Name: ____________________ Red ID _____________________ Grade: ____________

Instructions: Closed book, closed notes. Use engineering paper. When you are finished, staple your work in sequence (1 to 5), and return this sheet with your work.

1. (20%) A steep rectangular channel with S_o = 0.015 changes abruptly to another rectangular channel of slope S_o = 0.004 and of the same width. The friction factor (1/8 of Darcy-Weisbach) in both channels is f= 0.004. The discharge is q = 20 cfs ft^-1. What is the length of the resulting C₃ profile on the downstream channel?

2. (20%) A hydraulically wide channel is operating at Froude number F = 0.25. The unit-width discharge is q = 3 m²s^-1. What is Lagrange's relative celerity? What are two Langrange absolute celerities (usptream and downstream)?

3. (20%) You are observing the rising flood stage of a major river. At your observation point, at a certain time the discharge is 300 m³ s^-1, and the stage is rising at the rate of 8 mm hr^-1. The surface width of the river at this point, and for several kilometers upstream, is 105 m. What is your quick estimate of the present discharge at a point located 10 km upstream of your observation point?

4. (20%) Please answer each question in one clear and concise paragraph:
   • What is the rationale for the labyrinth spillway? When does it cease to work as intended?

   • Compare kinematic, diffusion, and dynamic waves in terms of their celerities and diffusivities.

   • At what Froude and Vedernikov numbers do kinematic, diffusion and dynamic wave coalesce?

   • What is the difference between the Schaake and Li methods to solve the kinematic wave equation? Which method is more stable? Which method is more accurate?

5. (20%) Write a 300-word essay either (a) defending or (b) attacking the Muskingum-Cunge method. Please consider content, grammar, and spelling.