Pump and Fan Affinity Laws Calculator

How the flow, the head or pressure and the power of a pump or fan change with speed and impeller size.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

The affinity laws describe a pump or fan running at a different speed. Flow is proportional to speed. Head (or pressure) is proportional to speed squared. Power is proportional to speed cubed. So a small increase in speed needs a much bigger increase in power: 10 percent more speed means about 33 percent more power.

For geometrically similar machines the diameter also enters: flow with diameter cubed, head with diameter squared and power with diameter to the fifth. For a fan the pressure and power also scale with the air density.

Formulas used

  • Q_2 = Q_1\,\frac{N_2}{N_1}
  • H_2 = H_1\left(\frac{N_2}{N_1}\right)^2
  • P_2 = P_1\left(\frac{N_2}{N_1}\right)^3

Worked example

With the default numbers in the calculator above:

  1. Speed ratio and diameter ratio: 1.207 and 1
  2. New flow: 60.34
  3. New head or pressure: 43.7
  4. New power: 26.37

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Why does a small speed rise need so much more power?

Power goes with the cube of speed. 10 percent more speed gives 1.1 cubed, about 1.33 times the power.

How much energy does a slower pump save?

A lot. Running at 80 percent speed uses about half the power (0.8 cubed is 0.51), which is why variable speed drives save energy.

Do the laws hold for a trimmed impeller?

Only roughly. Use the pump maker's trimmed curve for an exact answer.

Related calculators

Further reading: White, Fluid Mechanics; Munson, Young and Okiishi, Fundamentals of Fluid Mechanics; Crane Technical Paper 410.

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