 # Temperature rise in centrifugal pumps

Section summary
1. Definition
2. Calculation
3. Use

## 1. Definition

When liquid is going through a centrifugal pump, most of the energy is transferred as a pressure - head - increase, but a small part of it is dissipated and heats up the fluid. It is usually not a problem at the pump design through since the flow through the pump is high, but the temperature increase can be higher at low flow and will definitively create problem at no flow. The temperature increase at no / low flow will also allow to calculate the minimal flow required to avoid thermal problems with a centrifugal pump.

## 2. Calculation

How to calculate the rate of temperature rise in a centrifugal pump ?

#### 2.1 Temperature rise in centrifugal pump at no flow

In US units With :
ΔTr = temperature increase in pump (°F/min)
Pso = pump power at no flow (BHP)
W1 = weight of liquid in the pump (lb)
Cp = specific heat of the liquid in the pump (BTU/lb/°F)

In SI units - adapted from With :
ΔTr = temperature increase in pump (°c/min)
Pso = pump power at no flow (kW)
W1 = weight of liquid in the pump (kg)
Cp = specific heat of the liquid in the pump (kJ/kg/°c)

#### 2.2 Temperature rise in centrifugal pump at low flow

In US units With :
ΔTr = temperature increase in pump (°F/min)
H = pump head at no flow, low flow at the corresponding efficiency η (ft)
Cp = specific heat of the liquid in the pump (BTU/lb/°F)
η = efficiency of the pump at low flow- decimal value

In SI units - adapted from With :
ΔTr = temperature increase in pump (°c/min)
H = pump head at no flow, low flow at the corresponding efficiency η (m)
Cp = specific heat of the liquid in the pump (kJ/kg/°c)
η = efficiency of the pump at low flow- decimal value

#### 2.3 Temperature rise of the liquid in centrifugal pump in normal operation

In normal operation, part of the energy transferred from the shaft is lost in heat, the other behind converted as pressure for the liquid. The formula below is proposed to estimate by how much the liquid is heated up when passing through the pump. With :
ΔTliquid = temperature increase of the liquid through the pump (°c)
Qshaft = shaft power at the corresponding efficiency η (kW)
m = throughput of liquid through the pump (kg/s)
Cp = specific heat of the liquid in the pump (kJ/kg/°c)
η = efficiency of the pump at low flow- decimal value

## 3. Use of temperature rise in pumps

The calculation of the temperature increase at low flow should be used to calculate the minimal flow that needs to be ensured through a centrifugal pump, often thanks to a bypass line, in order to make sure the heat is not damaging the pump.

Source

Applied process design volume 1, Ludwig, Gulf Professional, page 207