Stream power

Stream power is the rate of energy dissipation against the bed and banks of a river or stream per unit downstream length. It is given by the equation:

where Ω is the stream power, ρ is the density of water (1000 kg/m³), g is acceleration due to gravity (9.8 m/s²), Q is discharge (m³/s), and S is the channel slope.

It can be derived by the fact that if the water is not accelerating and the river cross-section stays constant (generally good assumptions for an averaged reach of a stream over a modest distance), all of the potential energy lost as the water flows downstream must be used up in friction or work against the bed: none can be added to kinetic energy. Therefore, the potential energy drop is equal to the work done to the bed and banks, which is the stream power.

We know that change in potential energy over change in time is given by the equation:

where water mass and gravitational acceleration are constant. We can use the channel slope and the stream velocity as a stand-in for ${\displaystyle {\Delta z}/{\Delta t}}$: the water will lose elevation at a rate given by the downward component of velocity ${\displaystyle u_{z}}$. For an channel slope (as measured from the horizontal) of ${\displaystyle \alpha }$:

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