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

PROBLEM 2

1. Find the upstream Froude number:

   f = S_c = S_o  (downstream) = 0.004

   S_o = S_c F₁²

   F₁² = S_o / S_c = 0.016 / 0.004 = 4

   F₁ = 2   ANSWER.

2. Find the upstream flow depth:

   F₁² = v²/(gy₁) = q²/(gy₁³) = 4

   y₁ = [q²/(4 g)]^1/3 = [2.4² /(4 × 9.81)]^1/3 = 0.527 m.    ANSWER.

3. Find the downstream flow depth:

   F₂² = v²/(gy₂) = q²/(gy₂³) = 1

   y₂ = [q²/g]^1/3 = [2.4² /9.81]^1/3 = 0.837 m.    ANSWER.

4. S_o = Δy/Δx

   Δx = Δy / S_o = (y₂ - y₁) / S_o = (0.837 - 0.527) / 0.004

   Δx = 77.5 m.   ANSWER.

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