Name: ________________________ S.S. No. _________________ Grade: ____________

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. (35%) 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 = 800 cfs
   Side slope: z = 2
   Manning n = 0.02
   Bottom slope: S_o = 0.00065
   Angle of repose: theta = 30^o
   Permissible tractive stress (on level ground): tau_L = 0.2 lb/ft²
   [Hint: Try different bottom widths until the design discharge is satisfied].
   

2. (35%) 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 = 0.002. The upstream flow is supercritical, and the discharge is q = 2 m³/s/m. Immediately upstream of the weir, the flow is subcritical, with depth 5 m.

   (a) Sketch the possible water surface profile and indicate its type.
   (b) Calculate the upstream flow depth.
   (c) Calculate the sequent depth using the hydraulic jump equation (Eq. 3-21).
   (d) 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. (30%) Please answer the following questions in a brief statement.

   (a) How many types of water surface profiles are they?
   (b) What are the five end values encountered in water-surface profiles? [Hint: one is S_o.]
   (c) What is the difference between steady gradually varied flow and uniform flow?
   (d) What is the difference between steady gradually varied flow and unsteady flow?
   (e) State three differences between the direct-step and standard-step methods of steady gradually varied flow computation.
   (f) What happens when a channel is dredged without a change in discharge?