**FIGURE 6-1** Stream flow energy definition. HGL is the hydraulic gradient line, which corresponds to the water surface line (WSL).

the loss of energy head (h_{L}) long the stream is energy slope (also known as the friction slope) multiplied by distance, or , where the friction slope *Sf* is approximated by use of Manning’s equation, *n* is the Manning’s roughness coefficient, *R _{h}* is the hydraulic radius, and AL is the channel length.

Conventional impounded hydropower works by recovering energy that would have been lost due to friction in a free-flowing stream or river (Figure 6-2). Specifically, as water flows from the stream into the impounded reservoir, the velocity is reduced as the depth of water increases, reducing the velocity head and the associated friction loss. In a deep reservoir the velocity, and therefore the friction loss per unit length, approaches zero near the dam. Therefore, the total available energy head at the dam location is approximately equal to the potential energy head, *E _{p}* =

More recently, the potential for recovery of hydrokinetic energy in streams has attracted increasing attention. In-stream hydrokinetic energy is recovered by deploying a single turbine unit or an array of units in a free-flowing stream (see Figure 6-3 for centerline view of a turbine array along a river reach). It is notable that the water surface will continue to rise in the upstream direction along the array until a new equilibrium normal depth is achieved due to the impedance of the devices. The distance required to reach the new equilibrium depth is approximately the water depth times the bottom slope, so the new depth will not be reached if the array is shorter than this. This back effect is expected to propagate further upstream from the array field; its distance is dependent on the overall water surface rise at the array, which itself is dependent on the density of deployed turbine units.