LINEAR AND ANGULAR-MOMENTUM CONSERVATION IN HYDRAULIC JUMP

The present paper deals with the integral conservation of linear momen tum and angular momentum in the stationary hydraulic jump in a wide re ctangular channel. The flow is considered to be divided into a mainstr eam, that conveys the total Liquid discharge, and a roller, in which n o average mass transport occurs. Referring to the infinitely large cas e, a purely two dimensional motion is considered. The interface betwee n the two flow regions is a streamline, corresponding to a stream func tion value equal to the total discharge per unit width. The present ap proach consists in satisfying the mechanical balances of mass, momentu m and angular momentum, while no (large scale) constitutive relation i s assumed for the turbulent motion of the liquid. Regarding the stress tensor, hydrostatic normal pressure distribution is assumed, while no thing is assumed regarding shear stresses, except that viscous stresse s are negligible with respect to turbulent stresses. A paradox is put in evidence, that in the classical hydraulic jump (specific force cons erving solution) angular momentum conservation is apparently not satis fied. Taking into account of integral balances not only in terms of li near horizontal momentum but also of linear vertical momentum and angu lar momentum the paradox is overcome. Under some simplified assumption s regarding uniform horizontal velocity distribution in the mainstream , and negligibility of horizontal momentum and angular momentum in the roller with respect to other terms, an analytical solution is obtaine d in terms of free surface profile, mainstream thickness and roller th ickness. Average shear stresses acting on the mainstream by the roller and power losses for unit weight may be theoretically derived. Assumi ng as known the growth rate of the mainstream at the beginning of the jump, also the length of jump, here assumed identical to the length of the roller, may be determined, together with the volume of the roller , the volume of the mainstream and the volume of the whole stream betw een the sequent depths.