Studies on the maximal harvestable hydropower in open channels – Application to a water wheel and a turbine

This work is about the upper limit for the hydropower gained in an open channel by a water wheel or turbine. As a consequence of the energy equation it is proved, that the upper limit per unit depth of the channel is 2 / 5 2 / 3 5/2 2/5) ( eff H g  . Hereby, the effective water height eff H is the sum of the specific energy g u h E 2 / 2 1 1 1   and the drop of the ground level z  . Analogous to Albert Betz and his work about wind turbines, a dimensionless coefficient of performance is introduced. The results are compared with two different experimental data sets.