CIV E 530 - OPEN-CHANNEL HYDRAULICS FALL 2011 - MIDTERM 2 - SOLUTION

PROBLEM 1

1. S_o = S_c F₁²

   F₁² = S_o / S_c = 0.0025 / 0.0025 = 1

   F₁ = 1   ANSWER.

2. F₁² = v²/(gy₁) = q²/(gy₁³) = 1

   y₁ = (q²/g)^1/3 = (2²/9.81)^1/3 = 0.741 m.    ANSWER.

3. v₁ = q / y₁ = 2 / 0.741 = 2.697 m/s    ANSWER.

4. Because the u/s flow is critical, the water-surface flow profile type is C₁.    ANSWER.

5. S_o = Δy/Δx

   Δx = Δy / S_o = (y₂ - y₁) / S_o = (3.5 - 0.741) / 0.0025

   Δx = 1103.6 m.    ANSWER.