Final answer:
To determine which channel design requires less wood for lining - triangular or rectangular - the wetted perimeters for each design must be calculated, and the one with the smaller wetted perimeter will be more material-efficient.
Step-by-step explanation:
The question deals with the design of a wooden-lined channel for water conveyance and the determination of which design would require less lining material. To compare the amount of wood needed for triangular and rectangular channels, one must calculate the surface areas of wood in contact with the water for both designs. For a symmetrical triangular channel with a 90° center angle, the sides at the water level will be equal, and the surface area of wood in contact with the water will be equivalent to two side lengths (since the base does not require lining). The rectangular channel with a sill width equal to the height will have a perimeter that includes the base and the two sides. The comparison requires the application of trigonometry and geometry to determine the dimensions that will convey a flow of 2 m/s on a slope of 1/80 m/m.
To minimize the wood used, the design with the smallest wetted perimeter for a given cross-sectional area of flow should be chosen. The percentage difference between the two designs can then be calculated by comparing the wetted perimeters or the surface areas of wood required for each design.