Hydraulic Diameter Calculator

The equivalent diameter for a non-circular duct or channel — D_h = 4A / P — so you can use Reynolds number, friction factor and pressure-drop formulas that assume a round pipe.

Section

Units

Width a (in)

Height b (in)

Hydraulic diameter—

Making Round-Pipe Formulas Work on Any Shape

Reynolds number, friction factor and Darcy-Weisbach were all written for round pipe. Real ducts are rectangular, annular, or open channels. The hydraulic diameter is the trick that lets you keep using those formulas: it is the diameter of the round pipe that would behave the same way.

D_h = 4A / P

A is the flow cross-section area and P is the wetted perimeter — the length of wall actually touching the fluid. Compute D_h, then drop it straight into the pipe-flow equations in place of the diameter.

Hydraulic Radius Is Not Half the Diameter

The classic mistake. Hydraulic radius R_h = A / P, but hydraulic diameter is four times that, not two: D_h = 4 R_h. Open-channel work uses R_h; pipe-flow work uses D_h. Mixing them throws Reynolds and friction off by a factor of four.

Common Sections

Section	Hydraulic diameter
Circular (diameter D)	D
Square (side a)	a
Rectangle (a by b)	2ab / (a + b)
Concentric annulus	D_outer – D_inner
Open rectangular channel	4by / (b + 2y)

Frequently Asked Questions

What counts as wetted perimeter?

Only the boundary where fluid touches a solid wall. In a full duct that is the whole perimeter; in an open channel the free surface at the top is excluded.

Is it exact?

No — it is an engineering approximation that works well for turbulent flow in compact shapes. For laminar flow or very elongated sections, shape-specific corrections are more accurate.

Why does a round pipe give D_h = D?

Because 4 times (pi D-squared / 4) divided by (pi D) equals D. The formula is calibrated so the round-pipe case returns the actual diameter.

Related calculators

Reynolds Number Calculator — use D_h as the length scale.
Friction Factor Calculator — relative roughness uses D_h.
Pressure Drop Calculator — Darcy-Weisbach with the equivalent diameter.
Pipe Flow Calculator — flow and velocity for the section.

For education and preliminary design. The equivalent-diameter method is an approximation; for laminar flow, extreme aspect ratios or precise work, use shape-specific solutions.