الفهرس 
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Abstract
The objective of the present study is to investigate the free radial hydraulic
Jump in contracted sloping channels. In the theoritical study, the dimensional
analysis was employed to relate the different factors affecting the studied
phenomena. Moreover, the continuity equation and the impulse-momentum
principles, were used to get expressions relating the initial Froude number and the main hydraulic characteristics of the free radial hydraulic jump. Experiments were
conducted in rectangular channel. Models with different contraction ratio (e =
0.333,0.447,0.547,0.647,0.753) with the same angle of divergence (4° 5\ 36.33\\)
were tested for six bed slopes (0,0.002,0.005,0.01,0.017,0.023) under the same flow conditions.
Using the experimental data, relationships were plotted describing the main characteristics of the free radial hydraulic jump. The experimental data was analyzed and the results were presented graphically in a number of charts.
It was found that radial jump gives relative depth, relative length of jump
less than the corresponding rectangular jump, the best contraction ratio which
gives the shortest relative length, relative depth, relative tail water depth of jump and maximum energy loss is approximately about 0.5.
Finally, it was found that the experimental results were 111 a good
agreement with the theoretically derived equations.