Fluid mechanicsMVP
Hydraulic diameter
Effective diameter of a rectangular channel, for use in Reynolds-number and resistance formulas.
Inputs
Result
Enter values and calculate to see the result.
Interpretation
Enter the channel width and height to get the hydraulic diameter — the single length scale that lets circular-pipe formulas apply to a rectangular channel.
Formula
Dₕ = 2wh / (w + h)
Equivalent to 4·Area / Perimeter for a rectangle (exact).
Variables
| Symbol | Variable | Unit |
|---|---|---|
| Dₕ | Hydraulic diameter | m |
| w | Channel width | m |
| h | Channel height | m |
Assumptions & validity
This tool assumes:
- Rectangular cross-section.
- Dₕ = 2wh/(w+h) is the exact specialisation of Dₕ = 4·Area/Perimeter to a rectangle.
Worked example
A channel is 100 µm wide and 50 µm tall.
Dₕ = 2 × 100 × 50 / (100 + 50) = 10000 / 150 ≈ 66.7 µm