Instructions: Closed book, closed notes. Use engineering paper. When you are finished, staple your work in sequence (1 to 4), and return this sheet with your work.

1. (20%) What is the discharge in a rectangular channel of bottom width b = 5 m, bed slope S_o = 0.0025, Manning's n= 0.015, and flow depth y = 0.8 m?

2. (30%) A long channel of rectangular cross section has a bed slope S_o = 0.0045 and (dimensionless Chezy) friction factor f = 0.0045. The unit-width discharge in the channel is 1 m³/s/m. A weir (located at the downstream end of the channel) produces a water-surface profile immediately upstream of it. Immediately upstream of the weir, the flow depth is 2.4 m.
   1. Calculate the normal-depth Froude number 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 type of water-surface profile prevails immediately usptream of the weir?
      

   5. What is the length of the water-surface profile, measured from the weir to the location where the channel is at normal depth?.
      

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

   1. What is the minimum value of Manning's n? Where does it apply? What is the maximum value of Manning's n? Where does it apply?

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

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

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

   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 (preestablished) 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?
      

4. (20%) Do a tabular comparison between the direct-step and standard-step methods of steady gradually varied flow computation. State at least eight differences.