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. (25%) A weir is located at the downstream end of a wide rectangular channel of bottom slope S_o = 0.0025 and dimensionless Chezy friction factor f = 0.0025. The unit-width discharge in the wide rectangular channel is q = 0.4 m³/s/m. Immediately upstream of the weir, the flow is subcritical, with depth 1.5 m.
   • Calculate the Froude number of the normal flow in the upstream channel.
     

   • Calculate the normal flow depth in the upstream channel.
     

   • Calculate the normal flow velocity in the upstream channel.
     

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

   • Calculate the length of the water-surface profile.
     

   
   

   
   

   
   

   
   

   
   

2. (25%) 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 2.3 m³/s/m. Find the length of the C₃ water surface profile in the critical flow channel.

   
   

   
   

   
   

   
   

   
   

3. (25%) Please answer the following questions in a brief statement.

   1. What is the difference between the brute force method and Newton's iteration to solve the normal depth equation?

   2. What is the minimum and maximum values of Manning's n observed in practice?

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

   4. In gradually varied flow in a hydraulically wide channel, the flow depth gradient S_y is a function of three parameters. What are these?

   5. When the water is clear of sediment, does it tend to erode the boundary more, or less? Why?

4. (25%) State five (5) differences between the direct step and standard step methods of steady gradually varied flow computation.