A36-in-diameter pipeline carries oil (sg = 0.89) at 1 million barrels per day (bbl/day). the friction head loss is 13 ft/1000 ft of pipe. it is planned to place pumping stations every 10 mi along the pipe. estimate the horsepower which must be delivered to the oil by each pump.

144540.16735 hp

Explanation:

Diameter of pipe = 36 in

Specific gravity of oil = 0.89

ρ = Density of oil = 0.89×62.2407

Q = Flow rate of oil = 1×10⁶ bbl/day = 1×10⁶×5.61458/86400 =  64.9836033565 ft³/s

hf = 13 ft/1000ft = 0.013 ft/ft

for 10 miles

hf = 0.013×10×5280 = 686.4 ft

g = Acceleration due to gravity = 32.17405 ft/s²

Power

P = ρQghf

⇒P = 0.89×62.2407×64.9836033565×32.17405×686.4

⇒P = 79497097.342 ft lbf/s

1 ft lbf/s = 0.0018181817 hp

79497097.342 ft lbf/s = 144540.16735 hp

∴ Horsepower which must be delivered to the oil by each pump is  144540.16735 hp