## Pi Ah Q

where

"Mechanical" f _ ^ _ ps P. Efficiency f Vm _ PS _ PS

Volumetric f _ Q dD

Approximate formulas for the three component efficiencies of Eq. 8 will be given further on. Their product yields the overall pump efficiency as defined in Eq. 5, and reflects the following division of the pump losses:

a. External drags on the rotating element due to i) bearings, ii) seals, and iii) fluid friction on the outside surfaces of the impeller shrouds—called "disk friction"; the total being PD _ PS — PI. Generally, the major component of PD is the disk friction, and the "mechanical efficiency" is that portion of the shaft power that is delivered to the fluid flowing through the impeller passages.

b. Hydraulic losses in the main flow passages of the pump; namely, inlet branch, impeller, diffuser or volute, return passages in multistage pumps, and outlet branch. The energy loss per unit mass is g^HL _ g(H, — AH), the ratio of output head AH to the input head Hi being the hydraulic efficiency. This is the major focus of the designer for typical centrifugal pump geometries (which are associated with normal "specific speeds"—to be defined later). The other two component efficiencies are then quite high and of relatively little consequence.

c. External leakages totaling QL leaking past the impeller and back into the inlet eye. This leakage has received its share of the full amount of power PI _ pg AH, (Q + QL) delivered to all the fluid (Q + QL) passing through the impeller. This leakage power is PL _ pg AHH, Ql, which is lost as this fluid leaks back to the impeller inlet. The remaining fluid input power is thus (PI — PL) _ pg AHH, Q, the ratio of this power to the total (Pi) being the volumetric efficiency.

There are exceptions to this convenient model for dividing up pump losses. The main exception is that if the pump has an open impeller, that is, one without either or both shrouds, that portion of the total leakage QL disappears. The leakage now occurs across the blade tips and affects the main flow passage hydraulic losses. The volumetric efficiency is now higher, but the hydraulic efficiency is lower. In that case disk friction is still present, as the impeller still has to drag fluid along the adjacent stationary wall(s). Another exception—for closed impellers—is that disk friction is fundamentally an inefficient pumping action, the fluid being flung radially outward2; and this can result in a slight increase in pump head if the fluid on the outside of an impeller shroud or disk is pumped into the main flow downstream of the impeller.

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