gpm x psi / 1715 = hydraulic horsepower
is the horsepower equivalent of “lifting” a continuous volume rate of fluid to the height in ft represented by the pressure involved (as if a tall, open overflowing stand-pipe were connected to measure the pressure). The weight of fluid directly controls the pressure in a standpipe: 520 psi is the bottom pressure of a 1,000-ft column of 10 lb/gal (ppg) fluid. To pump in a gallon at the bottom and move a gallon out the top is equivalent to lifting 10 pounds through 1,000 ft, or 10,000 ft-lb. A volume of 3.3 gal/min (gpm) at these conditions is 33,000 ft-lb/min, or 1 horsepower (hp). Because it is the calculation of fluid relations, it is referred to as hydraulic horsepower. It can be calculated for any part of the system according to the pressure relations for that part of the system. Thus, 3.3 gpm and 520 psi, or 1,715 gpm and 1 psi means 1 horsepower. For any other properties of fluid pumped, 520 psi represents a different height but always the same ft-lb/gal pumped.