Section 4: Soil and Water Conservation Engineering
Open Channel Flow
Subtopic: Most Economical Section
Question Statement:
For a trapezoidal open channel section with side slopes $1:m$ (horizontal : vertical), the most hydraulically efficient cross-section corresponds to a side slope angle of:
Options:
(A) 60^\circ \text{ to horizontal (half-hexagon)}
(B) 45^\circ \text{ to horizontal}
(C) 30^\circ \text{ to horizontal}
(D) 90^\circ \text{ to horizontal (vertical sides)}
Answer Key:
A
Step-by-Step Solution & Explanation
The most efficient trapezoidal channel forms a half regular hexagon with side slope angle $\theta = 60^\circ$ ($m = 1/\sqrt{3} \approx 0.577$), minimizing wetted perimeter for a given flow area.