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A pipe of diameter 300 mm and length 3500 m is used for the transmission of power by water.
The total head at the inlet of the pipe is 500 m. Find the maximum power available at the outlet of
the pipe, if the value of f f
DATA
d :=300mm
L :=3500m
H
in
:=500m
f f
ρ 1000
kg
m
3
SOLUTION
h L
H
in
:= =166.667 m
Q 1
m
3
s
Given
h L
8 Q
2
π
2 g
4f f
L
d
5
H
in
maximum power transmission
Q Find Q( ) 0.
m
3
s
H
out
H
in
h L
:= - =333.333 m
P ρ g H out
:= Q=789.501 kW
A pipe line of length 2000 m is used for power transmission. If 110.3625 kW power is to be
transmitted through the pipe in which water having a pressure of 490.5 N/cm^2 at inlet is flowing.
Find the diameter of the pipe and efficiency of transmission if the pressure drop over the
length of pipe is 98.1 N/cm^2• Take f f
DATA
L :=2000m
P :=110.3625kW
p 1
N
cm
2
:= =4.905 MPa
p 1_
N
cm
2
:= =0.981 MPa
f f
ρ 1000
kg
m
3
SOLUTION
p 2
p 1
p 1_
:= - =3.924 MPa
H
in
p 1
ρ g
:= =500.171 m
H
out
p 2
ρ g
:= =400.137 m
h L
p 1_
ρ g
:= =100.034 m
Q 1
m
3
s
:= d :=1m
Given
P ρ g H out
= Q
h L
8 Q
2
π
2 g
4f f
L
d
5
Q
d
:= Find Q d( , ) Q 0.
m
3
s
= d =0.126 m
η
H
out
H
in
(ii)
η :=90%
H
in
p 1
ρ g
:= =500.171 m
η
H
out
H
in
= H
out
η H in
:= =450.154 m
h L
H
in
H
out
:= - =50.017 m
Q 1
m
3
s
:= d :=1m
Given
P ρ g H out
= Q
h L
8 Q
2
π
2 g
4f f
L
d
5
Q
d
:= Find Q d( , ) Q 0.
m
3
s
= d =0.138 m
A nozzle is fitted at the end of a pipe of length 300 m and of diameter 100 mm. For the maxim um
transmission of power through the nozzle, find the diameter of nozzle. Take f f
DATA
L :=300m
d :=100mm
f f
ρ 1000
kg
m
3
SOLUTION
h L
H
in
= for maximum power transmission with nozzle included
h L
8 Q
2
π
2 g
4f f
L
d
5
H
in
8 Q
2
π
2 gd n
4
h L
d n
d
5
8 f f
L
1
4
:= = 0.026 m
Find the maximum power transmitted by a jet of water discharging freely out of nozzle fitted to a
pipe = 300 m long and 100 mm diameter with co-efficient of friction as 0.01. The available head
at the nozzle is 90 m.
DATA
L :=300m
d :=100mm
f f
H
out
:=90m
ρ 1000
kg
m
3
SOLUTION
d n
d
5
8 f f
L
1
4
:= = 0.025 m
Q 1
m
3
s
Given
H
out
8 Q
2
π
2 g d n
4
Q Find Q( ) 0.
m
3
s
P ρ g H out
:= Q=18.799 kW
for maximum power transmission with nozzle included
The rate of flow of water through a pipe of length 2000 m and diameter 1 m is 2 m^3/s. At the end
of the pipe a nozzle of outside diameter 300 mm is fitted. Find the power transmitted through the
nozzle if the head of water at inlet of the pipe is 200 m and co-efficient of friction for pipe is 0.01.
DATA
L :=2000m
d :=1m
Q 2
m
3
s
d n
:=300mm
H
in
:=200m
f f
ρ 1000
kg
m
3
SOLUTION
h L
8 Q
2
π
2 g
4f f
L
d
5
:= =26.45 m
H
out
H
in
h L
:= - =173.55 m
P ρ g H out
:= Q=3403.896 kW
