The most general Pump model is given as a function of volumetric flowrate of the intake p_{\rm in} and discharge pressure p_{\rm out}:
(1) | q = q(p_{\rm out}, p_{\rm in}) |
The electrical power consumption \displaystyle W = \frac{dE}{dt} is given by:
(2) | W(q,p) = \eta(q) \cdot q \cdot (p_{\rm out}-p_{\rm in}) |
where
\eta | pump efficiency |
In most practical cases the pump model (1)depends on the diffference between intake and discharge pressure p_{\rm out} - p_{\rm in} and called pump characteristic curve (see Fig. 1):
(3) | q = q(p_{\rm out} - p_{\rm in}) |
Fig. 1. Pump Characteristic Curve |
A popular pump proxy model is given by quadratic equation:
(4) | 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- p_{\rm in})/p_{\rm max}) \ } \right] |
(5) | \eta(q) = 4 \, \eta_{\rm max} \cdot q/q_{\rm max} \cdot ( 1 - q/q_{\rm max}) |
where
p_{\rm max} | maximum pressure gain that pump can exert over the input pressure p_{\rm in} |
---|---|
q_{\rm max} | maximum flowrate that pump can produce |
k_f | curvature of the pump characteristics (dimensionless) |
\eta | pump efficiency |
\eta_{\rm max} | maximum pump efficiency |
See also
Natural Science / Engineering / Device / Pump
Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation (PFS)