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A popular pump proxy model is given by quadratic equation:
| LaTeX Math Block |
|---|
| anchor | q_pump |
|---|
| alignment | 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 |
|---|
| alignment | 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 ] |
|
| LaTeX Math Block |
|---|
|
\eta(q) = 4 \, \eta_{\rm max} \cdot q/q_{\rm max} \cdot ( 1 - q/q_{\rm max}) |
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