Instructions: Open book, open 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%) An inherently stable channel, of constant hydraulic radius in the overflow section (see figure below), has a rectangular [base] channel section of width B = 5 m, and flow depth d = 1 m. Assuming for simplicity a trapezoidal cross section for the overflow section (i.e., the flow above d = 1 m), provide a rough estimate of the top width at a depth d = 2 m, measured from the channel bottom.

2. (20%) A horizontal channel of length L = 500 m is designed to convey Q = 5 m³/s from a reservoir to a free overfall. The bottom width is b = 2 m, and side slope z = 1.5. The channel is lined with gabions and the Manning's n recommended by the manufacturer is n = 0.028.

   • What is the headwater depth (accuracy to 1 cm) required to pass the design discharge?

   • What is the tailwater depth, that is, the critical flow depth at the downstream boundary?

   [Hint: Use ONLINE_WSPROFILES_32].

3. (20%) Calculate the initial and sequent depths y₁ and y₂ of a hydraulic jump, given the unit-width discharge q = 0.1 m²/s, and the energy loss ΔE = 0.65 m. [Hint: Assume a low F₁, then calculate y₂/y₁, y₁, v₁ and a new F₁. Compare new value with assumed value; if different, increment F₁ a suitable amount and iterate, until a match is obtained].

4. (20%) An irrigation canal has a mean velocity u = 0.7 m/s, mean flow depth d = 1 m, and slope S = 0.005 m/m. Estimate the minimum time of gate opening T_o to avoid a surge.

5. (20%) You are observing the rising flood stage of a major river in a study reach AB of length L = 10 km. At your observation point at the downstream point B, the discharge is Q_B = 300 m³/s and the stage is rising at the rate of r_B = 3.2 mm/hr. The average surface width of the river in the study reach is W = 180 m. Estimate the present discharge at point A. How could this estimate be improved?