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 = 0.004 and dimensionless Chezy friction factor f = 0.004. 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 1.8 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 supercritical flow channel with S_o = 0.03 flows into a critical flow channel of S_o = 0.003. The dimensionless Chezy friction factor f is the same is both channels. The unit-width discharge is 2.5 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.

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

   • 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.

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