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. (20%) What is the discharge in a rectangular channel of bottom width b = 10 m, bed slope S_o = 0.001, Manning's n= 0.025, and flow depth y = 1 m?

2. (20%) A 10-ft high weir is located at the downstream end of a wide rectangular channel of bottom slope S_o = 0.0045 and Darcy-Weisbach friction factor f_D = 0.036. The unit-width discharge in the wide rectangular channel is 5.68 cfs/ft.
   1. Calculate the upstream Froude number.
      

   2. Calculate the upstream flow depth.
      

   3. What is the type of water-surface profile immediately upstream of the weir?

   4. Calculate the length of the water-surface profile.

3. (60%) Please answer the following questions in a brief statement.
   1. What are rolls waves? When and where do they typically form?

   2. What is the minimum value of Manning's n that can be achieved in practice? What type of surface would that be? In the absence of more information, what is the value of Manning's n generally adopted for small upstream natural streams?

   3. How does the composite value of Manning's n change from very low flow (Example: a river drought) to very high flow (the Probable Maximum Flood) in a typical natural stream?

   4. Why is Newton's law of viscosity applicable to laminar free-surface (overland) flow?

   5. Why is the permissible tractive force method preferred over the permissible velocity method in the design of open channels over erodible materials?

   6. What is the typical range of the angle of repose of noncohesive materials?

   7. Why does a canal with clear water have a lower permissible unit tractive force than a canal with high content of fine sediment?

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

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

   10. What are the five characteristic values to which the flow depth gradient S_y tends in WSP computations?
       To which ones is S_y asymptotic in the upstream or downstream end?

   11. Which one is the most common type of WSP? When does it occur?

   12. Do a tabular comparison between the direct-step and standard-step methods of steady gradually varied flow computation. State at least seven differences.