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. (30%) 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 = 0.5 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 (See w.s. profile below).
     

2. (30%) A hydraulically wide 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 (f = 0.003). The unit-width discharge is q = 2.5 m²/s. Find the length of the C₃ water surface profile in the critical flow channel (See w.s. profile below). [Hint: Calculate the upstream Froude number and the upstream flow depth, then calculate the downstream flow depth; then calculate the length of the profile by geometry.]

   
   

3. (20%) Please answer the following questions in a brief statement.

   • Why is it necessary to design a channel to operate with a minimum Froude number?

   • 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 are the five asymptotic values to which the water surface tend to in gradually varied flow?

   • How many types of water surface profiles are they? Which ones are horizontal?

4. (20%) State eight (8) differences between the direct step and standard step methods of steady gradually varied flow computation.