What is Water Power?

May 07
2009

Hydraulic or Water Power comes from the combination of water flow rates and pressure differences.

The power available in a stream of water is given as “P” where:

P = Hydraulic Power

= Efficiency × Pressure difference × Volume rate of water flow

= Joules/Second

= Watts¹

Note: This is hydro power including hydro turbine efficiency (losses in heat from friction & turbulence.) P is the power which is the amount of work that can be done (Joules) in a unit of time (1 second) which is also known as Watts. Watts have the same units regardless of whether it is Watts in fluid flow or in electricity flow.

In terms of physical parameters the basic gravity driven water power equation becomes -

$P=\eta\cdot\rho\cdot g\cdot h\cdot\dot v$ = Efficiency × Pressure difference × Volume rate of water flow

Where:

$P =$ power (J/s or watts)
$η =$ turbine efficiency
$ρ =$ density of water (kg/m³) or (lb-mass/ft³)
$g =$ acceleration of gravity (9.81 m/s²) or (32 ft/s²)
$h =$ head (m) or (ft). For still water, this is the difference in height between the inlet and outlet surfaces. Moving water has an additional component added to account for the kinetic energy of the flow. The total head equals the pressure head plus velocity head.
$\dot v$ = Water volume flow rate (m³/s) or (ft³/s)

We’ll be revisiting this hydro-energy relationship more in the future. I have a request to work up an example or two for reference as well. I’m working on it, it just takes is a bit of time, and we’ll keep on blogging SmallHydro too…

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I have included reference to both metric (SI) and English units above. In a upcoming post I’ll elaborate on key Hydropower calculations for each system.

Ref 1: Frank M. White, “Fluid Mechanics,” McGraw Hill, 1979 , pp 180-188

More information on Water Power can be found on Wikipedia – Water Turbine article.
More on physics of power found on Wikipedia.

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