Generating an empirical discharge coefficient formula for regular polygonal multi-orifices: Experimental and numerical insights

This study derives empirical formulas to predict Cd for regular multi-polygonal orifices with varying numbers of sides. Using Buckingham’s π-Theorem, dimensional analysis identified dimensionless parameters influencing Cd, supporting the development of empirical correlations. Experimental tests and CFD simulations evaluated the effects of geometric parameters, including orifice spacing-to-diameter ratio (S/d), head-to-diameter ratio (h/d), and the number of polygon sides (m). The study examined Cd for five orifice shapes: circular, triangular, square, pentagonal, and hexagonal, extending the analysis to additional polygons numerically. The results revealed inverse sigmoidal relationships between (S/d) and (h/d) with Cd for all tested shapes, stabilizing upward at S/d = 1.5 and h/d = 20 and downward at S/d = 7 and h/d = 190. Cd decreased with increasing polygon sides (m) but began to rise beyond 16 sides, as polygons with higher side counts more closely approximate circular geometry, resulting in reduced flow resistance, ultimately approaching the circular shape’s value. Empirical discharge coefficient formulas derived through sigmoidal limit analysis showed that Cd values for multi-orifice polygons range between 0.528 and 0.773.