ANS:D - half hexagon in the form of trapezoid.

The most efficient channel section depends on various factors including the hydraulic conditions, available space, and construction constraints. However, among the options provided, the semi-circular channel section is often considered the most efficient. Semi-circular channels offer several advantages:

1. Hydraulic Efficiency: The semi-circular shape provides a smooth flow path with minimal resistance to flow. This reduces energy losses due to friction and improves hydraulic efficiency.
2. Uniform Flow: The shape of the semi-circular channel promotes more uniform flow velocities across the cross-section, reducing the likelihood of flow separation and turbulence.
3. Structural Stability: The semi-circular shape distributes hydraulic forces evenly along its perimeter, enhancing structural stability and reducing the risk of erosion or scouring.
4. Erosion Resistance: The smooth and continuous curvature of the semi-circular channel minimizes the potential for erosion and sediment deposition, leading to longer-term stability.

While rectangular, triangular, and trapezoidal channels are also commonly used and may be suitable for specific applications, the semi-circular channel is often preferred for its hydraulic efficiency and stability, especially in situations where maintaining a constant flow rate and minimizing energy losses are important considerations.