Solution for Gravity Flow Under a Sluice Gate

Solutions to flow under a sluice gate yield profiles and discharge coefficients for gate opening to total head ratios in the range 0.1 ≤ b/H ≤ 0.6. Comparison with experimental data reveals that variables not considered have a small but significant effect on the flow. The solution consists in mapping the complex-potential plane into an auxiliary plane in which the flow boundaries lie on the real axis. A line distribution of vorticity proportional to the unknown derivative of elevation with respect to velocity potential, together with the Bernoulli equation on the free surfaces, leads to an integral equation which exactly describes the influence of gravitational attraction, discharge and flow geometry. A numerical, iterative procedure is used to solve the equation by digital computer to the desired accuracy.