Kinematic characteristics of a hydraulic jump on a sloping apron

Abstract

A hydraulic jump (Fig. 1) is a jet stream accompanied by the formation of an eddy zone, according to the current viewpoint. One of the main problems of a hydraulic calculation of such streams is to establish the distribution law of the mean velocity over the cross section of the flow, depth of water within the eddy zone and at its end, and the length of this zone. Investigations by many authors show that the flow within the hydraulic jump both in a horizontal and sloping channel corresponds to the model of flow in a plane turbulent wall jet [1] in which the vertical velocity distribution obeys the SchlichtIng relation [1,2] for the main part of the jet. The jet character of flow in hydraulic structures enables us to approach the solution of many problems in this area from positions of the theory of turbulent jets propagating in a bounded space. Here it is assumed that the cross sections are plane and the pressure of the fluid is distributed over the depth of the flow according to the law of hydrostatics.To determine the regularities of change of the average free surface in the entire eddy zone and length of the eddy of the free jump, the equations of motion of a fluid in the boundary layer following from the Reynolds system of equations of motion are used [3]. As a result of solving these equations, with the assumptions adopted above, the following relations associating the depth of the flow h with the longitudinal coordinate x coinciding with the bottom of the flow are obtained:for i ~ 0.12 ~a (h --hi)

Energy Dissipators and Hydraulic Jump

“…D-jumps were analysed by Bunyan (1958) , Smith (1959), Rajaratnam (1963, Wielogorski and Wilson (1970), Mura , Ohashi, et al (1973) , Rajaratnam and Murahari (1974) , and Mikhalev and Hoang (1976) .…”

Experimental analysis of hydraulic jump at high froude numbers

“…Kindsvater [4] classi ed jumps on the sloped channel according to their toe position relative to the channel bottom kink: A-jump for which the toe is at the kink, B-jump is the intermediate of A-and C-jumps, C-jump for which the end of roller is above the kink, and D-jump where the entire roller region is on the sloping channel. After the Kindvater's study, many studies have been conducted on these types of jumps [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Their main ndings can be summarized as follows; (i) The energy dissipation rate decreases from A jump to D jump due to reduction in the force of hydraulic jump with the increasing tail water depth, (ii) The hydraulic characteristics of the classical jump and the A-jump are similar, (iii) Regarding the decay of Loading [MathJax]/jax/output/CommonHTML/fonts/TeX/fontdata.js bottom shear velocity, the sloping and the classical jumps are identical (iv) The roller lengths of C-and Djumps are almost identical, (v) D-jumps are located between the classical jump and the classical wall jet as regards the decay of maximum forward velocity, (vi) The maximum bottom velocities and maximum surface velocities are near the side-walls and along the centerline of the channel, respectively.…”

Experimental Analysis of Hydraulic Jump at High Froude Numbers

“…Kindsvater [4] classi ed jumps on the sloped channel according to their toe position relative to the channel bottom kink: A-jump for which the toe is at the kink, B-jump is the intermediate of A-and C-jumps, C-jump for which the end of roller is above the kink, and D-jump where the entire roller region is on the sloping channel. After the Kindvater's study, many studies have been conducted on these types of jumps [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Their main ndings can be summarized as follows; (i) The energy dissipation rate decreases from A jump to D jump due to reduction in the force of hydraulic jump with the increasing tail water depth, (ii) The hydraulic characteristics of the classical jump and the A-jump are similar, (iii) Regarding the decay of bottom shear velocity, the sloping and the classical jumps are identical (iv) The roller lengths of C-and Djumps are almost identical, (v) D-jumps are located between the classical jump and the classical wall jet as regards the decay of maximum forward velocity, (vi) The maximum bottom velocities and maximum surface velocities are near the side-walls and along the centerline of the channel, respectively.…”