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LaTeX Math Block
anchorpump_m
alignmentleft
\dot m  = M(p_{\rm out}, p_{\rm in})

It's often presented in terms of intake volumetric flowrate:

LaTeX Math Block
anchorY440Npump_q
alignmentleft
q = q_{in} = \frac{\dot m}{\rho(p_{in})}  = \frac{M(p_{\rm out}, p_{\rm in})}{\rho(p_{in})}

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In most practical cases  the pump model 

LaTeX Math Block Reference
anchorpump_q
 depends on the difference between intake and discharge pressure 
LaTeX Math Inline
body--uriencoded--p_%7B\rm out%7D - p_%7B\rm in%7D
 and called Pump Characteristic Curve (see Fig. 1):

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