Abstract
Mathematical model for dredging a trapezoidal open channel with hydraulic jump is developed using conditions of geometrical and dynamical similarities coupled with continuity and interpolation technique. Parameters like cross-sectional area, wetted perimeter, hydraulic mean depth, mean velocity etc. are determined in both the original and new (excavated) channels. A channel flow problem is solved using the model and the results obtained attest to the validity and efficiency of the model. Further application of the model in Bernoulli's equation leads to the energy dissipated in the jump for both the original and new channels. This application enables other parameters like jump efficiency, relative energy loss, power loss and height of the jump to be determined also and compared in both channels.
Highlights
An open channel is a duct through which a liquid flows with a free surface; viz: spillways, canals, rivers, aquaducts, etc
Mathematical model for dredging a trapezoidal open channel with hydraulic jump is developed using conditions of geometrical and dynamical similarities coupled with continuity and interpolation technique
The results suggested that the hydraulic jumps were effective aerators and that the rate of detrainment was comparatively smaller at the largest Froude numbers
Summary
An open channel is a duct through which a liquid flows with a free surface; viz: spillways, canals, rivers, aquaducts, etc. France (1981) studied a jet assisted hydraulic jump in an open channel He investigated the stability of the hydraulic jump and the effectiveness of jets over a wide range of operating conditions. Nikmehr and Tabebordbar (2010) carried out research in jump study on four adverse slopes, -0.00125, -0.0025, -0.00375 and -0.005 in two cases of rough and smooth beds Their results showed that the sequent depth ratio and the length of the jump were greater on smooth beds than rough beds for the same slopes and Froude number. Chanson (2011) investigated experimentally the bubbly two phase flow properties of steady and strong hydraulic jumps Their results demonstrated that the strong air entrainment rate and the depth-averaged void-fraction data highlighted a rapid deaeration of the jump roller. By comparing them,we observe that some of the parameters exhibit interesting characteristics
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