EXERCISE 2 Power supplied to a pump N depends on the dischar

EXERCISE 2: Power supplied to a pump, N, depends on the discharge, Q, the pump head, HP, and the specific weight of the fluid. Find the expression for the power by dimensional analysis.

Solution

The power gained by the fluid from a pump or fan can be expressed as:

P = m w          (1)

where

P = power (W)

m = mass flow rate (kg/s)

w = specific work (Nm/kg, J/kg)

Specific Work

Specific work - w - can be expressed:

w = g h           (2)

where

h = head (m)

g = acceleration of gravity (9.81 m/s²)

Mass Flow Rate

Mass flow rate - m - can be expressed:

m = Q      (3)

where

= density (kg/m³)

Q = volume flow rate (m³/s)

Combining (1), (2) and (3) the power gained by the fluid from a pump or fan can be expressed as:

P = Q g h       (4)

With specific weight expressed as:

= g          (5)