Fluid Mechanics
Computes the hydraulic diameter (Dh = 4A/P) for circular, annular, rectangular, elliptical, triangular, and open-channel cross sections — the equivalent diameter used to apply circular-pipe Reynolds number, friction factor, and Nusselt number correlations to non-circular flow passages.
Cross Section
Cross section
Results
Flow area (A)
—
mm²
Wetted perimeter (P)
—
mm
Hydraulic diameter (Dh)
—
mm
Hydraulic Diameter — General Definition
A is the flow cross-sectional area; P is the wetted perimeter — the portion of the boundary actually in contact with the fluid. For closed conduits (circular, annular, rectangular, elliptical, triangular) P is the full perimeter. For open channels (trapezoidal, partially filled pipe) the free liquid surface is excluded from P.
Shape formula
D_h is a defined equivalent diameter, not an exact geometric quantity — substituting it for D in circular-pipe correlations (Re, Darcy friction factor, Nu) is a standard engineering approximation. Accuracy degrades for highly non-circular, re-entrant, or extreme-aspect-ratio sections; consult correlation-specific validity ranges (e.g. Gnielinski, Colebrook) before relying on D_h in a non-circular duct. Elliptical perimeter uses Ramanujan's second approximation (error < 0.04% for all aspect ratios). Source: Çengel & Cimbala, Fluid Mechanics: Fundamentals and Applications.