Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Flow in open channels
Question Statement:
Which of the following statements are TRUE regarding the most hydraulically efficient trapezoidal channel section?
Options:
(A) The hydraulic radius $R$ is equal to half the flow depth ($y / 2$)
(B) The side slope angle with the horizontal is $60^\circ$ ($m = 1/\sqrt{3}$)
(C) The top width is equal to the sum of the two side slopes
(D) The hydraulic depth is equal to twice the flow depth
Answer Key:
A, B, C
Step-by-Step Solution & Explanation
For the most economical/efficient trapezoidal channel section:
1. Hydraulic radius $R = y / 2$ (Option A is TRUE).
2. Side slopes make an angle of $60^\circ$ with the horizontal, meaning side slope ratio $z = 1/\sqrt{3}$ (Option B is TRUE).
3. A semicircle drawn with center at the water surface and radius $y$ touches the three sides, which leads to top width $T = 2 \times (\text{sloping side length}) / 2 = \text{sum of side slope lengths}$ (Option C is TRUE).
4. Hydraulic depth $D = A/T \ne 2y$; it is $0.75 y$ (Option D is FALSE).