The most general Pump model is given as:

(1)	$\begin{array}{l}\displaystyle p_{\rm out}= F(q, p_{\rm in})\end{array}$

In many practical cases it simplifies (see Fig. 1) to:

(2)	$\begin{array}{l}\displaystyle p_{\rm out}= ( p_{\rm max} - p_{\rm in}) * F(q/qmax)\end{array}$

The pump characteristic curve $\begin{array}{l}F(x)\end{array}$ can be usually approximated by quadratic equation:

(3)	$\begin{array}{l}\displaystyle F(x)= (1- x^m)^n, \, m > n\end{array}$

and usually $\begin{array}{l}n=0.5\end{array}$ and $\begin{array}{l}m=1\end{array}$ : $\begin{array}{l}F(x)= \sqrt{1- x}\end{array}$ .

Fig. 1. Pump Characteristic Curve

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See also