Flow invariants in a channel obstructed by a line of inclined rods

An experiment is conducted in a rectangular channel obstructed by a transverse line of four inclined cylindrical rods. The pressure on the surface of a central rod and the pressure drop through the channel are measured varying the inclination angle of the rods. Three assemblies of rods with different diameters are tested. The measurements were analyzed applying momentum conservation principles and semi-empirical considerations. Several invariant dimensionless groups of parameters relating the pressure at key locations of the system with characteristic dimensions of the rods are produced. It was found that the independence principle holds for most of the Euler numbers characterizing the pressure at different locations, that is, the group is independent of the inclination angle provided that the inlet velocity projection normal to the rods is used to non-dimensionalize the pressure. The resulting semi-empirical correlations can be useful for designing similar hydraulic units.