PUMPING OF FLUIDS 121
Solution
Cross-sectional area of pipeD/ 4 0. 0025 ^2 D 0 .00049 m^2.
Volumetric flowrateD 1. 3 / 1. 84 ð 1000 D 0 .00071 m^3 /s.
Velocity in the pipe,uD 0. 00071 / 0. 00049 D 1 .45 m/s
ReDud/ D 1. 84 ð 1000 ð 1. 45 ð 0. 025 / 0. 025 D 2670This value of the Reynolds number lies within the critical zone. If the flow were
laminar, the value ofR/u^2 from Fig. 3.7 would be 0.003. If the flow were turbulent,
the value ofR/u^2 would be considerably higher, and this higher value should be used
in subsequent calculation to provide a margin of safety. If the roughness is taken as
0.05 mm,e/dD 0. 05 / 25 D 0 .002 and, from Fig 3.7,R/u^2 D 0 .0057.
The head loss due to friction,
hfD 4 R/u^2 l/du^2 /g (equation 3.20)D 4 ð 0. 0057 30 / 0. 025 1. 452 / 9. 81 D 5 .87 mzD12 m so that the total headD 17 .87 m.
The theoretical power requirement, from equation 8.61, is:powerD 17. 87 ð 1. 3 ð 9. 81 D227 WIf the pump is 50% efficient, actual powerD 227 / 0. 5 D454 W
A PTFE lined centrifugal pump and lead or high silicon iron pipe would be suitable
for this duty.
PROBLEM 8.19
A petroleum fraction is pumped 2 km from a distillation plant to storage tanks through a
mild steel pipeline, 150 mm in diameter, at the rate of 0.04 m^3 /s. What is the pressure
drop along the pipe and the power supplied to the pumping unit if it has an efficiency of
50%? The pump impeller is eroded and the pressure at its delivery falls to one half. By
how much is the flowrate reduced? Density of the liquidD705 kg/m^3. Viscosity of the
liquidD 0 .5mNs/m^2. Roughness of pipe surfaceD 0 .004 mm.
Solution
Cross-sectional area of pipeD/ 4 0. 152 D 0 .0177 m^2.
Velocity in the pipeD 0. 04 / 0. 0177 D 2 .26 m/s.
Reynolds numberD 0. 705 ð 1000 ð 2. 26 ð 0. 15 / 0. 5 ð 10 ^3 D 4. 78 ð 105
eD 0 .004 mm,e/dD 0. 004 / 150 D 0 .000027 and from Fig. 3.7,R/u^2 D 0. 00165
The pressure drop is:PfD 4 R/u^2 l/du^2 (equation 3.18)
PfD 4 ð 0. 00165 2000 / 0. 15 705 ð 2. 262 D 316 ,900 N/m^2 or 320 kN/m^2