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Internal efficiency

In accordance with DIN EN 12723:2000 the internal efficiency (ηi) of a centrifugal pump is the ratio between pump power output (PQ) and the pump input power (P) minus mechanical losses (PL.m).
Innerer_Wirkungsgrad_Formel_1

If the pump power output (PQ) is replaced by (P − PL.i − PL.m), then the following equation applies: See Fig. 1 Head


Innerer_Wirkungsgrad_Formel_2

The mechanical power losses mainly comprise the friction losses of pump bearings (e. g. plain bearings and rolling element bearings) and shaft seals. The following relationship exists between the internal efficiency (ηi), pump efficiency (η) and the mechanical efficiencym).
Innerer_Wirkungsgrad_Formel_3

Efficiency scale-ups usually relate to internal efficiencies. These can also be determined on the basis of an analysis of the internal losses (PL.i) of the centrifugal pump (see Head).

The power loss (PL.i) comprises:

All internal losses cause the fluid handled to heat up, resulting in a temperature difference (ΔT). The heat radiation through the pump casing can be ignored in this context.

Innerer_Wirkungsgrad_Formel_4

g      Acceleration due to gravity in m/s2
H      Head in m
c      Specific heat capacity in J ∙ (kg · K)-1
ΔT   Temperature difference in K or °C

If the fluid is transported through the pump several times in succession as is the case in test facility circuits (see Pump test facility), the useful power output converted into heat in the circuit (e. g. in the throttling element or in the piping) is added to the heat developed inside the pump from one cycle to the next, meaning that cooling may be required.