A trapezoidal section is of depth 'y', base 'B' and side slope 'Z'. Find the wetted perimeter of the trapezoidal section.
- A2y(1 + Z²)1/2
- BB + 2y(1 + Z²)1/2Correct
- CB + y(1 + Z²)1/2
- Dy(1 + Z²)1/2
Solution
Concept
Wetted perimeter is the length of the channel boundary in contact with water: the bed plus the two sloping sides.
Formula
P = B + 2y(1 + Z2)1/2
Step-by-step solution
1. With side slope Z:1 (H:V), each side goes Zy horizontally and y vertically. 2. Length of one sloping side = (y2 + Z2 y2)1/2 = y(1 + Z2)1/2. 3. There are two sides, so their length is 2y(1 + Z2)1/2. 4. Add the bed width B: P = B + 2y(1 + Z2)1/2.
Explanation
Water touches the bed and both sloping sides of the channel. Each side has length y(1 + Z²)1/2. So the wetted perimeter is B + 2y(1 + Z²)1/2.
Why the other options are wrong
A: Leaves out the bed width B. C: Counts only one sloping side. D: Gives only one sloping side and no bed.
Shortcut
P = bed + 2 × side length, where side length = y√(1+Z²).
Common mistake
Forgetting the bed width or taking only one side slope.
Correct answer: B) B + 2y(1 + Z²)^(1/2)