## Centrifugal Pump Curve Fitting

Pump manufacturers provide Head versus Flow curve for various
pump models. This article shows how to convert it into a 2^{nd}
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 2^{nd} 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.

`= 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`

Resources

- Spreadsheet for Centrifugal Pump Curve Fitting