Reliability of Steady Surface Profile in Irrigation Canal

A reliability problem in irrigation canal systems where the water demand fluctuates stochastically is examined. A flow model of open channel with control structures is developed to include the lateral withdrawal, in which the flow rate is suddenly changeable temporally and spatially. Discussion is focussed on the propriety of a steady flow surface profile for an averaged water demand pattern. Assuming that the temporal evolution of unsteady flow surface profile is a Markov process, the theory of statistics is applied. Since the probability density function is governed by the Fokker-Planck partial differential equation, evaluating the reliability that the disturbance of surface profile around the steady state is small enough, is reduced to solving the heat equation deduced from a geometrical consideration. The acquired concept is applied to the design problem of a reliable steady surface profile. Computations are performed through roughly two stages, i.e., the approximation of the diffusion tensor that constitutes the coefficient matrix of the governing equation using the flow model and the diagonalization of the diffusion tensor.