development of a new hydraulic relationship for submerged slide gates

Slide gates are one of the most common gates used in hydraulic structures. these gates are often in practice hydraulically submerged. the usual method to determine the flow passes through the gate is solving simultaneously the energy and the momentum nonlinear equations by a numerical method. in this manuscript, a large number of various cases of gate sizes and flows are considered and solved numerically by using these two equations to obtain a database. this database is converted to dimensionless groups and then a direct relationship is developed by using three-dimensional curve fitting. the results obtained by the developed relationship are compared with those obtained by the numerical common method. the comparison results in a good agreement which indicates that the developed relationship is accurate and simple to be used in the design of slide gates.