Unformatted text preview: 15. Theory for a Horizontal Jump A jump which occurs on a steep channel slope can be affected by the difference in
water-weight components along the flow. The effect is small, however, so that the classic theory assumes that the jump occurs on a horizontal bottom.
You will be pleased to know that we have already analyzed this problem in Sec.
10.1. A hydraulic jump is exactly equivalent to the strong fixed wave in Fig. 10.4b,
where the change in depth y is not neglected. If V1 and y1 upstream are known, V2
and y2 are computed by applying continuity and momentum across the wave, as in Eqs.
(10.7) and (10.8). Equation (10.9) is therefore the correct solution for a jump if we interpret C and y in Fig. 10.4b as upstream conditions V1 and y1, with C
V and y
y being the downstream conditions V2 and y2, as in Fig. 10.12b. Equation (10.9) becomes
2 gy1 ( 1) where
y2/y1. Introducing the Froude number Fr1
dratic equation for , we obtain
y1 1 (10.42)
1/2 V1/(gy1) and solving this qua- 8 Fr...
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This note was uploaded on 10/27/2009 for the course MAE 101a taught by Professor Sakar during the Spring '08 term at UCSD.
- Spring '08