CIV E 530 - OPEN-CHANNEL HYDRAULICS SPRING 2008 - MIDTERM 2 - SOLUTION

PROBLEM 2

1. S_o = S_c F₁²

   F₁² = S_o / S_c = 0.004 / 0.004 = 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 = 2.699 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 - 0.741) / 0.004 = 564.75 m.    ANSWER.