Centrifugal Pumps Design and Application 2nd ed - Val S. Lobanoff, Robert R. Ross (Butterworth-Heinemann, 1992)

20 Centrifugal Pumps: Design and Application
with the square of their size. This is easily understood if we realize that
the peripheral velocities, which are the product of impeller diameter and
RPM, will be the same for the two pumps if the diameter increase is inversely
proportional to the RPM increase. The head, being proportional
to the square of the peripheral velocity, will also be the same. If the velocities
are the same, the capacities will be proportional to the areas, i.e.
to the square of the linear dimensions.
As a corollary, the linear dimensions of similar pumps working against
the same head will change in direct proportion to the ratio of the square
root of their capacities, and the RPM in inverse proportion to the same
ratio, This permits selection of a model pump for testing as an alternative
to building a full-size prototype. The selected model must agree with the
following relationship:
where D 1} Nj, HI, and 171, are model diameter, speed, head, and efficiency,
and D, N, H and 17, are prototype diameter, speed, head, and efficiency,
n will vary between zero and 0.26, depending on relative surface
roughness.
Other considerations in the selection of a model are:
1. Head of the model pump is normally the same as the prototype
head. However, successful model testing has been conducted with
model head as low as 80% prototype head.
2. Minimum diameter of the model impeller should be 12 in.
3. Model speed should be such that the specific speed remains the
same as that of the prototype.
4. For meaningful evaluation prototype pump and model pump must
be geometrically similar and flow through both kinematically similar.
5. Suction requirements of model and prototype should give the same
value of sigma (see Chapter 9).
An example of model selection is described in detail in the Hydraulic
Institutes Standards, 14th Edition.