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. (25%) A weir is located at the downstream end of a wide rectangular channel of bottom slope S_o = 0.0035 and dimensionless Chezy friction factor f = 0.0035. 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.
     

   • Calculate the length of the C₁ water-surface profile.
     

2. (25%) A hydraulically wide supercritical flow channel with S_o = 0.025 flows into a critical flow channel of S_o = 0.004. The dimensionless Chezy friction factor f is the same is both channels. The unit-width discharge is 2.2 m²/s. 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.

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

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

   • What is the typical range of variation of the angle of friction φ in granular materials (sand and gravel)?

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

   • What, in your opinion, should be done to manage the Oroville reservoir safely, in view of the failure of the spillways?

4. (25%) State eight (8) differences between the direct step and standard step methods of steady gradually varied flow computation.