Application of specific speed in new pump design

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

A pump manufacturer was requested to submit a proposal for the design,
manufacture, testing, and installation of  four identical single stage pumps. Each
pump will be rated for 95,000 gallons per minute (GPM) and 1500 feet of head, at
1780 RPM.

The manufacturer has not yet built a pump of this size. Given the short time frame
with which to submit a proposal, there was no sufficient time to do an initial
design concept, predict and simulate a predicted performance, and do some CFD
analysis to validate the hydraulic design.

So how did it respond to the inquiry? By size-factoring, or modelling, an existing
and proven pump design based on the concept of specific speed. The application
calls for pumps with a specific speed (Ns) of:

Ns = [ 1,780 x (95,000)^0.50] / [ (1,500)^0.75] = 2,276

Next, the manufacturer checked its existing same type product line for the biggest
pump it has ever built whose specific speed is within + or - minus 5% of the
calculated Ns (or, Ns of 2160 to 2390.) It found a smaller but similar pump type, a
28x30x30 pump, with a specific speed of 2200. Using this pump size as a model,
and applying the principles of size-factoring, it was able to offer a newly designed
pump, a size 40x40x42, complete with predicted performance, preliminary linear
dimensions, and estimated component weights.

The procedures for size-factoring will not be discussed in this article but is