Discharge coefficient for a water flow through a bottom orifice of a conical hopper

Discharge coefficients for water flow through a vertical, circular orifice at the bottom of a conical hopper were experimentally studied in the present paper. The conical hopper consists of a cylindrical hopper of inside diameter of 48 cm and a bottom cone of side slope of 45°. Experiments were carried out under different orifice diameters and water heads. The dependence of the discharge coefficient on the orifice diameter and water head was analyzed, and then an empirical relation was developed by using a dimensional analysis and a regression analysis. The results show that the larger orifice diameter or higher water head have a smaller discharge coefficient and the orifice diameter plays more significant influence on the discharge coefficient than the water head does. The discharge coefficient of water flow through a bottom orifice is larger than that through a sidewall orifice under the similar conditions of the water head, orifice diameter, and hopper size.