Irrigation Water Conveyance and Application Methods
Subtopic: Design of irrigation channels and underground pipelines
Question Statement:
Which of the following geometric and hydraulic conditions satisfy the criteria for the MOST ECONOMIC (hydraulically efficient) trapezoidal open channel section?
Options:
(A) The hydraulic radius $R$ is equal to half of the flow depth ($R = y/2$)
(B) The top water surface width is equal to twice the sloping side length ($T = 2 \cdot \text{side}$)
(C) A semi-circle can be inscribed tangent to the bed and both side slopes
(D) The side slope makes an angle of $60^\circ$ with the horizontal ($1:\sqrt{3}$ slope) for minimum wetted perimeter
Answer Key:
A, B, C, D
Step-by-Step Solution & Explanation
1. For the most economical trapezoidal section, hydraulic radius $R = \frac{A}{P} = \frac{y}{2}$. (Statement A is True)
2. The top width $T = 2 y \sqrt{1 + m^2} = 2 \times$ (sloping side length). (Statement B is True)
3. A semi-circle with center at the water surface and radius equal to flow depth $y$ is tangent to the bottom and sides. (Statement C is True)
4. For a trapezoidal section with variable side slopes, the wetted perimeter is minimized when the cross-section forms a regular half-hexagon, where side slopes are at $60^\circ$ to the horizontal ($m = 1/\sqrt{3}$). (Statement D is True)