Instructions: Closed book, closed notes. Use engineering paper. When you are finished, staple your work in sequence (1 to 3), and return this sheet with your work.

1. (30%) Calculate the design flow depth and bottom width of a trapezoidal channel to be excavated in noncohesive alluvial material, with the following conditions:

   Discharge: Q = 1000 cfs;
   Side slope: z = 2;
   Manning n = 0.02;
   Bottom slope: S_o = 0.00055;
   Angle of repose: θ = 30^o;
   Permissible tractive stress on level ground: τ_L = 0.3 lb/ft²

   [Hint: Calculate flow depth y based on permissible tractive stress on the sides, and then try several bottom widths b until the design discharge is satisfied].
   

2. (30%) A weir is located at the downstream end of a wide rectangular channel with bottom slope S_o = 0.01 and friction factor (1/8 of Darcy-Weisbach friction factor) f = S_c = 0.0025. The upstream flow is supercritical, and the steady discharge is q = 2 m³/s/m. A hydraulic jump forms in the steep channel. Immediately upstream of the weir, the flow is subcritical, with depth 5 m.
   
   • Calculate the upstream Froude number.
     
   • Calculate the upstream flow depth.
     
   • Calculate the sequent depth using the hydraulic jump equation (Eq. 3-21).
     
   • Assuming a nearly horizontal profile downstream of the hydraulic jump, calculate the approximate distance from the downstream end of the hydraulic jump to the weir.
     

3. (40%) Please answer the following questions in a brief statement.
   • How many types of water surface profiles are they?
     
   • What are the five upstream/downstream distinct values of depth gradient encountered in water-surface profiles?
     
   • What is the difference between steady gradually varied flow and uniform flow? Give an example of an application of each.
     
   • What is the difference between steady gradually varied flow and steady rapidly varied flow? Give an example of an application of each.
     
   • What is the difference between steady gradually varied flow and unsteady flow? Give an example of an application of each.
     
   • State five differences between the direct-step and standard-step methods of steady gradually varied flow computation.
     
   • What is the exponent of the rating under laminar flow conditions?
     
   • What happens when a channel is dredged partially without a change in discharge? What happens when a channel is dredged throughout its length without a change in discharge? How can dredging affect the hydrology? Explain.