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

\dot m  = M(p_{\rm out}, p_{\rm in})

It's often presented in terms of intake volumetric flowrate:

q = q_{in} = \frac{\dot m}{\rho(p_{in})}  = \frac{M(p_{\rm out}, p_{\rm in})}{\rho(p_{in})}

where

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 with 3 inputs ():

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

Real pumps have non-constant friction coefficient which often modelled as a 3^rd order polynomial and the overall real-pump model taking 6-inputs.

Many pumps can be normally adjusted by the variation of the working frequency which affects the maximum pump flowrate and maximum pressure gain as:

q_{\rm max} = q^*_{\rm max}  \cdot \frac{f}{f^*}

\delta p_{\rm max} = \delta p^*_{\rm max}  \cdot \left( \frac{f}{f^*} \right)^2

where

See also

Natural Science / Engineering / Device / Pump

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

References