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
fluid density as a function of fluid pressure |
The electrical power consumption is given by:
W = \eta(q) \cdot q \cdot (p_{\rm out}-p_{\rm in}) |
where
pump efficiency |
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}) |
Fig. 1. Example of Pump Characteristic Curve. |
A popular pump proxy model is given by the quadratic equation:
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\eta(q) = 4 \, \eta_{\rm max} \cdot q/q_{\rm max} \cdot ( 1 - q/q_{\rm max}) |
where
maximum pressure gain that pump can exert over the input pressure | |
maximum flowrate that pump can produce | |
total hydraulic pump friction (dimensionless) | |
pump efficiency | |
maximum pump efficiency |
Many pumps can be normally adjusted by the variation of the working frequency which affects the maximum pump flowrate and maximum pressure gain as:
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where
maximum intake flowrate at the working frequency | maximum pressure gain at the working frequency | adjusted working frequency | |||
maximum intake flowrate at the nominal frequency | maximum pressure gain at the nominal frequency | nominal frequency |
Natural Science / Engineering / Device / Pump
Physics / Fluid Dynamics / Pipe Flow Dynamics / Pipe Flow Simulation (PFS)
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