Use and application of Affinity Laws

Q - Is there a mathematical proof for affinity laws?

A -  Chapter 5 of the book Centrifugal and Axial Flow Pumps by A. J. Stepanoff
discusses the mathematical development of affinity laws. But there is no better
proof for affinity laws than the consistent pump test results conducted under
carefully controlled and monitored test laboratories confirming their validity.

Q - Other than for predicting the performance of a pump due to a change in
impeller diameter, or speed, is there another practical use for affinity laws?

A - Affinity laws can be used in modelling, or size factoring, an existing pump to
design a new size pump from scratch. But they should be applied only to pumps
of similar design. Example, using affinity laws to model, or size factor, a single
suction pump to design a new double suction pump will have inaccurate result -
they should be both of the same type.

Q - The affinity laws show the changes to both capacity and head for a given
change in impeller diameter. How are the affinity laws used to estimate the new
impeller diameter if I want to reduce the head only, say by 10%, if the capacity and
speed are to remain the same?

A -The answer is available by request. [ * ]

Q - We have a centrifugal pump driven by a diesel engine through a clutch and a
gearbox. During the summer months we want to increase its flow rate 10%, from
1000 GPM to 1100 GPM. Based on Affinity Laws we can increase the engine
speed 10%, from 800 RPM to 880 RPM, to get the 10% increase in flow rate. But
this will also increase the head 21%.

The pump is used for irrigation so we only want to increase its flow rate, and not
its head. Assuming the head is 30 feet, at what speed should we run the engine?

A - The answer is available by request . [ * ]