For a triangular section with depth y and side slope Z, the wetted perimeter can be calculated using the following formula:
Wetted Perimeter (P) = 2y(1 + Z2)^0.5
Where:
y = depth of the triangular section
Z = side slope (horizontal distance/vertical distance)
1 + Z2 is under the square root
Derivation:
In a triangular section, if the depth is y and the side slope is Z:
- The horizontal distance from the vertical centerline to the sloped side is Z × y
- The sloped side length = (y2 + (Zy)2)^0.5 = y(1 + Z2)^0.5
- Since there are two sloped sides, total sloped perimeter = 2y(1 + Z2)^0.5
- The bottom (wetted bed) is zero for an ideal triangular section
Therefore, the wetted perimeter of a triangular section = 2y(1 + Z2)^0.5
This formula is used in hydraulic calculations for open channel flow analysis.