Wetted Perimeter Calculator

P — length of channel boundary in contact with the flowing fluid (free surface not included). Supports rectangular, trapezoidal, triangular, full/partial circular, and semi-circular sections.

Open Channel Flow · Pipe Flow

Inputs

Channel / pipe cross-section:

Dimension units:

Bottom width b (m)

Flow depth y (m)

Theory

Wetted perimeter formulas by shape:

Shape	P	Note
Rectangular	b + 2y	3 sides; top free surface excluded
Trapezoidal	b + 2y√(1+z²)	Bottom + 2 sloped sides
Triangular (V-notch)	2y√(1+z²)	b = 0; 2 sloped sides only
Circular (full)	πD	Full circumference, no free surface
Circular (partial)	D × arccos(1−2y/D)	Arc length only
Semi-circular	πD/2	Half circumference; flat top is free surface

Best hydraulic section (minimum P for given A):

Rectangle: b = 2y (half-square — width equals twice depth)

Trapezoid: z = 1/√3 ≈ 0.577 (60° side angle — half-hexagon)

Circle: full pipe is hydraulically most efficient

The best hydraulic section minimises wetted perimeter for a given area, which maximises R_h and therefore maximises discharge for given slope and roughness.

Circular pipe partial fill — key points:

Maximum R_h at y/D ≈ 0.81 (not at full pipe)

Maximum Q at y/D ≈ 0.94 (with Manning's equation)

Full pipe: R_h = D/4, P = πD