Application of specific speed in pump selection

There are many ways the concept of specific speed can be applied in
pump selection. Here is one example:

A chemical plant has a process requirement for 3,000 gallons per minute (GPM),
and 900 feet head. It was estimated that a pump of this size, operating at 3560
RPM, will require a 1,000 HP motor driver based on an assumed pump efficiency
of 80%. The plant has two spare 500 HP motors and control panels that they want
to use so they would like to buy two smaller pumps. (Besides, the lead time for
buying a new 1,000 HP motor is well beyond their start-up schedule.)

How should one go about selecting the two pumps on the basis of these facts
alone, assuming all other factors have equal weight and are to be ignored?

SOLUTION:

The two pumps can be selected to operate either is series, or in parallel
connection.

For pumps to operate in series, each pump will be rated for 3,000 GPM and 450
feet head. The pump specific speed is:

Ns = [ 3,560 x (3,000)^0.50] / [ (450)^0.75] = 1996

For pumps to operate in parallel, each pump will be rated for 1,500 GPM and 900
feet head. The pump specific speed is:

Ns = [ 3,560 x (1,500)^0.50] / [ (900)^0.75] = 839

For simplicity, CENTRIFUGAL-PUMP.ORG uses the U.S. system of units in the calculations
through-out this web site.

Many charts have been published for estimating the efficiency of pumps based on
their flow rates and specific speed. It was observed that no matter how
well-designed the pumps are their peak efficiency is still correlated to their
hydraulic size. (Some would call it the hydrodynamic size.)

Based on using one of those efficiency charts [ * ], it is estimated that a pump with
a flow rate of 3000 GPM and NS of 1996 would have an efficiency of 86%. In
comparison, a pump with a flow rate of 1500 GPM and Ns of 839 would have an
efficiency of 77%  - a significant difference of 9 points.

Expectedly, different efficiency charts will show different values of estimated
efficiencies but the point to keep in mind is the significant relative difference in the
efficiencies.