Question

A channel is constructed of unfinished concrete. It is 10 ft wide, has a slope of 0.005 and carries a flow of 120 cu.ft/s. The flow encounters an obstruction that rises 0.5 ft above the channel bottom. Will a hydraulic jump occur? Justify your answer

Answer 1

Manning's roughness constant. nis 0.017. Width, b is equal to 10 feet. Slope, S, is equal to 0.005. Flow, Q is equal to 120ft/sec Manning equation 10y43 120 = 10 ft x y a (0.005) 0.017 (10+2y) 120=193.065x), (1042. yx = 4.3917ft Normal depth is 4.3917 feet. 120 )? Energy of flow before the obstruction is 4.3917+ (10x 4.3917) 2. = 4.5076ft 2x32.2 122 ) Critical flow depth is equal to s equal to = 1.6475ft Upstream of flow is subcritical as flow happens at normal depth that is above the critical depth (_12012 Specific energy at critical flow is equal to 1.6475+ 10x1.6475 -= 2.4713ft 2x32.2

Apply energy equation between the sections just upstream and downstream of obstruction as below. 4.5076ft=2.4713+Az Az = 2.0363ft Minimum height of obstruction that will cause the flow over the obstruction to reach critical depth is 2.0363 feet >0.5 feet) Also, the energy available over the obstruction is 4.0076 feet and is more than the minimum specific energy required (2.4713 feet) to not go below the critical depth of 1.6475 feet. Hence, the obstruction will not cause the hydraulic jump to occur by choking.