Approximate Pressure Distribution in an Accelerating Launch-Vehicle Fuel Tank

A detailed derivation of the equations governing the pressure in a generic liquid-fuel launch vehicle tank subjected to uniformly accelerated motion is presented. The equations obtained are then for the Space Shuttle Superlightweight Liquid-Oxygen Tank at approximately 70 seconds into flight. This generic derivation is applicable to any fuel tank in the form of a surface of revolution and should be useful in the design of future launch vehicles