Tips & Tricks for Chemical Engineers
Pump manufacturers provide Head versus Flow curve for various pump models. This article shows how to convert it into a 2nd order polynomial using Excel's LINEST function. This curve can then be used to predict pump head curve at diffent impellor diameter and pump speed based on Affinity Laws.
Pump head versus flow curve is available for impellor diameter 210 mm. Estimate modified head vs flow curve at impellor diameter 250 mm.
|Flow (m³/h)||Head (m)|
LINEST function in Excel is used to do 2nd order polynomial curve fitting to get constants a0,a1 and a2.
Head(x) = a2.x² + a1.x + a0
LINEST function formula is copied in an empty cell e.g G8.
After copying the formula, select the range G8:I10 starting with formula cell. Press F2, and then press CTRL+SHIFT+ENTER. Resulting array G8, H8 & I8 provides value for a2,a1 & a0.
The Affinity Laws for centrifugal pumps are used to determine the performance of a pump at different impeller diameters or speeds. Head vs flow curve are related by Affinity laws for impeller diameter change as follows:
Head vs flow curve for speed change are related as follows:
Q2/Q1 = D2/D1 = r
H2/H1 = (D2 / D1)² = r²
Q2/Q1 = N2/N1 = R
H2/H1 = (N2 / N1)² = R²
Modified head vs flow curve is obtained as
Head'(x) = a2.x² + a1.r.x + a0.r²
Head'(x) = a2.x² + a1.R.x + a0.R²
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