Solution of Flow under Sluice Gate

The problem is considered for an analytic perturbation solution with a realistic mathematical model such that the gate opening is relatively small and the upstream free surface is horizontal. Solutions for the discharge and contraction coefficients are obtained in terms of a small parameter. Conformal mapping, analytic continuation and perturbation methods combined to obtain the solution correctly up to the second order. The discharge and contraction coefficients which are obtained from the solutions are compared with those obtained by others. Flow under a sluice gate of variable angle is separately dealt with by similar procedures. Due to complexity resulting from the variable angle, solutions for the coefficients of discharge and contraction have been obtained only up to the first order. From the Bernoulli equation on free surfaces, the boundary equations and conditions are obtained for the Ω-function. From solutions for the Ω-function, the second order perturbation solutions are obtained for a vertical sluice gate.