An oil pipeline is 15 inches in diameter and 14 mile long Th

An oil pipeline is 15 inches in diameter and 1/4 mile long. The oil has specific gravity SG = 0.860, and is to be accelerated from rest to its normal operating velocity of 15 ft/s in one minute. Calculate the pressure (in psi) needed at the end of the pipeline to give the required acceleration.

Solution

Acceleration = 15 / 60   = 0.25 ft/s^2

Mass of Oil   = 0.86 * 62.428 * pi * (15/12)^2 * 1320 / 4   = 87040.9 lb

Force = pressure * pi * 1.25^2 / 4    = Mass of oil * Acceleration

pressure   = 87040.9 * 0.25 * 4 / (pi * 1.25^2 )    = 123.138 psi