Derive equation for pressure to push pig through pipe line
A 20" diameter pipe is 7243 meters long and is being cleaned by a pig apparatus. Derive an equation for the required pressure given by a compressor to push a pig through a pipe while it pushes fuel oil #2 into a tank at the end of the pipe. The change in elevation is unknown, as well as the the current amount of liquid in the tank.
Please derive this equation for pressure.