CIV E 530 - OPEN-CHANNEL HYDRAULICS FALL 2019 - MIDTERM 2 - SOLUTION

PROBLEM 2

1. Find the upstream Froude number:

   f = S_c = S_o  (downstream) = 0.003

   S_o = S_c F₁²

   F₁² = S_o / S_c = 0.03 / 0.003 = 10

   F₁ = 3.16   ANSWER.

2. Find the upstream flow depth:

   F₁² = v²/(gy₁) = q²/(gy₁³) = 10

   y₁ = [q²/(10 g)]^1/3 = [(2.5)² /10 × 9.81)]^1/3 = 0.399 m.    ANSWER.

3. Find the downstream flow depth:

   F₂² = v²/(gy₂) = q²/(gy₂³) = 1

   y₂ = [q²/g]^1/3 = [(2.5)² / 9.81]^1/3 = 0.860 m.    ANSWER.

4. S_o = Δy/Δx

   Δx = Δy / S_o = (y₂ - y₁) / S_o = (0.860 - 0.399) / 0.003

   Δx = 153.67 m.   ANSWER.

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