Section 4: Soil and Water Conservation Engineering
Open Channel Hydraulics & Manning Equation
Subtopic: Conditions for most economical sections
Question Statement:
Which of the following conditions is/are satisfied for the most economical (most efficient) open channel cross-sections?
Options:
(A) For a rectangular channel of depth $y$ and width $b$, the most economical condition is $b = 2y$
(B) For a triangular channel, the most efficient vertex angle is $90^\circ$ (side slopes $1:1$)
(C) For a trapezoidal channel, the hydraulic radius $R = y/2$
(D) The wetted perimeter is minimized for a given cross-sectional area and bed slope
Answer Key:
A, B, C, D
Step-by-Step Solution & Explanation
All four conditions are canonical theorems of open channel design:
1. Rectangular: $b = 2y$, $R = y/2$.
2. Triangular: central angle $\theta = 90^\circ$ (side slope $z = 1$).
3. Trapezoidal: semi-hexagon with $R = y/2$ and side slope $60^\circ$ to horizontal.
4. Maximum discharge for given area corresponds mathematically to minimum wetted perimeter $P$.
Hence, A, B, C, D are all true.