PUMPING OF FLUIDS 123
PROBLEM 8.21
600 litres/s of water at 320 K is pumped in a 40 mm i.d. pipe through a length of 150 m
in a horizontal direction and up through a vertical height of 10 m. In the pipe there is
a control valve which may be taken as equivalent to 200 pipe diameters and other pipe
fittings equivalent to 60 pipe diameters. Also in the line there is a heat exchanger across
which there is a loss in head of 1.5 m of water. If the main pipe has a roughness of
0.0002 m, what power must be delivered to the pump if the unit is 60% efficient?
Solution
Mass flowrate of waterD 600 ð 10 ^6 ð 1000 D 0 .6 kg/s.
Cross-sectional area of pipeD/ 4 0. 042 D 0 .00126 m^2.
Velocity of water in the pipeD 600 ð 10 ^6 / 0. 00126 D 0 .476 m/s.
ReDud/ D 1000 ð 0. 476 ð 0. 04 / 1 ð 10 ^3 D 1. 9 ð 104.
IfeD 0 .0002 m,e/dD 0 .005, and from Fig. 3.7,R/u^2 D 0 .0042.
The valve and fittings are equivalent to 260 pipe diameters which is equal to 260 ð
0. 04 D 10 .4 m of pipe.
The equivalent length of pipe is therefore 150 C 10. 4 D 160 .4m.
The head loss due to friction is:
hfD 4 R/u^2 l/du^2 /g (equation 3.20)D 4 ð 0. 0042 160. 4 / 0. 04 0. 4762 / 9. 81 D 1 .56 m∴ total headD 1. 56 C 1. 5 C 10 D 13 .06 m.
and: power requiredD 13. 06 ð 0. 6 ð 9. 81 / 0. 6 D128 W
PROBLEM 8.22
A pump developing a pressure of 800 kN/m^2 is used to pump water through a 150 mm
pipe 300 m long to a reservoir 60 m higher. With the valves fully open, the flowrate
obtained is 0.05 m^3 /s. As a result of corrosion and scaling the effective absolute roughness
of the pipe surface increases by a factor of 10. By what percentage is the flowrate reduced?
Viscosity of waterD1mNs/m^2.
Solution
800 kN/m^2 is equivalent to a head of 80, 000 / 1000 ð 9. 81 D 81 .55 m of water. If the
pump is required to raise the water through a height of 60 m, then neglecting kinetic
energy losses, the head loss due to friction in the pipeD 81. 55 60 D 21 .55 m.
The flowrate under these conditions is 0.05 m^3 /s.