Linear and angular momentum conservation for the hydraulic jump in converging channels

Abstract

This note is the final completion of a previously published work concerning the integral conservation of linear and angular momentum in the steady hydraulic jump in a linearly diverging channel [Valiani, A., Caleffi, V. (2011). Linear and angular momentum conservation in hydraulic jump in diverging channels. Adv. Water Res. 34(2), 227–242]. The same reasoning is applied to a linearly converging channel, and the theoretical framework, which is almost completely the same, is shown to remain valid. Using a proper mechanical scheme, an analytical solution is obtained for the free surface profile of the flow. This solution allows the determination of the sequent depths and their positions. Thus, the length of the jump, which is assumed to be equal to the length of the roller, is also found. The mainstream and roller thicknesses can also be derived. This model may be used to derive the average shear stress exerted by the roller on the mainstream and the related exact expression for the total power loss in the jump, allowing to demonstrate the internal consistency of the proposed conceptual scheme.