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A popular pump proxy model is given by quadratic equation:

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anchorq_pump
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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]

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


where

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bodyp_{\rm max}

maximum pressure gain that pump can exert over the input pressure 

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bodyp_{\rm in}

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bodyq_{\rm max}

maximum flowrate that pump can produce

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bodyk_f

curvature of the pump characteristics (dimensionless)

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body\eta

pump efficiency

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body\eta_{\rm max}

maximum pump efficiency

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bodyW

electrical consumption per unit time


See also

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Natural Science / Engineering / Device / Pump

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