Page 209 - Centrifugal Pumps Design and Application

High Speed Pumps 183

This expression may be described as the geometric form of specific speed
and shows first that specific speed is independent of rotational speed, and
secondly that specific speed is basically defined by the ratio of emission
throat diameter to impeller diameter, i.e., is related to the ratio of flow
capacity to head capacity of the pump stage. Since the head and flow co-
efficients of the P.E. pump do not range broadly, the specific speed of a
given P.E. pump geometry is expressed approximately as:

Accumulated experience reflecting the efficiency potential of well-de-
signed pumps versus specific speed are shown in Chapter 2. Impeller ge-
ometry trends toward relatively large diameters and small flow passage-
ways as specific speed decreases.
A first observation is that pumps with the highest efficiency potential
have a specific speed in the neighborhood of 2,000, and that efficiency
starts to drop substantially for specific speeds below 1,000. The funda-
mental reason for lowered efficiency potential at low specific speed lies
in the disproportionate losses incurred in low specific speed design, par-
ticularly disk friction and flow losses. Disc friction, neglecting a modest
Reynold's number modifier, is well known to vary as the cube of speed
and the fifth power of diameter. Pump power is proportional to the prod-
uct of pump head and flow or the cube of impeller diameter and speed,
3
(DN) . Then, without pretense of mathematical completeness, the impact
of disk friction on efficiency can be expressed as follows:

This expression illustrates the disproportionate influence of disk friction
on efficiency for low specific speed pumps which tend toward large di-
ameter impellers. Further, for a given head objective, design choices are
such that the product of DN is a constant, so indicating the general advan-
tage inherent in selection of high speed in return for a smaller impeller
diameter,
A second observation is at first disappointing in that a family of dimen-
sional parametric curves indicative of pump size appear on the otherwise
dimensionless N s—1? plot. Small pumps are always less efficient than hy-
draulically similar large pumps. The prime reason for this scale or size
effect is mostly easily explained by a pipe flow analogy: skin friction
arises from the inner circumference of the pipe and so is proportional to