Derivation of Reservoir’s Area-Capacity Equations

Area-capacity curves are usually used for reservoir flood routing, reservoir operation, determination of water surface area, and capacity corresponding to each elevation, reservoir classification, and reservoir sediment distribution. In this study, the similarity between the natural logarithmic function curve and the reservoir capacity curve is used to obtain the mathematical equation for dimensionless capacity curve. The obtained equation has only one unknown dimensionless parameter, named the “reservoir coefficient” $N$ . If the obtained dimensionless capacity equation is plotted on a log-log paper, for any values of $N$ , it will be approximately a straight line and the reciprocal of the line slope will be equal to the reservoir shape factor. The reservoir area equation and equation of reservoir coefficient are obtained by differentiating the reservoir capacity equation. Also, more precise values of $N$ for the area and capacity equations can be obtained by using the least-squares method. The obtained equations are evaluated with the area-capacity data from 16 reservoirs. This study shows that the obtained equations agree well with the actual data, and for reservoirs with the smoothed area-depth curve, the certainty of the obtained equations are more.