Hydraulic Power Calculator: P = rho g Q H

The power a pump puts into the fluid.

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

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • P_h = \rho gQH
  • Q = \frac{P_h}{\rho gH}
  • H = \frac{P_h}{\rho gQ}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the hydraulic power: hydraulic power = density of the fluid x gravitational field strength x flow rate x head
  2. Put the values in (every value in its SI unit): hydraulic power = 1000 x 9.80665 x 0.02 x 30
  3. The answer: hydraulic power: 5883.99 W
  4. The same answer in other units: 5.88399 kW; 7.89056 horsepower

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

A second worked example

A different case, with these numbers: What do you want to find? Head; Hydraulic power (leave it as it is if this is what you are finding) 5883.99 W; Flow rate (leave it as it is if this is what you are finding) 0.02 m3/s.

  1. The formula, arranged to find the head: head = (hydraulic power) / (density of the fluid x gravitational field strength x flow rate)
  2. Put the values in (every value in its SI unit): head = (5883.99) / (1000 x 9.80665 x 0.02)
  3. The answer: head: 30 m
  4. The same answer in other units: 294.199 kPa; 2.94199 bar; 98.4252 feet

Common questions

What is the formula for hydraulic power?

Density times gravity times the flow rate times the head. Moving 20 L/s of water against 30 m of head takes 5.9 kW.

How do I find the motor power for a pump?

Divide the hydraulic power by the pump efficiency, and then by the motor efficiency if you want the electrical power.

What is head?

The energy of the fluid as a height of the fluid column. 10 m of water is about 98 kPa.

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Further reading: Any fluid mechanics or pump text (hydraulic power).

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