Explicit solution for normal depth in parabolic-shape channel

Normal depth is the important hydraulic element for the design and operation of channel. But its analytic expression is a complex implicit function and can not be solved directly. Based on the economic practical section and uniform flow theory, this paper presents a new and explicit solution for normal depth in parabolic-shape channel through optimizing the model parameters by using R software and Marquardt method. The practical example and error analysis show that the maximum relative error of the established explicit equation is smaller than 0.55%, which is among the scope of engineering application. The proposed equation has clear physical concepts, convenient calculation and strong generality. It can provide a useful reference for the engineering design and operation management.