1. Gradually varied flow occurs over a section of rectangular channel with n = 0.013, S₁ = 0.005, and b = 2.5 m. At location 1 the depth is 1.05 m, and at location 2 it is 1.2 m. If the two locations are 50 m apart, find the flow rate and identify the water surface profile type that exists over the section. 2. Uniform flow occurs in a long rectangular channel with n = 0.012, So = 0.0163, and b = 1.8 m. The flow rate is Q = 0.35 m³/s. The channel is altered by raising the channel bottom by Az 100 mm for a short distance. The alteration is intended to act as a "smooth transition region" so that losses can be considered negligible. Determine what changes take place due to the presence of the transition. In your analysis include all relevant rapidly varied flow calculations, and identify any gradually varied flow profiles. 3. Water flows in a rectangular channel with n = 0.012, S₁ = 0.00087, and b = 4.0 m. The flow rate is Q = 33 m³/s. At the entrance to the channel, the water depth is y = 0.68 m, and at the downstream end of the channel a free-outfall condition exists. Perform a profile synthesis to determine the nature of the water surface over the length of the channel, showing all necessary calculations before numerically calculating the distance from the entrance to the hydraulic jump that exists in the channel using the standard step method. For the latter, increment the depth in 0.1 m intervals, rounding to the nearest 0.2 m, i.e. 0.68 m → 0.7 m → 0.8 m...y₁, where y₁ is the depth immediately upstream of the hydraulic jump. 4. A rectangular channel has a change in slope as shown in the figure below. The channel is 3.66 m wide, with n = 0.017, So₂ = 0.00228, and Q = 15.38 m3/s. a) Determine the depth that must exist in the downstream channel immediately upstream of the jump for a hydraulic jump to terminate in uniform flow conditions. b) If yo₁ = 0.6 m, calculate the length to the hydraulic jump L, using depth increments of 0.1 m in a standard step calculation y01 Lj y02