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A very long straight channel has a trapezoidal cross-section, with width b= a m at the bottom and the sides with slopes of IV:1H (i.e., m=1 in Figure 1). The longitudinal slope of the channel is 0.6%; the Manning roughness coefficient is ni = 0.014 m3s, but part of the channel, for a length L = 300 + 10 a m, is covered by some vegetation increasing the roughness coefficient to n2 = 0.04 m-"%s (Figure 2). The channel conveys water with a flow rate of Q = 10 mºs! Figure 1. Cross section of the channel, the slope of the sides of the channel is IVIH, --1). -0.014 m 5 =0.6% 1, +0.04 mis n = 0.014 ms Figure 2. Longitudinal section of the channel with the different roughness coefficients Tasks 1. Calculate the water depths required to fully identify the water surface profiles along the channel: 2. Provide a qualitative sketch of the water profiles along the channel with appropriate labels (1.e., MI, M2, M3, S1, S2, S3). 3. Calculate numerically water depths along the channel. If a jump forms in the channel, find its position. Use A or A' as references to define the distance where different profiles might start and end.
Calculation of all the water depths that need to be used to identify the water surface profiles along the channel. Provide an explanation of which water profiles (i.e., MI, M2, M3, S1, S2, S3) you might expect along the channel Qualitative sketch of the water profiles along the channel with appropriate labels (i.e., M1, M2, M3, S1, S2, S3) Numerical calculations of the water depths along the channel. Use 20 intervals (i.e., 21 values of depths) between the depths upstream and downstream of your calculations. Provide both tables with appropriate calculations and graphs of calculated water depths along the longitudinal coordinate (use A and A' as a reference for the calculation of the longitudinal coordinates)