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Pump Hydraulic Power and Shaft Demand

Calculate pump hydraulic power and shaft demand with local equations, selectable units and supported inverse relationships.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

HydPower = 0.981; ShaftPower = 1.22625; SpecSpeed = 0.20157103. Values use the worked example unit selections.

Ph = ρgQH; Pshaft = Ph/η; Ωs = ω√Q/(gH)^(3/4)

Worked example

Enter these known values and leave the other values blank.

Discharge (Q)
0.01 m³/s
Differential head (H)
10 m
Density of fluid (ρ)
1000 kg/m³
Acceleration due to gravity (g)
9.81 m/s²
Efficiency (η)
0.8 .
Revolutions (N)
600 rpm
Hydraulic power (P==h==)
0.981 kW
Shaft power (P==s==)
1.2263 kW
Specific speed (N==s==)
0.20157

Assumptions and limitations

  • Steady incompressible flow and total pump head are assumed. Efficiency is a fraction in (0,1]. Specific speed is the dimensionless angular-speed convention, not rpm/gpm/ft specific speed.
  • Unit selectors convert known physical quantities. Leave a supported unknown blank; derived inverse branches are limited by the stated model and available captured equations.
  • Traditional rpm-flow-head specific-speed selectors use conventional standard gravity 9.80665 m/s². This fixed convention is separate from the editable local gravity used in hydraulic power and the dimensionless model; specify the convention when comparing pump catalogs.

Common questions

What does this calculation assume?

Steady incompressible flow and total pump head are assumed. Efficiency is a fraction in (0,1]. Specific speed is the dimensionless angular-speed convention, not rpm/gpm/ft specific speed.

Can I solve for an input?

Where the captured model supplies an inverse, leave that quantity blank and enter the remaining known quantities. A positive square-root or principal trigonometric inverse may represent only one of multiple mathematical branches.

Which unit should I use for the worked example?

The example uses the initial metric unit selection beside each field. Change a unit using its selector to convert the same known quantity; switching a unit does not change the underlying physical value.

References

Restrict the physical model to non-singular dimensions and stated principal inverse branches; discrete gear/fringe counts are exact integers. The four traditional pump specific-speed selectors now use exact revolutions, international foot, US/imperial gallon/liter and standard-gravity conversion definitions in place of rounded legacy factors. Volumetric flow rates use exact US or imperial fluid-volume definitions and exact seconds per minute, hour and day. US gallons per minute use exactly 0.003785411784 cubic meters per gallon and 60 seconds per minute. Bookify uses exact customary mass and volume definitions for density units, replacing rounded factors in the reference. Bookify uses the exact relationship one revolution = 2π radians instead of the captured rounded angular-speed factor. Feet per second squared use exactly 0.3048 meters per second squared, replacing a rounded reciprocal factor. Mechanical horsepower uses exactly 550 foot-pounds-force per second instead of a rounded factor.

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