Fundamental Chemistry and Hydraulics - Mathematics and Statistics for the Environment - page 374

Use the following formulas to convert head into pressure:

• Centrifugal pumps

Head (ft) pecificgravity
2.

×

Pressure (psi) = (14.25)

31

• Positive displacement pumps

Head (ft) pecificweight
144

×

Pressure (psi) = (14.26)

14.2.5 C alCulating h orsepoWer and e FFiCienCy
When considering work being done, we consider the rate at which work is being done. This is called
power and is labeled as foot-pounds per second. At some point in the past, it was determined that
the ideal work animal, the horse, could move 550 pounds 1 foot in 1 second. Because large amounts
of work are also to be considered, this unit became known as horsepower. When pushing a certain
amount of water at a given pressure, the pump performs work. One horsepower equals 33,000 ft-lb/
min. The two basic terms for horsepower are

• Hydraulic horsepower (WHP)
• Brake horsepower (BHP)

14.2.5.1 Hydraulic Horsepower
One hydraulic horsepower equals

• 550 ft-lb/sec
• 33,000 ft-lb/min
• 2545 British thermal units per hour (Btu/hr)
• 0.746 kw
• 1014 metric HP

To calculate the hydraulic horsepower (WHP) using flow in gpm and head in feet, use the following
formula for centrifugal pumps:

Flow (gpm)head (ft) pecificgravity
39

× ×

WHP = (14.27)

60

When calculating horsepower for positive displacement pumps, common practice is to use psi for
pressure. Then the hydraulic horsepower becomes

Flow (gpm)pressure (psi)
3960

×

WHP = (14.28)

14.2.6 p ump e FFiCienCy and b raKe h orsepoWer (bhp)
When a motor-pump combination is used (for any purpose), neither the pump nor the motor will be
100% efficient. Simply put, not all the power supplied by the motor to the pump (brake horsepower)
will be used to lift the water (hydraulic horsepower); some of the power is used to overcome friction