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%) A weir is located at the downstream end of a wide rectangular channel of bottom slope S_o = 0.003 and dimensionless Chezy friction factor f = 0.003. The unit-width discharge in the wide rectangular channel is q = 0.5 m³/s/m. Immediately upstream of the weir, the flow is subcritical, with depth 2 m.
   1. Calculate the Froude number of the normal flow in the upstream channel.
      

   2. Calculate the normal flow depth in the upstream channel.
      

   3. Calculate the normal flow velocity in the upstream channel.
      

   4. What is the type of water-surface profile extending from the weir in the upstream direction?
      

   5. Provide a quick estimate of the length of the water-surface profile.
      

   
   

   
   

   
   

   
   

   
   

2. (35%) A supercritical flow channel with S_o = 0.03 flows into a critical flow channel of S_o = 0.003. The boundary friction f is the same is both channels. The unit-width discharge is 1.5 m³/s/m. Find the length of the C₃ water surface profile in the critical flow channel.

   
   

   
   

   
   

   
   

   
   

3. (30%) Please answer the following questions in a brief statement.

   1. What is the main difference between the Manning and Chezy formulas?

   2. What is freeboard? When is it OK to use the freeboard?

   3. What is the normal range of variation of the angle of repose θ of noncohesive materials?

   4. How many types of water surface profiles (WSP) are there in gradually varied flow (GVF)? Which water surface profiles are completely horizontal?

   5. In gradually varied flow in a hydraulically wide channel, the flow depth gradient S_y is a function of three (geometric and physical) parameters. What are these?

   6. What are the five characteristic values to which the flow depth gradient S_y tends in WSP computations?