Page 208 - Centrifugal Pumps Design and Application

182 Centrifugal Pumps: Design and Application

Then, if the rotational speed is changed by some factor x, we have:

So we see that specific speed is unchanged with change in rotational
speed; head and flow change in such a way as to keep specific speed con-
stant,
Mathematically, the specific speed expression is seen to vary from zero
at zero flow or shutoff, to infinity at zero head or cutoff. By definition,
specific speed has meaning only at the best efficiency point or flow rate
at which maximum efficiency occurs. Then, the head expression can be
expanded to read

Flow is proportional to the product of tip speed and discharge throat area
according to the following expression

In the flow expression, it is seen that the flow coefficient, $, is simply
the ratio of discharge throat velocity to impeller tip speed. It is at first
surprising to note that <£ = 1.3 at cutoff indicates that throat velocity is
outrunning the impeller tip speed by 30%. This is in reality the case, and
is explained by conversion of the bowl static head into velocity head so
that total head, less losses, appears as velocity head in the discharge
throat.
Further perception of the meaning of specific speed for RE. pumps is
desirable. To provide this insight, we simply insert the head and flow
expressions of Equations 11-7 and 11-8 involving impeller diameter,
throat diameter and speed into the specific speed expression

which yields an alternate expression for specific speed: