The most general Pump model is given as a function of volumetric flowrate of the intake  and discharge pressure :

q = q(p_{\rm out}, p_{\rm in})

The electrical power consumption   is given by:

W =  \eta(q) \cdot q \cdot (p_{\rm out}-p_{\rm in})

where

In most practical cases  the pump  model  depends on the difference between intake and discharge pressure  and called pump characteristic curve (see Fig. 1):

q = q(p_{\rm out} - p_{\rm in})

A popular pump proxy model is given by the quadratic equation:

q = \frac{q_{\rm max}}{2 \cdot k_f} \cdot \left[ -1 + k_f +  \sqrt{ (1 + k_f)^2 - 4 \cdot k_f \cdot (p_{\rm out}- p_{\rm in})/\delta p_{\rm max}) \ } \, \right]

p_{\rm out} = p_{\rm in} +  \delta p_{\rm max} \cdot \left[ 1+ 
(k_f -1 ) \cdot \frac{q}{q_{\rm max}} - k_f \cdot \left( \frac{q}{q_{\rm max}} \right)^2
 \right ]

\eta(q) = 4 \, \eta_{\rm max} \cdot q/q_{\rm max} \cdot ( 1 -  q/q_{\rm max})

where

The plunger pump and centrifugal pumps are normally adjusted by working frequency 

See also

Natural Science / Engineering / Device / Pump

Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation (PFS)

References