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## THE THERMODYNAMIC METHOD

For both thermodynamic and ‘conventional’ measurement techniques, pump parameters are summarised by the following expression (the Pump Equation):

η.ME.PW = q.ρ.g.H ..........(equation 1)

(S.I. units are used in the following)

The left-hand side of equation (1) is the electrical power (watts, or joules per second) applied to the fluid, after losses in the motor drive and pump: -

η is the pump efficiency (expressed as a fraction)

ME is the motor and drive efficiency (expressed as a fraction)

PW is the electrical power to the motor (watts)

The right-hand side of equation 1 is the energy per second imparted to the fluid, and also has the units of watts (joules per second): -

q is flow rate, in m³/s

ρ is the fluid density, in kg/ m³, and is a function of temperature and pressure

g is the acceleration due to gravity, in m/s²

H is pump total head, in m

In the thermodynamic method, the pump efficiency, η, is determined from changes in enthalpy (internal energy per unit mass), using temperature and pressure probes. The calibration of these probes can be readily checked on-site. The uncertainty in η is primarily due to the uncertainty in differential temperature measurements. This is minimised by Robertson Technology’s CoolTip™ dual sensor temperature probes.

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

q = η.ME.PW / (ρ.g.H)

Thus flow rate can be derived without the need for a separate flow meter.

###### MEASUREMENT OF PUMP EFFICIENCY

η = EH / EM for pumps    (for turbines, η = EM / EH)

where EH is the hydraulic energy per unit mass of fluid

and EM is the mechanical energy per unit mass of fluid

EH = dp / ρ and EM = a . dp + cp . dt

dp is the differential pressure, and

dt is the differential temperature

These parameters are measured by the temperature and pressure probes.

cp is the specific heat capacity, a is the isothermal coefficient, and ρ is the fluid density. These are known for the fluid (e.g. ISO 5198 Tables for water). For slurries, the fractions of liquids and solids must also be known. These can be calculated from the slurry and solids densities.

###### ADVANTAGES OF THE THERMODYNAMIC METHOD

Accurate measurements of both pump efficiency and flow rate can be made, without the need for a conventional flow meter.

The thermodynamic technique requires measurement of only two parameters, temperature and pressure, to determine pump efficiency. Due to the advances we have made in accurate and stable temperature measurement, the uncertainty in pump efficiency measurements is typically less than 1%. Decisions on pump refurbishment or system control can be taken with confidence.

System-related energy savings can be optimised by monitoring of pump combinations.

The equipment is easy to install, with minimum disruption to operations.

Calibration checks can be carried out on-site.