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A popular pump proxy model is given by the quadratic equation with 3 inputs (| LaTeX Math Inline |
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| body | --uriencoded--\%7B q_%7B'rf max%7D, \delta p_%7B\rm max%7D, k_f \%7D |
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):
| LaTeX Math Block |
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| anchor | q_pump |
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| alignment | left |
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| 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 |
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| anchor | q_pump |
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| alignment | left |
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| 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 |
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| body | --uriencoded--\delta p_%7B\rm max%7D |
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| maximum pressure gain that pump can exert over the input pressure |
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| maximum flowrate that pump can produce |
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| total hydraulic pump friction (dimensionless) |
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| pump efficiency |
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| maximum pump efficiency |
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Real pumps have non-constant 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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