## Run of the River

Run of the river power plants use the kinetic energy of a river instead of collecting water to use potential energy.  The plant will form a small reservoir behind it to ensure stable flow through the pen-stock of the dam.  The energy to turn the turbine in the dam comes straight from the velocity of the flowing river.  However, due to the lack of significant reservoir, run of the river plants are dependent on the seasonal flow of the river and as such power generation is not steady and can be intermittent.

http://en.wikipedia.org/wiki/Run-of-the-river_hydroelectricity#/media/File:Chief_Joseph_Dam.jpg

The power available from a run of the river power plant is also very easy to calculate and find and is based on the kinetic energy portion of the energy transport by mass equation.

$P=\rho *Q*V^2*0.5*ɳ$
(Taken from Basic Thermodynamics by Cengel and Boles)

Where ρ is the density of the river, Q is the flow of the river in volume per second, V is the velocity of the river at the plant, and $P=\rho *Q*V^2*0.5*ɳ$ is the efficiency of the turbine and generator at converting the energy.