CIV E 530 - OPEN-CHANNEL HYDRAULICS SPRING 2004 - MIDTERM 1 - SOLUTION

PROBLEM 1

The specific energy principle:

y₁ + V₁²/(2g) = y₂ + V₂²/(2g)

From continuity:

V₁ = q/y₁

V₂ = q/y₂

y₁ + q²/(2gy₁²) = y₂ + q²/(2gy₂²)

[q²/(2g)] [(1/y₁²) - (1/y₂²)] = y₂ - y₁

[q²/(2g)] = (y₂ - y₁) / [(1/y₁²) - (1/y₂²)]

[q²/(2g)] = (y₂ - y₁) / [(y₂² - y₁²)/( y₁² y₂²)]

q²/(2g) = (y₁² y₂²) /(y₁ + y₂)

y_bar = (y₁ + y₂)/2

q= y₁ y₂ (g/y_bar)^1/2

y_bar = 0.25

q = 0.4 × 0.1 (9.81/0.25)^1/2

q = 0.25 m²/s   ANSWER.

Problem 2

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