Hydraulic Diameter Calculator

Calculate hydraulic diameter, flow area, and wetted perimeter for two common internal-flow sections.

Engineering screening tool—verify inputs and results independently. Use at your own risk.

Cross-section dimensions

Use one unit for every dimension. The area result uses that unit squared.

Hydraulic diameter, D_h

13.33mm

Fully wetted rectangle

Flow area, A200.00 mm²

Wetted perimeter, S60.00 mm

Blue regions are flow area; every outlined boundary is wetted.

How to use

Select Fully wetted rectangle or Concentric annulus.
Select one length unit, then enter both required dimensions in that unit. For an annulus, keep 0 ≤ d < D.
Select Calculate to update D_h, A, and S. Valid input edits also update the result automatically.
Select Reset to restore the rectangle mode, mm, and the default dimensions.
Use D_h only in a correlation that explicitly supports hydraulic diameter. Check area and wetted perimeter before carrying the result forward.
Correct any warning before using a result. Do not use these fixed modes for partially filled channels, eccentric annuli, deforming passages, or methods that require a different characteristic length.

Worked example

For a fully wetted rectangular duct with a = 10 mm and b = 20 mm, the calculator gives A = 200.00 mm², S = 60.00 mm, and D_h = 13.33 mm. This equivalent diameter may be passed to a compatible internal-flow screening correlation.

Equations used

D_h = 4A/S

D_h is hydraulic diameter, A is open cross-sectional flow area normal to the flow, and S is the wetted solid-boundary perimeter.

Fully wetted rectangle:

A = ab; S = 2(a+b); D_h = 2ab/(a+b)

a and b are the two positive internal side lengths. All four walls are wetted.

Concentric annulus:

A = π(D²−d²)/4; S = π(D+d); D_h = D−d

D is the positive inside diameter of the outer boundary; d is the nonnegative outside diameter of the inner pipe, with d < D. π is the circle constant. Both circular boundaries are wetted.

Theory and method

Hydraulic diameter converts flow area and wetted perimeter into the characteristic length used by many internal-flow Reynolds-number, friction, and heat-transfer correlations. It equals the physical diameter for a full circular pipe. For noncircular passages it is an equivalence parameter, not a claim that the section is circular.

The model assumes fully filled internal flow, rigid geometry, one consistent unit, four wetted rectangle walls, and concentric annulus boundaries. It does not calculate roughness, Reynolds number, friction factor, entrance or fitting losses, pressure drop, flow rate, or heat transfer. For a partially filled open channel, S must include only the boundary actually touching the fluid; that geometry is outside these two modes.

Reference: the standard internal-flow definition D_h = 4A/S used in fluid-mechanics and heat-transfer correlations.