Hydraulic jumps in trapezoidal and circular channels

Reliable prediction of upstream and downstream depths in a hydraulic jump is essential for hydraulic design in open channels. A series of algorithms is proposed for estimating the ratio of conjugate depths in a hydraulic jump in a horizontal channel over a range of Froude numbers and for a range of different trapezoidal and circular sections running part-full. By solving the momentum equation using appropriate values for the depth of centroid below the free surface, an iterative approach is proposed that uses the Newton–Raphson method and produces satisfactory agreement with recent published experimental data. The resulting graphs of conjugate depth ratio y 2/y 1 against F 1 were also used to form the basis of a series of equations of best-fit lines that could be used as first approximations for use in hydraulic design problems. The results obtained were also used to predict the energy loss in the hydraulic jump. It is envisaged that the algorithms described here could be incorporated into standard design spreadsheets for use by practitioners involved in civil engineering hydraulics design.