Effect of Speed Variation

Head-Discharge characteristic of a given pump is always referred to a constant speed. If such characteristic at one speed is know, it is possible to predict the characteristic at other speeds by using the principle of similarity. Let A, B, C are three points on the characteristic curve (Fig. 37.4) at speed .

For points A, B and C , the corresponding heads and flows at a new speed are found as follows:

From the equality of term [Eq. (3.1)] gives

	(since for a given pump D is constant)	(37.6)

and similarly, equality of term [Eq. (3.1)] gives

	(37.7)

Applying Eqs. (37.6) and (37.7) to points A, B and C the corresponding points and are found and then the characteristic curve can be drawn at the new speed

Thus,

and

which gives

or		(37.8)

Equation (37.8) implies that all corresponding or similar points on Head-Discharge characteristic curves at different speeds lie on a parabola passing through the origin. If the static lift becomes zero, then the curve for system characteristic and the locus of similar operating points will be the same parabola passing through the origin. This means that, in case of zero static life, for an operating point at speed , it is only necessary to apply the similarity laws directly to find the corresponding operating point at the new speed since it will lie on the system curve itself (Figure 37.4).