Application of specific speed in hydraulic re-rates

There are many ways the concept of specific speed can be applied in
hydraulic re-rates. Here is one example:

An engineering firm was doing a feasibility study on using a radial flow , 20x20x22
(*) pump, in a flood control system. The pump was originally rated for 20,000
gallons per minute (GPM), and 400 feet head, at 1780 RPM. The proposed new
rated conditions are 40,000 GPM, 200 feet head, using some existing motors.

(*) 20" suction nozzle  x 20" discharge nozzle x 22" maximum impeller diameter pump size.

The firm contacted the original vendor (A)  to study the feasibility of the hydraulic
re-rate. Engineers from vendor A reviewed the operating conditions, pulled out
some drawings, reviewed some test curves, and after two days came back with
the conclusion that the re-rate is not feasible.

Not satisfied with that answer, the firm contacted pump vendor B and made the
same inquiry. Within 15 minutes of receiving the inquiry its engineer come back
with the same conclusion that the re-rate is not doable.

Questions:

1. Why was the hydraulic re-rate not feasible?
2. Why did it take two days for vendor A, but only 15 minutes for vendor B, to arrive
at that conclusion?

The simple answers: specific speed! And, apparently, the engineer of vendor B
knows how to use that concept to respond quickly to its customer inquiry.

Let us analyze the situation and, for simplicity, let us assume that the pump
should be operating close to its best efficiency point (BEP) at both original and
proposed re-rate conditions.

Based on its original rated conditions, the pump specific speed would have been:

Ns = [1,780 x (20,000)^0.50] / [(400)^0.75] = 2,814

^ is used here as an exponential symbol.

This value of specific speed confirms that the pump is of radial flow design, even
if the actual NS deviates slightly from this value depending on the actual location
of its BEP.

To meet the re-rate conditions, the pump specific speed (Ns) should be:

Ns = [1,780 x (40,000)^0.50] / [(200)^0.75] = 6,694

Even if a slight deviation from this Ns value is allowed to account for the actual
location of its BEP, when re-rated, this Ns value indicates that it will require a
pump of mixed flow design to meet the re-rate conditions.

There is simply no way a radial flow pump can be modified to become one of a
mixed-flow design. The engineer from vendor A failed to realize this and wasted
valuable time to review and made some lay-outs on something whose result is
quite obvious to the engineer from vendor B.

It is, of course, very simplistic to turn down a potential business opportunity on
one factor alone so such conclusion should be validated in some other way. In
this situation, one way of validating it is to estimate the impeller diameter required
to meet both the original and the re-rate conditions.

The impeller diameter required to develop a certain head can be estimated
roughly from the equation:

D =  [ (3,377,200 x H) / (N)^2 ]^0.50

Where:

D = required impeller diameter, in inches
H = developed head, in feet
N = pump speed, in RPM

The derivation of this equation is available on request from www.centrifugal-pump.org.

For the original rated condition, the impeller diameter required to develop 400 feet

D =  [ (3,377,200 x 400) / (1,780)^2 ]^0.50 = 20.6"

This is approximately 93.6% of the 22" maximum impeller diameter (or,
20.6/22=0.936)

For the re-rate condition, the impeller diameter required to develop 200 feet head
is approximately:

D =  [ (3,377,200 x 200) / (1,780)^2 ]^0.50 = 14.6"

This is approximately 66.4% of the 22" maximum impeller diameter (or,
14.6/22=0.664)

The above figures indicate that, even assuming for the sake of discussion, the
pump could be converted from being a radial flow type into a mixed flow type, still
the impeller diameter required to meet the reduced head would fall below the
acceptable minimum diameter for the pump.

Rule-of-thumb by www.centrifugal-pump.org: Typical acceptable minimum
impeller diameter, as a percentage of maximum diameter, for various pump types
are: