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The most general Pump model is given as (see Fig. 1)a function of volumetric flowrate of the intake

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body--uriencoded--p_%7B\rm in%7D
 and discharge pressure 
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body--uriencoded--p_%7B\rm out%7D
:

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anchorpump
alignmentleft
q = q(p_{\rm out}, p_{\rm in})

where 

LaTeX Math Inline
body--uriencoded--F(q, p_%7B\rm in%7D)
 is called pump characteristic curve.

x

The power consumpotion is given by:

...

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body\eta

pump efficiency


In most practical cases pump characteristic curve has negligible dependence on intake cases  the pump  model 

LaTeX Math Block Reference
anchorpump
depends on the diffference between  intake and discharge pressure 
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body--uriencoded--p_%7B\rm out%7D - p_%7B\rm in%7D
 and called pump characteristic curve (see Fig. 1):

LaTeX Math Block
anchorKD0ZN
alignmentleft
p_{\rm out} q = q(p_{\rm inout} +  \delta- p_{\rm max} \cdot \cdot F(q/q_{\rm max}) 

...

LaTeX Math Inline
bodyF(x =0) = 0

...

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bodyF(x =1) = 1

...

in})


The pump characteristic curve 

LaTeX Math Inline
bodyF(x)
 can be usually approximated by the following equation:

...