Pump Curve and System Curve Calculator: Operating Point

Where a pump runs: the crossing of its head-flow curve with the system curve.

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

A centrifugal pump delivers less head as the flow rises: that is its curve, from the pump maker. The pipework it feeds needs head to lift the liquid (the static head) plus head to overcome friction, which grows with the square of the flow: that is the system curve. The pump runs where the two curves cross.

Enter at least three points read from the pump curve, the static head, and one flow at which you know the friction head (from the pipe pressure drop calculator). The calculator fits a smooth curve through your points, finds the crossing, and draws both curves. A throttled valve raises the system curve and moves the point to a lower flow.

Formulas used

  • H_{pump}(Q) = a + bQ + cQ^2
  • H_{system}(Q) = H_{static} + K Q^2
  • H_{pump}(Q) = H_{system}(Q)

Worked example

With the default numbers in the calculator above:

  1. Pump curve fitted through your points: H = 40 + 0 Q + -0.02 Q²
  2. System friction coefficient: 0.02
  3. System curve: H = 10 + 0.02 Q²
  4. Operating flow: 27.39 (flow units)
  5. Operating head: 25 (head units)

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

Common questions

Where do I get the pump curve?

From the pump maker's data sheet or catalogue, for the impeller diameter and speed you have.

Why does the flow fall when I close a valve?

The valve adds friction, so the system curve gets steeper and crosses the pump curve at a lower flow.

What else should I check at the operating point?

The pump efficiency, the power and the NPSH required at that flow. The point should be near the best efficiency point.

Related calculators

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

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