Horsepower refers to the amount of energy that must be supplied to operate a pump. An understanding of how to calculate horsepower and how to read and interpret the horsepower data shown on the pump performance curve is necessary to choose the correct size of driver for the pump. There are several commonly designated expressions for horsepower. Water horsepower (WHP) refers to the output of the pump handling a liquid of a given specific gravity, with a given flow and head. The formula for WHP, in USCS units, is

where Q is the flow rate in gpm, H is the TH in feet, and SG is the specific gravity. The constant 3960 is used when the units are as described in Equation 2.12. The constant is obtained by dividing 33,000 (the number of ft-lb/min in one horsepower) by 8.34 (the number of pounds per gallon of water). If Q is given in cubic feet per second, Equation becomes:

Using SI units, the power WHP in watts is given by

**WHP = 9797 × Q × H × SG**

where Q is the flow rate (in m3/s) and H is the TH (in m).

If Q is given in liters per second, Equation becomes

**WHP = 9.797 × Q × H × SG**

Brake horsepower (BHP) is the actual amount of power that must be supplied to the pump to obtain a particular flow and head. It is the input power to the pump, or the required output power from the driver. The formula for BHP, using the same units as Equation , is

where η is the pump efficiency.

Other equations for BHP can be written using other USCS or SI units, by taking Equations , and adding pump efficiency, η, in the denominator, as is done in Equation above

BHP is indicated on the pump performance curve as a function of pump capacity, and is used to select an appropriate size of motor (or other driver type) for the pump. Note that the BHP is a function of specific gravity. If the pumped liquid’s specific gravity is other than 1.0, the BHP curve should be adjusted accordingly, either by the manufacturer or by the engineer making the motor selection.

Still another horsepower term that is used in studies and discussions of pumping systems is wire-to-water horsepower. This term describes the required power input into the driver, and is found by dividing BHP by the motor efficiency. In the case of a pump using a variable-speed device or other auxiliary driving equipment such as a gear box, BHP is divided by the combined efficiency of all of the driver components to obtain the wire-to water horsepower.

**BHP **is greater than **WHP** because of the fact that a pump is not a perfectly efficient machine. There are actually four factors that cause a centrifugal pump to be less than perfectly efficient, as described below.

**A. Hydraulic Losses**

This term is a summary of internal losses in the impeller and volute or diffuser due to friction in the walls of the liquid passageways and the continual change of direction and recirculation of the liquid as it moves through the pump.

**B. Volumetric Losses**

This term refers to the leakage of a usually small amount of liquid from the discharge side of a centrifugal pump to the suction side (the equivalent of slip in a positive displacement pump). The liquid leaks past the wear rings in a closed impeller pump and past the front edges of the vanes in an open impeller pump. (Refer to Chapter 4, Section II.A) Other volumetric losses occur between stages of multistage pumps, past some thrust balancing devices (which are discussed in Chapter 4, Section II), and through leak age at seals and packing. Volumetric losses increase as internal clearances are opened up due to wear and erosion in the pump. This causes the pump to run less efficiently and increases BHP, as well as reducing flow and total head that the pump produces.

**C. Mechanical Losses**

This term refers to the frictional losses that occur in the moving parts of pumps that are in contact (bearings and packing or seals).

**D**.** Disk Friction Losses**

If the pump impeller is thought of as a rotating disk, rotating in very close proximity to a fixed disk (the casing), there is a frictional resistance to this rotation known as disk friction.