The most general Pump model is given as (see Fig. 1):

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

In most practical cases it has a linear dependance on incharge pressure $\begin{array}{l}p_{\rm in}\end{array}$ :

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

where $\begin{array}{l}F(x =0) = 0\end{array}$ and $\begin{array}{l}F(x =1) = 1\end{array}$ .

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

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

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

Fig. 1. Pump Characteristic Curve

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See also