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The Hydraulic Jump in Converging Channels: An Integral Mechanical Balance

Author(s): Alessandro Valiani; Valerio Caleffi

Linked Author(s): Alessandro Valiani

Keywords: No Keywords

Abstract: This paper studies the integral conservation of linear and angular momentum in the steady hydraulic jump in a linearly converging channel, following the recent research line of the authors concerning the same phenomenon in a linearly diverging channel. The flow is considered divided into a mainstream, tha conveys the total liquid discharge, and a roller, where no average mass transport occurs. No macroscopic rheologica relationship is assumed, so mass, momentum and angula momentum integral balances are independent relationships Normal stresses are assumed hydrostatically distributed on each vertical and viscous stresses are assumed negligible with respect to turbulent stresses. Horizontal velocity is considered uniform in the mainstream and horizonta momentum and angular momentum in the roller are neglected with respect to their mainstream counterparts. Using such simplified assumptions an analytical solution is obtained for the free surface profile of the flow, which is fundamental for finding the sequent depths and their positions. Such solution permits to compute the jump length, which is assumed equal to the roller length. Mainstream and roller thicknesses can also be derived. The model may also be used to theoretically derive the average shear stresses exerted by the roller on the mainstream and the power losses per unit weight. This final relationship, which returns the well-known classical expression for total power loss in the jump, demonstrates the internal consistency of the mechanical model.


Year: 2012

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