Solution of Continuity and Momentum Equations of a Travelling Hydraulic Jump by Using an Iterative Operator

4. Solution of Continuity and Momentum Equation of Travelling Hydraulic Jump by Using an Iterative Operator The continuity and momentum principles are applicable to a travelling or stationary hydraulic jump as well as to a long ware motion. There is, however an energy defect across hydraulic jump whereas the energy conservation principle remains applicable across a long wave. Keeping this energy defect in view, a solution by numerical analysis of the non-linear hyperbolic partial differential equations of continuity and momentum for the case of a travelling hydraulic jump has been suggested in this paper also showing how the profile of a travelling hydraulic jump can be obtained analytically at any instant during its motion in tho space, once the initial profile of the jump is determined by the method of characteristics.