Airflow and ducts
Equivalent diameter of a rectangular duct (Huebscher)
- where
- Huebscher equivalent diameter, same flow and friction (mm)
- duct width (mm)
- duct height (mm)
- hydraulic diameter, 4 × area / perimeter (mm)
Explain this equation
Finds the diameter of a round duct that carries the same airflow with the same friction loss per metre as a rectangular duct. Use it to read round-duct friction charts for rectangular ducts or to convert between shapes.
a and b are the rectangle's sides. D_e is Huebscher's equivalent diameter. D_h, the hydraulic diameter, is four times the area divided by the perimeter, simplified to 2ab/(a + b).
Huebscher fitted the powers 0.625 and 0.25 so that friction and flow both match; the round duct ends up slightly smaller in area than the rectangle. The hydraulic diameter matches friction only at equal velocity.
Sense check: 300 × 200 mm gives about 266 mm equivalent diameter, a little larger than the 240 mm hydraulic diameter. A square duct's equivalent diameter is about 1.09 times its side.
Watch out: don't mix the two diameters; use D_e with the total flow, D_h with the actual rectangular velocity.
The diameter of a round duct that has the same friction loss per metre at the same airflow as a rectangular duct. Use it to read friction charts or to swap between round and rectangular sizes.
Enter your values to see the result.
Good to know
The Huebscher equivalent diameter keeps both flow and friction the same, so a round duct of this size carries the same air at the same pressure drop per metre (at a slightly higher velocity). The hydraulic diameter 4A/P gives the same friction only at the same velocity; use it with the actual rectangular velocity in Darcy–Weisbach.
Common mistake
Using the hydraulic diameter with the round-duct flow on a friction chart, or using an equal-area diameter, both of which understate the friction in rectangular ducts.
Limits
Valid for normal aspect ratios (roughly up to 8:1). Flat-oval ducts have their own equivalent-diameter equation in ASHRAE Fundamentals chapter 21.
Sources
- ASHRAE Handbook — Fundamentals (2017), chapter 21 Duct design: Darcy–Weisbach and Colebrook equations, Huebscher equivalent diameter De = 1.30(ab)^0.625/(a + b)^0.25
- Engineering ToolBox: Equivalent diameter (Huebscher equation; 300 × 200 mm gives 266 mm, 300 × 500 mm gives 420 mm)
- CIBSE Guide C: Reference data (2007), chapter 1 (properties of humid air) and chapter 4 (flow of fluids in pipes and ducts)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the equipment manufacturer’s data, CIBSE guidance, BS EN 378, the F-gas Regulations and your company procedures. Refrigerant work needs the correct F-gas certification.