Optimum point in a river regulation curve

In the study of river regulation, for more than 100 years engineers have used the interrelation between the chronological series of river flows and the size of active reservoirs. In general, two variables are used: regulated flow q (or demand D) and the size of the active reservoir R. This paper proposes a third variable, the time of regulation (emptying and filling of reservoir) that applies to any size of reservoir. Mathematical analysis of q = f(R) leads to a graphical construction to determine point P, which is the optimum set of regulated flows or releases q, the size of the active reservoir R and the regulation time T for the river at a selected site based on the hydrological characteristics of the river. Once P is determined in the river regulation curve, it is easy to see how the storage decreases or increases, allowing the choice of the active reservoir size for a project. As P is a breaking point, it is important to determine whether building a reservoir of this specific size is economically feasible when its total cost is taken as a point of reference. If so, then one may consider building a larger reservoir if the topographical features of the valley permit and other concerns allow. The best solution, economically, may be to design smaller reservoirs that satisfy the economic constraints of the project. This method is a rapid and accurate way of comparing the regulation potential of several rivers or sites for the same river and can be used for preliminary and final designs.