Fit Head-Flow Rate Data to a Pump Curve - Maple Help

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Fit Head-Flow Rate Data to a Pump Curve

Introduction

This application will fit experimental head-flow rate data to a polynomial pump curve.

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 > $\mathrm{flowData}≔\left[\begin{array}{cc}4& 15\\ 6& 14.5\\ 8& 13.75\\ 10& 12.70\\ 12& 11.25\\ 14& 9.5\end{array}\right]:$
 > $\mathrm{p1}≔\mathrm{plot}\left(\mathrm{flowData},\mathrm{style}=\mathrm{point},\mathrm{symbol}=\mathrm{solidcircle},\mathrm{symbolsize}=20,\mathrm{labels}=\left["Flow Rate \left(cfm\right)","Head \left(ft\right)"\right],\mathrm{labeldirections}=\left[\mathrm{horizontal},\mathrm{vertical}\right]\right)$

Curve Fitting

 > $f≔a-b\cdot {Q}^{2}:$
 > $\mathrm{bestFitCurve}≔\mathrm{LeastSquares}\left(\mathrm{flowData},Q,\mathrm{curve}=a-b\cdot {Q}^{2}\right)$
 ${\mathrm{bestFitCurve}}{≔}{15.6238973536488}{-}{0.0306535685645549}{}{{Q}}^{{2}}$ (3.1)
 > $\mathrm{p2}≔\mathrm{plot}\left(\mathrm{bestFitCurve},Q=4..14\right):$
 > $\mathrm{display}\left(\mathrm{p1},\mathrm{p2},\mathrm{axesfont}=\left[\mathrm{Arial}\right],\mathrm{labelfont}=\left[\mathrm{Arial}\right]\right)$
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