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LaTeX Math Block
anchorq_pump
alignmentleft
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
anchorQ056T
alignmentleft
\eta(q) = 4 \, \eta_{\rm max} \cdot q/q_{\rm max} \cdot ( 1 -  q/q_{\rm max})

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where

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

maximum pressure gain that pump can exert over the input pressure 

LaTeX Math Inline
bodyp_{\rm in}

LaTeX Math Inline
bodyq_{\rm max}

maximum flowrate that pump can produce

LaTeX Math Inline
bodyk_f

curvature of the pump characteristics (dimensionless)

LaTeX Math Inline
body\eta

pump efficiency

LaTeX Math Inline
body\eta_{\rm max}

maximum pump efficiency

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