Thermodynamic Equation

We are constantly asked about the thermodynamic equation. In this short article, we will share with you, the basic concepts of the equation.


The thermodynamic method measures pump efficiency directly. It has advantages over other comparable technologies such as ultrasonic and electromagnetic flow measurement in that the thermodynamic sensors can be fitted to any size pipe diameter with no requirement for straight lengths of pipe.


The pump equation (1) can be used in either the thermodynamic or conventional measurement techniques.


ηp ηm.Pkw  =   ρ.g.QH      (1)


ηp =

Pump efficiency

ρ =

Fluid density

ηm =

Motor efficiency

g =

acceleration due to gravity

Pkw =

Electrical power to the motor

Q =

Flow rate



H =

Pump head


In the thermodynamic method, the pump efficiency, ηp, is determined from changes in enthalpy (internal energy per unit mass), using temperature and pressure probes. The only unknow parameter in equation (1) is the flow rate Q, since all other parameters can be measured using site sensors.


The flow rate, Q, is determined from equation (1):


Q =        (2)


Knowing parameters H, Pkw, ηp, and Q allows the pump performance curve to be recreated onsite under normal operating conditions.


Pump Efficiency is measured directly using changes in temperature and pressure measurements across the pump. The equation describing this process is outlined below.



ηp =




ηp =           (3)


Equation (3) shows a very simplified thermodynamic equation for the measurement of pump efficiency



Ko & Ks are constants


The flow rate Q is cancelled from equation (3) leaving only pump efficiency as a calculated parameter.


Knowing pump efficiency, pump head and power to the motor, it is now possible to calculate pump flow rate using equation (2).





We hope this article clarifies the basic concepts of the thermodynamic equations. The actual equations run over 5 x A4 pages.