3600 x N
r
x 1000 ) / (N
c
x T )

in watts

Where,

N
r
=
Number of revolution of
Energy meter.

N
c
= Energy meter constant.

3

Output power ( P
o
) :

P
o

= w

Q
a
H

in watts

Where,

w =
Specific weight
of water

Q
a

= Actual

dischar
ge in

H =

4
.
Efficiency (
η

) :

η

= P
o
/ P
i

in %

OBSERVATION &
TABULATION:

Area of Collecting tank

(A)

= l x b

= 0.4 m x 0.4 m

= 0.16
m
2

Energy meter constant

(
N
c

)

=
1200 rev / kwh

SI.
NO

SUCTION

( H
s

)

DELIVERY

( H
d
)

TOTAL

H

=
H
s
+
H
d

TIME
FOR
-
--

cm
RISE
OF

H
2
O

( t )

TIME
FOR
-
---

rev
OF
EM
DISC

( T )

ACTUAL
DISCHARGE

(
Q
a
)

INPUT
POWER

( P
i

)

OUTPUT
POWER

( P
o
)

EFFICIENCY

(
η

)

mm

Of
Hg

m

Of
H
2
O

kg/
c

m
2

m

Of

H
2
O

m

Of

H
2
O

sec

sec

m
3
/ s

watts

watts

%

MODEL CALCULATION:

No : )

1 mm of
Hg =
13.6/1000
m
of

H
2
O

1
kg
/ c

m
2

=
10.33 m of H
2
O

1.

Actual

Discharge

(Q
a
)
:

Area of Collecting tank
(A)

=
l x b

=
----

x
-----

=
----------

m
2

Actual Discharge (Q
a
)

= Ah / t

=
----
x
---
/
----

=
---------

m
3
/

s

2.

Input Power ( P
i

):

Input Power ( P
i

)

=
( 3600 x N
r
x 1000 ) / (N
c
x T

)

=

=
--------

watts

3.
Outp
ut power ( P
o
) :

Output power P
o

= w Q
a
H

=

=
--------

watts

4.
Eff
iciency ( η ) :

Eff
iciency ( η ) =
P
o
/ P
i

=

=
---------
%

PROCEDURE:

Close the delivery
gate valve completely.

Start the motor and adjust the gate valve to the required pressure and
delivery.

The pressure and vaccum gauge readings.

The time ‘T’ for ‘N’ revolutions of energy meter disc.

The
time‘t’

for ‘h’ cm ris
e of water collecting tank.

Switch off the motor
.

Calculate the input, output and efficiency.

GRAPH:

1.

2.

Discharge Vs Output

3.

Discharge Vs Efficiency

RESULT:

The performance of
centrifugal

pump is conducted and characteristi
cs curves are
drawn.

EX.NO: PERFORMANCE TEST ON
RECIPROCATING

PUMP

Date:

AIM:

To conduct the performance test on
reciprocating

pump and to draw the
characteristic curves.

APPARATUS REQUIRED:

1.

Reciprocating

Pump Set
-
up.

2.

Sto
p Watch.

3.

Meter Scale.

4.

Collecting tank.

FORMULAE:

5.

Actual Discharge

(Q
a
)
:

Q
a

= Ah / t in m
3
/ s

Where,

A = Area of the tank in m of water,

h = Height of water rise for the given time ‘t’ in m of water,

t = Time taken for rise of water in s

2.
Input Power ( P
i

):

P
i
=
(3600

x N
r
x
1000)

/ (N
c
x
T)

in watts

Where,

N
r =

Number of revolution of Energy meter.

N
c
= Energy meter constant.

a.

Output power ( P
o
) :

P
o

= w Q
a
H

in watts

Where,

w = Specific weight of water

Q
a

=

Actual discharge in

4
.
Efficiency (
η

) :

η

= P
o
/ P
i

in %

OBSERVATION & TABULATION:

Area of Collecting tank ( A ) = l x b

= 0.4 m x 0.4 m

= 0.16
m
2

Energy meter constant

(
N
c

) = 1200 rev / kwh

SI.
NO

SUCTION
HEA
D

( H
s

)

DELIVERY

( H
d
)

TOTAL

H

=
H
s
+H
d

TIME
FOR
-
--

cm
RISE
OF

H
2
O

( t )

TIME
FOR
-
---

rev
OF
EM
DISC

( T )

ACTUAL
DISCHARGE

(
Q
a
)

INPUT
POWER

( P
i

)

OUTPUT
POWER

( P
o
)

EFFICIENCY

(
η

)

mm

Of
Hg

m

Of
H
2
O

kg/
c

m
2

m

Of

H
2
O

m

Of

H
2
O

sec

sec

m
3
/ s

watts

watts

%

MODEL CALCULATION: (Reading No : )

1 mm of
Hg = 13.6/1000 m of H
2
O

1
kg/ c m
2
= 10.33 m of H
2
O

1.
Actual
Discharge

(Q
a
)
:

Area of Collecting tank ( A )
= l x b

=
----

x
-----

=
----------

m
2

Actual Discharge (Q
a
)

= Ah / t

=
----
x
---
/
----

=
---------

m
3

/ s

2.

Input Power ( P
i

):

Input Power ( P
i

) =
( 3600 x N
r
x 1000 ) / (N
c
x T

)

=

=
--------

watts

3.
Ou
tput power ( P
o
) :

Output power P
o

= w Q
a
H

=

=
--------

watts

4.
Efficiency ( η ) :

Eff
iciency ( η ) =
P
o
/ P
i

=

=
---------
%

PROCEDURE:

Close the delive
ry gate valve completely.

Start the motor and adjust the gate valve to the required pressure and
delivery.

The pressure and vaccum gauge readings.

The time ‘T’ for ‘N’ revolutions of energy meter disc.

The
time‘t’

for ‘h’ cm r
ise of water collecting tank.

Switch off the motor
.

Calculate the input, output and efficiency.

GRAPH:

4.

5.

Discharge Vs Output

6.

Discharge Vs Efficiency

RESULT:

The performance of reciprocating pump is conducted and character
istics curves
are drawn.

EX.NO: PERFORMANCE TEST ON
GEAR

(OIL
)

PUMP

Date:

AIM:

To conduct the performance test on
gear

(
o
il)

pump and to draw the characteristic
curves.

APPARATUS REQUIRED:

1.
Gear

(Oil
)

Pump Set
-
up.

6.

Stop Watch
.

7.

Meter Scale.

8.

Collecting tank.

FORMULAE:

9.

Actual Discharge

(Q
a
)
:

Q
a

= Ah / t in m
3
/ s

Where,

A = Area of the tank in m of water,

h = Height of water rise for the given time ‘t’ in m of water,

t = Time taken for rise of water in s

2.
In
put Power ( P
i

):

P
i
= (3600 x N
r
x 1000) / (N
c
x T)

in watts

Where,

N
r =

Number of revolution of Energy meter.

N
c
= Energy meter constant.

a.

Output power ( P
o
) :

P
o

= w Q
a
H

in watts

Where,

w = Specific weight of water

Q
a

= Actual

discharge in

4
.
Efficiency (
η

) :

η

= P
o
/ P
i

in %

OBSERVATION & TABULATION:

Area of Collecting tank ( A ) = l x b

= 0.4 m x 0.4 m

= 0.16
m
2

Energy meter constant

(
N
c

) = 1200 rev / kwh

SI.
NO

SUCTION
HEA
D

( H
s

)

DELIVERY

( H
d
)

TOTAL

H

=
H
s
+H
d

TIME
FOR
-
--

cm
RISE
OF

H
2
O

( t )

TIME
FOR
-
---

rev
OF
EM
DISC

( T )

ACTUAL
DISCHARGE

(
Q
a
)

INPUT
POWER

( P
i

)

OUTPUT
POWER

( P
o
)

EFFICIENCY

(
η

)

mm

Of
Hg

m

Of
H
2
O

kg/
c

m
2

m

Of

H
2
O

m

Of

H
2
O

sec

sec

m
3
/ s

watts

watts

%

MODEL CALCULATION: (Reading No : )

1 mm of
Hg = 13.6/1000 m of H
2
O

1
kg/ c m
2
= 10.33 m of H
2
O

1.

Actual

Discharge

(Q
a
)
:

Area of Collecting tank
(A)

= l x b

=
----

x
-----

=
----------

m
2

Actual Discharge (Q
a
)

= Ah / t

=
----
x
---
/
----

=
---------

m
3
/ s

2.

Input Power ( P
i

):

Input Power ( P
i

) =
( 3600 x N
r
x 1000 ) / (N
c
x T

)

=

=
--------

watts

3.

Output

power ( P
o
) :

Output power P
o

= w Q
a
H

=

=
--------

watts

4.
Efficiency ( η ) :

Eff
iciency ( η ) =
P
o
/ P
i

=

=
---------
%

PROCEDURE:

Close the delive
ry gate valve completely.

Start the motor and adjust the gate valve to the required pressure and
delivery.

The pressure and vaccum gauge readings.

The time ‘T’ for ‘N’ revolutions of energy meter disc.

The time‘t’ for ‘h’ cm r
ise of water collecting tank.

Switch off the motor
.

Calculate the input, output and efficiency.

GRAPH:

7.

8.

Discharge Vs Output

9.

Discharge Vs Efficiency

RESULT:

The performance of reciprocating pump is conducted and character
istics curves
are drawn.

EX.NO:
FLOW THROUGH VENTURIMETER

Date:

AIM:

To conduct the test on
venturimeter

and
to determine

the
c
o
-
efficient of discharge.

APPARATUS REQUIRED:

1.

Venturimeter

Set
-
up.

2.

Stop Watch.

3.

Meter Scale.

4.

Collecti
ng tank.

FORMULAE:

1.

Theoretical

Discharge

(Q
th
)
:

Q
th

=
a
1

a
2

√(2gH) /
√(

a
1
2

-

a
2
2
) in
m
3
/ s

Where,

a
1

= Area of the
venturimeter inlet
,

a
1

= Area of the venturimeter outlet,

H

=

2. Actual

Discharge

(Q
a
)
:

Q
a

= Ah / t in m
3
/ s

Where,

A = Area of the tank in m of water,

h = Height

of water rise for the given time

‘t’ in m of water,

t =
Time taken for rise of water in s

3.

Co
-
efficient of discharge

( Cd)
:

Cd =
Q
a

/
Q
th

Where,

Q
t

=
Theoritical

discharge in

m
3
/ s

Q
a

= Actual discharge in
m
3
/ s

OBSERVATION & TABULAT
ION:

Area of Collecting tank (A) = l x b

= 0.4 m x 0.4 m

= 0.16
m
2

SI.

NO

MANOMETERS

H= X
(Sm
-
S
f
)
/S
f

TIME
TAKEN
FOR
-----

cm RISE

OF
WATER

( t )

DISCHARGE

CO
-
EFFICIENT
OF
DISCHARGE
(
Cd )

h
1

h
2

X=
(h
1

h
2)

THEORI
TICAL

( Q
th

)

ACTUAL

( Q
a
)

cm

cm

cm

m of
H
2
O

sec

m
3
/s

m
3
/s

MODEL CALCULATION: (Reading No : )

1 mm of
Hg = 13.6/1000 m of H
2
O

1.

Actual
Discharge

(Q
a
)
:

Are
a of Collecting tank (A)

= l x b

=
----

x
-----

=
----------

m
2

Actual Discharge (Q
a
)

= Ah / t

=
----
x
---
/
----

=
---------

m
3
/ s

Theoretical Discharge

(Q
th
)
:

a
1 = (3.14/4) x
d
1
2

=

a
2 = (3.14/4) x
d
2
2

=

Q
th

= a
1

a
2

√(2gH) / √(

a
1
2

-

a
2
2
) in m
3
/ s

=
----
x
---
/
----

=
---------

m
3
/ s

2.

C
o
-
efficient of discharge ( Cd):

Cd =
Q
a

/
Q
th

PROCEDURE:

Note the diameters.

Close the
outlet

valve
completely, Inlet

valve is opened fully.

The outlet
valves are opened slightly and note

The outlet valves are

closed tightly and note the time‘t’ for ‘h’ cm rise of
water in collecting tank.

Switch off the motor
.

Calculate the

a
verage Co
-
efficient of venturimeter
.

GRAPH:

RESULT:

Average Co
-
efficient of venturimeter,

Cd =

EX.NO:
FLOW THROUGH ORIFICE
METER

Date:

AIM:

To conduct the test on
orifice
meter

and to determine the co
-
efficient of discharge.

APPARATUS REQUIRED:

5.

Orifice
meter

Set
-
up.

6.

Stop Watch.

7.

Meter Scale.

8.

Collecting tank.

FORMULAE
:

3.

Theoretical Discharge

(Q
th
)
:

Q
th

= a
1

a
2

√(2gH) / √(

a
1
2

-

a
2
2
) in m
3
/ s

Where,

a
1

= Area of the orifice
meter inlet,

a
1

= Area of the orifice
meter outlet,

2. Actual Discharge

(Q
a
)
:

Q
a

= Ah / t in m
3
/ s

Where,

A = Area of the tank in m of water,

h = Height

of water rise for the given time ‘t’ in m of water,

t = Time taken for rise of water in s

4.

Co
-
efficient of discharge ( Cd):

Cd =
Q
a

/
Q
th

Where,

Q
t
= Theoritical discharge in m
3
/ s

Q
a

= Actual discharge in m
3
/ s

OBSERVATION & TABULAT
ION:

Area of Collecting tank (A) = l x b

= 0.4 m x 0.4 m

= 0.16
m
2

SI.

NO

MANOMETERS

H= X
(Sm
-
S
f
)
/S
f

TIME
TAKEN
FOR
-----

cm RISE

OF
WATER

( t )

DISCHARGE

CO
-
EFFICIENT
OF
DISCHARGE
( C
d )

h
1

h
2

X=
(h
1

h
2)

THEORI
TICAL

( Q
th

)

ACTUAL

( Q
a
)

cm

cm

cm

m of
H
2
O

sec

m
3
/s

m
3
/s

MODEL CALCULATION: (Reading No : )

1 mm of
Hg = 13.6/1000 m of H
2
O

1.

Actual
Discharge

(Q
a
)
:

Area

of Collecting tank (A)

= l x b

=
----

x
-----

=
----------

m
2

Actual Discharge (Q
a
)

= Ah / t

=
----
x
---
/
----

=
---------

m
3
/ s

Theoretical Discharge

(Q
th
)
:

a
1 = (3.14/4) x
d
1
2

=

a
2 = (3.14/4) x
d
2
2

=

Q
th

= a
1

a
2

√(2gH) / √(

a
1
2

-

a
2
2
) in m
3
/ s

=
----
x
---
/
----

=
---------

m
3
/ s

4.

Co
-
efficient of discharge ( Cd):

Cd =
Q
a

/
Q
th

PROCEDURE:

Note the diameters.

Close the outlet valve completely, Inlet valve is opened fully.

The outlet valves are opened slightly and note the manometric readings.

The outlet valves are
closed tightly and note the time‘t’ for ‘h’ cm rise of
water in collecting tank.

Switch off the motor
.

Calculate the a
verage Co
-
efficient of orifice
meter
.

GRAPH:

RESULT:

Average Co
-
efficient of
orifice
meter,
Cd =

EX.NO: PERFORMANCE TEST ON
PELTON WHEEL

Date:

AIM:

To conduct the performance test on
pelton wheel

and to draw the characteristic
curves.

APPARATUS REQUIRED:

1.

Pelton wheel

Set
-
up.

2.

Tachometer

3.

Weights

FORMULAE:

10.

Actual Discha
rge

(Q
a
)
:

Q
a

=
a
1

a
2

√(2gH) / √(

a
1
2

-

a
2
2
) in m
3
/ s

Where,

a
1

= Area of the

a
1

= Area of the

2.
Input Power ( P
i

):

P
i

= w Q
a
H

in watts

Where,

w = Specific weight of water

Q
a

= Actual discharge in

3.
Output p
ower ( P
o
) :

P
o = (2x3.14 NT) / 60

Where,

N = speed in r.p.m

T = Torque in N
-
m

4
.
Efficiency (
η

) :

η

= P
o
/ P
i

in %

OBSERVATION & TABULATION:

Area of Collecting tank ( A ) = l x b

= 0.4 m x 0.4 m

= 0.16

m
2

Energy meter constant

(
N
c

) = 1200 rev / kwh

SI.
NO

Spring
Balance

Ventu
rimete
r
g

Net
Hea
d

Spee
d

ACTU
AL
DISC
HAR
GE

(
Q
a
)

INPUT
POWER

( P
i

)

OUTPUT
POWER

( P
o
)

EFFICIE
NCY

(
η

)

w

m

m

r.p.m

m
3
/ s

watts

watts

%

MODEL CALCULATION: (Reading No : )

1 mm of
Hg = 13.6/1000 m of H
2
O

1
kg/ c m
2
= 10.33 m of H
2
O

1.
Actual
Discharge

(Q
a
)
:

Area of Collecting tank ( A ) = l x b

=
----

x
-----

=
----------

m
2

Actual Discharge (Q
a
)

= Ah / t

=
----
x
---
/
----

=
---------

m
3
/ s

2
.

Input Power ( P
i

):

P
i

= w Q
a
H

=

=
--------

watts

3.
Output power ( P
o
) :

Output power
P
o

= (2x3.14 NT) /
60

=

=
--------

watts

4.
Efficiency ( η ) :

Eff
iciency ( η ) =
P
o
/ P
i

=

=
---------
%

PROCEDURE:

.Start the motor

The discharge valve is opened slowly

The
spring scale

The

Speed of the turbine.

Switch off the motor
.

Calculate the input, output and efficiency.

GRAPH:

10.

11.

Vs Output

12.

Vs Efficiency

RESULT:

The performance of
pelton wheel

is conducted and characteristics curves are
drawn.

EX.NO: PERFORMANCE TEST ON
FRANCIS TURBINE

Date:

AIM:

To cond
uct the performance test on
francis turbine

and to draw the characteristic
curves.

APPARATUS REQUIRED:

1.

Francis turbine

Set
-
up.

2.

Tachometer

3.

Weights

FORMULAE:

11.

Actual Discharge

(Q
a
)
:

Q
a

= a
1

a
2

√(2gH) / √(

a
1
2

-

a
2
2
) in m
3
/ s

Where,

a
1

= Area of
the

a
1

= Area of the

2.
Input Power ( P
i

):

P
i

= w Q
a
H

in watts

Where,

w = Specific weight of water

Q
a

= Actual discharge in

3.Output power ( P
o
) :

P
o = (2x3.14 NT) / 60

Where,

N = speed
in r.p.m

T = Torque in N
-
m

4
.
Efficiency (
η

) :

η

= P
o
/ P
i

in %

OBSERVATION & TABULATION:

Area of Collecting tank ( A ) = l x b

= 0.4 m x 0.4 m

= 0.16
m
2

Energy meter constant

(
N
c

) = 1200
rev / kwh

SI.
NO

Spring
Balance

Ventu
rimete
r
g

Net
Hea
d

Spee
d

ACTU
AL
DISC
HAR
GE

(
Q
a
)

INPUT
POWER

( P
i

)

OUTPUT
POWER

( P
o
)

EFFICIE
NCY

(
η

)

w

w

w

m

m

r.p.m

m
3
/ s

watts

watts

%

MODEL CALCULATION: (Reading No : )

1 mm of
Hg = 13.6/1000 m of H
2
O

1
kg/ c m
2
= 10.33 m of H
2
O

1.
Actual
Discharge

(Q
a
)
:

Area of Collecting tank ( A ) = l x b

=
----

x
-----

=
----------

m
2

Actual Di
scharge (Q
a
)

= Ah / t

=
----
x
---
/
----

=
---------

m
3
/ s

2.

Input Power ( P
i

):

P
i

= w Q
a
H

=

=
--------

watts

3.
Output power ( P
o
) :

Output power
P
o

= (2x3.14 NT) / 60

=

=
--------

watts

4.
Efficiency ( η ) :

Eff
iciency ( η ) =
P
o
/ P
i

=

=
---------
%

PROCEDURE:

.Start the motor at no load condition

The discharge valve is opened slowly

Speed of the turbine.

Switch off the motor
.

Calculate the input, output and efficiency.

GRAPH:

4.

5.

6.

RESULT:

The performance of
francis turbine

is conducted and characteristics curves are
drawn.

EX.NO:
FLOW THROUGH
PIPES ( MAJOR LOSSES)

Date:

AIM:

To
determine the friction factor for the given pipe
.

APPARATUS REQUIRED:

9.

Pipe friction apparatus
.

10.

Stop Watch.

11.

Meter Scale.

12.

Collecting tank.

FORMULAE:

1.

Actual
Dischar
ge

(Q
a
)
:

Area of Collecting tank (A)

= l x b

Actual Discharge (Q
a
)

= Ah / t

Where,

a = Area of the pipe

A
= Area of the collecting tank

h

2. Velocity ( V) :

a = 3.14xd
2

/4

Velocity

V =
Q
a

/a

3.
Friction factor

(f)
:

f = (2gdh
f
)/LV
2

Where,

h
f

L = Length of pipe

OBSERVATION & TABULATION:

Area of Collecting tank (A) = l x b

= 0.4 m x 0.4 m

= 0.16
m
2

SI.

NO

MANOMETERS

TIME
TAKEN
FOR
-----

cm RISE

OF
WATER

( t )

ACTUAL

DISCHARGE

( Q
a
)

Velocity

(V)

Friction
factor

(f)

(Velo
city)
2

h
1

h
2

X=
(h
1

h
2)

c
m

cm

cm

sec

m
3
/s

MODEL CALCULATION: (Reading No : )

1 mm of
Hg = 13.6/1000 m of H
2
O

1.

Actual
Discharge

(Q
a
)
:

Area of Collecting tank (A)

= l x b

=
----

x
-----

=
----------

m
2

Ac
tual Discharge (Q
a
)

= Ah / t

=
----
x
---
/
----

=
---------

m
3
/ s

2. Velocity ( V) :

a = 3.14xd
2

/4

=

V
elocity

V =
Q
a

/a

=

3.
Friction factor
:

f = (2gdh
f
)/LV
2

=

=

PROCEDURE:

Note the diameters.

Close the outlet valve completely, Inlet valve is opened fully.

The outlet valves are opened slightly and note the manomet

The outlet valves are closed tightly and note the time‘t’ for ‘h’ cm rise of
water in collecting tank.

Switch off the motor
.

Calculate the

Friction factor of the pipe
.

GRAPH:

2

RESULT:

Fric
tion factor of the pipe, f

=