"

# The Thermodynamic Method

Accurate pump efficiency measurements are necessary to determine the cost-effectiveness of performance-based maintenance, and for pump scheduling.

On-site constraints make it difficult to accurately measure pump efficiency under installed conditions by the same method that pump manufacturers traditionally use for works tests. For example, in the traditional technique, pump efficiency is calculated from the Pump Equation, requiring measurement of flow, head, and power. Of these parameters, flow is the most difficult to determine accurately. Many pumps do not have accurate, individual flow meters, which are high cost items, especially for larger diameter pipes, and can be difficult or impossible to install, calibrate, and maintain. Flow meter accuracy can be quite variable, depending on the pump's operating point and other factors, such as build-up of debris in pipes or on sensors.

The advent of the thermodynamic method has provided a solution to this problem. Now accurate measurements can be made on installed pumps. This is for several reasons.

Firstly, the thermodynamic method does not need a conventional flow meter.

Secondly, the thermodynamic technique requires measurement of only two parameters, temperature and pressure, to determine pump efficiency.

Thirdly, energy losses are effectively being measured. A 5% error in the measurement of losses (typically 20%) leads to a corresponding error in the pump efficiency measurement of 1%, for a pump operating at 80% efficiency. However, with the traditional technique, and 5% instrumentation accuracy, the error in the pump efficiency measurement would also be 5%.

And of course, by measuring power, the true mass flow through the pump may be determined, and the P22 Pump Monitor becomes an accurate flow meter. The simplified methodology is given below.

## Measurement of pump efficiency

 n = EH / EM for pumps where EH is the hydraulic energy per unit mass of fluid EM is the mechanical energy per unit mass of fluid

EH = dp / ρ   and   EM = a . dp + cp . dt
dp is the differential pressure
dt is the differential temperature
These are measured by the temperature and pressure probes.

cp is the specific heat capacity
a is the isothermal coefficient
ρ is the fluid density
These are known for the fluid (e.g. ISO 5198 Tables for water)

## Measurement of flow rate

The Pump Equation is
PW . ME . n (power imparted to fluid) = q . ρ . g . H (hydraulic power)

In international units:

 PW electrical power to the motor (kW) ME motor and drive efficiency n hydraulic efficiency q flow rate, in m3/s ρ fluid density, in kg/ m3 g acceleration due to gravity, in m/s2 H pump total head, in m

Rearranging the Pump Equation to obtain q:
q = n . ME . PW / ρ . g . H