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Centrifugal pumps generally obey what are
known as the pump laws. These laws state that the flow
rate or capacity is directly proportional to the pump speed;
the discharge head is directly proportional
to the square of the pump speed; and the power required by
the pump motor is directly
proportional to the cube of the pump speed. These laws are
summarized in the following equations. 
Using these proportionalities, it is possible
to develop equations relating the condition at one speed
to those at a different speed. 
Example: Pump Laws A cooling water pump is operating at a speed
of 1800 rpm. Its flow rate is 400 gpm at a
head of 48 ft. The power of the pump is 45 kW. Determine the
pump flow rate, head, and
power requirements if the pump speed is increased to 3600
rpm. 
It is possible to develop the characteristic
curve for the new speed of a pump based on the curve for
its original speed. The technique is to take several points
on the original curve and apply the pump
laws to determine the new head and flow at the new speed. The
pump head versus flow rate
curve that results from a change in pump speed is graphically
illustrated in Figure 8. 
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