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 =
Total head 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
HEAD
( H
s
)
DELIVERY
HEAD
( H
d
)
TOTAL
HEAD
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.
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.
Note the following readings,
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.
Discharge Vs Head
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
H = Total head 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
HEAD
( H
d
)
TOTAL
HEAD
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.
Note the following readings,
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.
Discharge Vs Head
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
H = Total head 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
HEAD
( H
d
)
TOTAL
HEAD
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.
Note the following readings,
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.
Discharge Vs Head
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
=
Total head
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
READING
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 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 venturimeter
.
GRAPH:
Discharge Vs Head
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,
H = Total head
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
READING
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:
Discharge Vs Head
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
H = Total head
2.
Input Power ( P
i
):
P
i
= w Q
a
H
in watts
Where,
w = Specific weight of water
Q
a
= Actual discharge in
H = Total head 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
Load
Spring
Balance
Net load
Ventu
rimete
r
readin
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
at no load condition
The discharge valve is opened slowly
The load is applied and
Note the following readings,
The
spring scale
readings.
The
pressure gauge reading
Speed of the turbine.
Switch off the motor
.
Calculate the input, output and efficiency.
GRAPH:
10.
Load
Vs Head
11.
Load
Vs Output
12.
Load
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
H = Total head
2.
Input Power ( P
i
):
P
i
= w Q
a
H
in watts
Where,
w = Specific weight of water
Q
a
= Actual discharge in
H = Total head 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
Load
Spring
Balance
Net load
Ventu
rimete
r
readin
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
The load is applied and Note the following readings,
The spring scale readings.
The pressure gauge reading
Speed of the turbine.
Switch off the motor
.
Calculate the input, output and efficiency.
GRAPH:
4.
Load Vs Head
5.
Load Vs Output
6.
Load Vs Efficiency
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
= Total head
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
= Heead loss
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
READING
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
ric 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
Friction factor of the pipe
.
GRAPH:
Head loss Vs (Velocity)
2
RESULT:
Fric
tion factor of the pipe, f
=
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