Centrifugal Pump Curve Fitting

Centrifugal Pump Curve Fitting

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 different impeller diameter and pump speed based on Affinity Laws.

Example
Pump head versus flow curve is available for impeller diameter 210 mm. Estimate modified head vs flow curve at impeller diameter 250 mm.

Flow (m³/h) Head (m)
4 15.00
6 14.50
8 13.75
10 12.70
12 11.25
14 9.50

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

centrifugal pump curve fitting

LINEST function formula is copied in an empty cell e.g G8.

 = LINEST(C10:C15,B10:B15^{1,2},TRUE,TRUE)

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.

Affinity Laws

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:

 Q2/Q1 = D2/D1 = r
 H2/H1 = (D2 / D1)² = r²

Head vs flow curve for speed change are related as follows:

 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

modified pump head curve

Download excel spreadsheet for Centrifugal Pump Curves

2 Replies to “Centrifugal Pump Curve Fitting”

  1. Thanks for going into the math behind finding the right head fitting for your centrifugal pump. It sounds like it is really important to know all of the variables that will be influencing your system like impeller size, flow, and head size. I’ll keep this in mind if I ever need to select the right centrifugal pump for any industrial systems I will develop.

  2. why not just enter the values for head and pressure, plot them and allow excel to do the curve fitting/ provide the equation for the best fit polynomial curve?

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