## O

At above Q, and h = Constant, and gAH = hnyA (UVe) 1 AH « N2D2 U = flr gAH

Ps pQgAH h

Ps pn3r2

constant

Figure 7a is the result of following these similarity rules for a given pump that undergoes a change in speed from full speed to half speed without a change in size. The similar Q at half speed for a given Q at full speed is half that at full speed. At each such halfspeed Q-value, the head AH is accordingly one-fourth of its full-speed value and the efficiency h is unchanged. One can avoid replotting the characteristic curves in this manner for every change in speed (and size) by expressing them nondimensionally in terms of Qs, C, h, and Ps. They then all collapse on one another as illustrated in Figure 7b. Note that a change in pump geometry or shape of the hydraulic passageways destroys this similitude and necessarily produces a new set of curves—shaped differently but similar to each other.

Similitude enables the engineer to work from a single dimensionless set of performance curves for a given pump model. This is a practical but special case of the more general statement that pump performance as represented by efficiency, head, and power, is more generally expressed in terms of the complete physical equation as follows:

h, AH, Ps = fct's. (Q, r2, fl, p, v, NPSH, {2-ph}, {gp}, {S},{/i})

where {/) is the infinite set of lengths that defines the pump stage geometry. A common group of these lengths is illustrated in Figure 8. Dimensionlessly, Eq. 34 becomes h, C, Ps = fct's. (Qs, Re, t2, {2-£}, {fp}, {2}, {Gi})

where the dimensionless quantities containing flow rate, viscosity and NPSH are respectively defined as follows:

where and ## Survival Treasure

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