Learning Objectives OPEN CHANNEL FLOW WORKSHEET 3 WATER SURFACE PROFILES 1. Learn about gradually varied flow and rapidly varying flow 2. Discuss different types of water surface profiles 3. Discuss the computation of downstream or upstream depth using the energy equation Water surface profiles Figure 1: Varied flow in open channels (Source: Mohtar 2000) The equation for water surface profile is given as follows: dy dx = S 0 S f 1 Fr 2 1
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Problem 1 (Example 4.6) Water flows in a trapezoidal channel in which the bottom width is 5m and the side slopes are 1.5:1. The channel lining has an estimated Manning s n of 0.04, and the longitudinal slope of the channel is 1%. If the flowrate is 60 m 3 /s and the depth of flow at a gaging station is 4m, classify the water surface profile, state whether the depth increases or decreases in the downstream direction, and calculate the slope of the water surface at the gaging station. Based on this watersurface slope, estimate the depth of flow 100 m downstream of the gaging station. 3
Problem 2 (4.44) Water flows at 36 m3/s in a rectangular channel of width 10 m and Manning s n of 0.03. If the depth of flow at a channel section is 3m and the slope of the channel is 0.001, classify the water surface profile. What is the slope of the water surface at the observed section? Would the water surface profile be much different if the depth of flow were equal to 2 m? 4
Problem 3 (4.45) Water flow at 30 m3/s in a rectangular channel of width 8m. Manning s n of the channel is 0.035. Determine the range of channel slopes that would be classified as steep and the range that would be classified as mild 5
Hydraulic jump The difference in energy between the supercritical and subcritical zones of a jump can be obtained by the momentum equation Depending the Froude number on the upstream side, the hydraulic jump can be classified as follows 6
Problem 4: (Example 4.8) Water flows down a spillway at a rate of 12 m3/s per unit meter of width into a horizontal channel, where the velocity into the channel entrance is 20 m/s. Determine the conjugate depth 7
Problem 5 A flume with a triangular cross section and side slope of 2:1 (H:V) contains water flowing at 0.3 m3/s at a depth of 15 cm. Verify that the flow is supercritical and calculate the conjugate depth 8
Problem 6 Water flows in a trapezoidal channel where the bottom width is 6 m and side slops are 2:1 (H:V). The channel lining has an estimated Manning s n of 0.045, and the slope of the channel is 1.5%. When the flowrate is 80 m3/s, the depth of flow at a gaging station is 5 m. Classify the watersurface profile, state whether the depth increases or decreases in the downstream direction, and calculate the slope of the water surface at the gaging station. On basis of the water-surface slope, estimate the depths of flow 100 m downstream and 100 m upstream of the gaging station 9
Problem 7 A trapezoidal canal has a longitudinal slope of 1%, side sloopes of 3:1 (H:V), a bottom width of 3.00 m and a Mannings n of 0.015 and carries a flow of 20 m3/s. The depth of the flow at a gaging station is observed to be 1.00 m. Answer the following (a) What is the normal depth of the flow in the channel? (b) What is the critical depth of the flow in the channel? (c) Classify the slope of the channel and the water surface profiles at the gaging station (d) How far from the gaging station is the depth of flow equal to 1.1m? Does the depth occur upstream or downstream of the gaging station? 10