Volume Flow and Temperature Rise in Pumps- Calculate temperature rise in pumps

No pump is perfect with [I]100%[/I] efficiency. The energy lost in friction and hydraulic losses are transformed to heat - heating up the fluid transported through the pump.
[img]http://www.egpet.net/vb/images/imported/2011/07/4.png[/img]
The temperature rise can be calculated as
[INDENT] [I]dt = P[SUB]s[/SUB] (1 - μ) / c[SUB]p[/SUB] q ρ (1)[/I]
[I]where [/I]
[I]dt = temperature rise in the pump ([SUP]o[/SUP]C)[/I]
[I]q = volume flow through the pump (m[SUP]3[/SUP]/s)[/I]
[I]P[SUB]s[/SUB] = brake power (kW)[/I]
[I]c[SUB]p[/SUB] = specific heat capacity of the fluid (kJ/kg[SUP]o[/SUP]C)[/I]
[I]μ = pump efficiency[/I]
[I]ρ = fluid density (kg/m[SUP]3[/SUP])[/I][/INDENT]Typical relation between the centrifugal pump flow, efficiency and power consumption, is indicated in the figure below:
[img]http://www.egpet.net/vb/images/imported/2011/07/5.png[/img]
[h=3]Example - Temperature rise in water pump[/h] The temperature rise in a water pump working at [B]normal conditions[/B] with flow 6 m[SUP]3[/SUP]/h (0.0017 m[SUP]3[/SUP]/s), brake power 0.11 kW and pump efficiency of 28% (0.28), can be calculated as
[INDENT] [I]dt = (0.11 kW) (1 - 0.28) / (4.2 kJ/kg[SUP]o[/SUP]C) (0.0017 m[SUP]3[/SUP]/s) (1000 kg/m[SUP]3[/SUP]) [/I]
[I] = [U]0.011[/U][SUP] o[/SUP]C[/I][/INDENT]If the flow of the pump is reduced by throttling the discharge valve, the temperature rise through the pump will increase. If the flow is reduced to [I]2 m[SUP]3[/SUP]/h (0.00056 m[SUP]3[/SUP]/s)[/I], the brake power is slightly reduced to [I]0.095 kW[/I] and pump efficiency reduced to [I]15% (0.15)[/I], the temperature rise can be calculated as

[INDENT] [I]dt = (0.095 kW) (1 - 0.15) / (4.2 kJ/kg[SUP]o[/SUP]C) (0.00056 m[SUP]3[/SUP]/s) (1000 kg/m[SUP]3[/SUP]) [/I]
[I] = [U]0.035[/U][SUP] o[/SUP]C[/I][/INDENT]With the standard documentation provided by a manufacturer it should be possible to express the temperature rise as a function of volume flow as shown in the figure below:
[img]http://www.egpet.net/vb/images/imported/2011/07/6.png[/img]