CIV E 530 - OPEN-CHANNEL HYDRAULICS SPRING 2006 - MIDTERM 2 - SOLUTION

PROBLEM 2

1. S_o = S_c F₁²

   F₁² = S_o / S_c = 0.005 / 0.005 = 1

   F₁ = 1   ANSWER.

2. F₁² = v²/(gy₁) = q²/(gy₁³) = 1

   y₁= (q²/g)^1/3 = (1²/9.81)^1/3 = 0.467 m.    ANSWER.

3. v₁²/(gy₁) = 1

   v₁= (gy)^1/2 = (9.81 × 0.467)^1/2 = 2.14 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 = (2.0 - 0.467) / 0.005 = 306.6 m.    ANSWER.