The Flow under Gravity of a Swirling Liquid through an Orifice-Plate

An examination has been made of the whirlpool formed when a perfect liquid possessing swirl passes under gravity through a circular sharp-edged hole in the base of a large tank. Relaxation methods were applied to determine the velocity distribution in the liquid and the shapes of the air-core and of the initial part of the emergent jet. In the numerical case considered, the swirl was large; and it was found that, except close to the orifice, the radial and vertical velocities were too small to influence the shape of the air-core within the tank. Below the orifice the liquid was emitted as a conical and rapidly thinning jet. In spite of the contraction at the edge of the hole, the discharge was not greatly different from that determined by Binnie & Hookings’ (ɪ948) approximate method for flow through a trumpet. Experiments with water were made for comparison with the calculations. It was noticed that under certain conditions of low swirl the annular jet assumed a cylindrical vibrating form. The theory of these oscillations, which was confirmed by observation, shows that, unless the air-core occupies a large fraction of the cross-section of the jet, the wavelength is nearly the same as that in a ‘solid’ jet of the same outer diameter.