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## Key

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A popular
pump proxy model is given by the quadratic equation with 3 inputs (

LaTeX Math Inline
body --uriencoded--\%7B q_%7B'rf max%7D, \delta p_%7B\rm max%7D, k_f \%7D
):

LaTeX Math Block
anchor q_pump left
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]
LaTeX Math Block
anchor q_pump left
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 ]

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LaTeX Math Inline
body --uriencoded--\delta p_%7B\rm max%7D

maximum pressure gain that pump can exert over the input pressure

LaTeX Math Inline
body p_{\rm in}

LaTeX Math Inline
body q_{\rm max}

maximum flowrate that pump can produce

LaTeX Math Inline
body k_f \in [0,1]

total hydraulic pump friction (dimensionless)

LaTeX Math Inline
body \eta

pump efficiency

LaTeX Math Inline
body \eta_{\rm max}

maximum pump efficiency

Real pumps have non-constant

LaTeX Math Inline
body k_f =k_f(q)
friction coefficient which often modelled as a 3rd 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:

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