Formula used
Hydraulic diameter converts a non-circular passage into an equivalent diameter for common internal-flow relationships. It uses the flowing area and only the boundary touching the fluid. The free surface is excluded for open channels.
How to use this calculator
- Select the passage shape that matches your pipe, duct, annulus, or open channel.
- Enter every required dimension and choose its unit.
- Enable flow analysis when Reynolds number, friction factor, head loss, or pressure drop is needed.
- Select output precision and the preferred diameter unit.
- Calculate, review the substituted formula, then copy or export the results.
Shape formulas and example data
| Shape | Area | Wetted perimeter | Hydraulic diameter | Example |
|---|---|---|---|---|
| Rectangular duct | W × H | 2(W + H) | 2WH / (W + H) | 600 mm × 300 mm |
| Square duct | S² | 4S | S | 400 mm side |
| Concentric annulus | π(Dₒ² − Dᵢ²)/4 | π(Dₒ + Dᵢ) | Dₒ − Dᵢ | 100 mm and 60 mm |
| Open rectangle | by | b + 2y | 4by / (b + 2y) | 2 m wide, 0.5 m deep |
| Trapezoidal channel | y[b + (z₁ + z₂)y/2] | b + y√(1+z₁²) + y√(1+z₂²) | 4A/Pᵥ | b = 2 m, y = 0.8 m, z = 1.5 |
| Partially filled pipe | Circular segment | Wetted arc length | 4A/Pᵥ | D = 1 m, depth = 0.6 m |
Understanding hydraulic diameter
Hydraulic diameter is an equivalent length used for non-circular internal flow. It allows Reynolds number and Darcy-Weisbach calculations to use familiar pipe-flow equations. It does not mean the passage is physically circular.
Wetted perimeter includes every boundary segment directly touching the moving fluid. For a closed duct, the complete internal perimeter is normally wetted. For an open channel, exclude the exposed water surface.
Hydraulic radius equals area divided by wetted perimeter, while hydraulic diameter equals four hydraulic radii. Both quantities describe how much flow area exists relative to boundary contact. Their distinction is important in hydraulic design work.
Equivalent-diameter methods work best where flow is reasonably developed and geometry remains uniform. Strong secondary flows, abrupt transitions, or extreme aspect ratios may reduce accuracy. Detailed computational or experimental analysis may then be necessary.
Frequently asked questions
What is hydraulic diameter?
It is four times the flow area divided by the wetted perimeter.
Is hydraulic diameter the same as pipe diameter?
Only for a completely filled circular pipe. Other shapes usually produce a different equivalent diameter.
What is wetted perimeter?
It is the length of the cross-section boundary that directly contacts the fluid.
Should an open-channel free surface be included?
No. The free surface is not part of the wetted perimeter.
Why is hydraulic diameter used in Reynolds number?
It provides an equivalent characteristic length for non-circular flow passages.
How is an annulus calculated?
For concentric circular surfaces, hydraulic diameter equals the outer diameter minus the inner diameter.
Can this calculator handle mixed units?
Yes. Each geometry input can use its own supported length unit.
How is friction factor estimated?
Laminar flow uses 64/Re. Higher Reynolds numbers use the Haaland approximation.
Are pressure-loss results exact?
They are engineering estimates and depend on reliable fluid properties, roughness, geometry, and fully developed flow assumptions.