Pump Head Calculator: Total Head, Power and NPSH from Gauge Readings

The total head a pump develops, worked out from the two gauge readings, with the power and the NPSH available at the suction flange.

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 head of a pump is the energy it adds to each newton of liquid. It is found by measuring the pressure at the suction flange and at the discharge flange and taking the difference, with two corrections that matter when the pipes are different sizes or the gauges are at different heights: the difference in height between the gauges, and the difference in the velocity heads V squared over 2g.

Because the head is measured between the two flanges, a lift or a flooded suction is already inside the readings. The textbook form of total head as suction head plus discharge head plus friction head is a way of building the same number from the tank levels, and its signs depend on whether the suction is a lift or flooded. The gauge method has no such sign trap.

NPSH available is found at the suction flange from the absolute pressure there, less the vapour pressure of the liquid, plus the velocity head, plus the height of the gauge above the pump centreline. It must exceed the NPSH required by the pump, with a margin, or the pump will cavitate.

Formulas used

  • H = \frac{p_d - p_s}{\rho g} + (z_d - z_s) + \frac{V_d^2 - V_s^2}{2g}
  • P_h = \rho g Q H
  • NPSH_a = \frac{p_{s,abs} - p_v}{\rho g} + \frac{V_s^2}{2g} + z_s

Worked example

With the default numbers in the calculator above:

  1. Velocity in each pipe: 2.546 m/s at the suction, 3.979 m/s at the discharge
  2. Head from the pressure difference: 37.79 m
  3. Height between the gauges: 0.5 m
  4. Difference of the velocity heads: 0.4764 m
  5. Total head of the pump: 38.77 m
  6. Hydraulic power (power given to the liquid): 7.591 kW
  7. Shaft power at the assumed efficiency: 10.84 kW
  8. Absolute suction pressure: 81.3 kPa absolute
  9. NPSH available at the pump: 8.396 m
  10. Margin over the NPSH required: 5.396 m

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

Common questions

Why is the velocity head included?

A gauge reads only the static pressure. The liquid also carries kinetic energy, which is different in the suction and discharge pipes when their diameters differ. The effect is small for slow flow, but it is easy to include and it is correct.

Do I add the suction lift to the head?

No. The suction gauge reading already shows whether the suction is a lift (a vacuum reading) or flooded (a positive reading). Using the difference between the two gauges takes care of it.

What if the suction pressure is a vacuum?

Enter it as a negative gauge pressure, for example minus 20 kPa. The calculator adds the atmospheric pressure to get the absolute pressure for the NPSH.

Is the shaft power exact?

No. It uses an assumed efficiency. Take the efficiency from the pump curve at your flow.

Related calculators

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

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