Basic Units of Measurement and Conversions - Basic Mathematics for Water and Wastewater Operators - page 45

h orsepoWer and e nergy C osts
In water/wastewater treatment and ancillaries, horsepower is a common expression
for power. One horsepower is equal to 33,000 ft-lb of work per minute. This value is
determined, for example, when selecting a pump or combination of pumps to ensure
adequate pumping capacity (a major use of calculating horsepower in water/waste-
water treatment). Pumping capacity depends on the flow rate desired and the feet of
head against which the pump must pump (effective height).
Calculations of horsepower are made in conjunction with a variety of treat-
ment plant operations. The basic concept from which the horsepower calculation
is derived is the concept of work. Work involves the operation of a force (lb) over
a specific distance (ft). The amount of work accomplished is measured in foot-
pounds (ft-lb):

ft × lb = ft-lb (2.18)

The rate of doing work (power) involves a time factor. Originally, the rate of doing
work or power compared the power of a horse to that of a steam engine. The rate
at which a horse could work was determined to be about 550 ft-lb/sec (or expressed
as 33,000 ft-lb/min). This rate has become the definition of the standard unit called
horsepower (see Equation 2.19).

Power (ft-lb/min)
33,000 ft-

Horsepower (hp) = (2.19)

lb/min/hp

In water/wastewater treatment, the major use of horsepower calculation is in
pumping stations. When used for this purpose, the horsepower calculation can be
modified as shown below.

Water Horsepower
The amount of power required to move a given volume of water a specified total head
is known as water horsepower (whp).

Pump rate (gpm)Tota × llhead (ft) × 8.34 lb/gal

Water horsepower (whp) = (2.20)

33,000 ft-lb/min/hp

■ Example 2.103
Problem : A pump must deliver 1210 gpm to a total head of 130 ft. What is the
required water horsepower?

Solution :

1210 gpm × 130 ft × 8.34 lb /gal

Required horsepower = = 40 whp

33,000 ft-lb/min/hp