Formula
The friction factor is the Altshul–Tsal fit used in ASHRAE Fundamentals. With absolute roughness and hydraulic diameter in millimetres, f′ = 0.11 (ε/Dh + 68/Re)^0.25. If f′ is at least 0.018, f = f′. Otherwise f = 0.85 f′ + 0.0028. Pressure drop is the Darcy–Weisbach equation, f × (L/D) × ρ × V² / 2, at standard air: density 1.204 kg/m³ and kinematic viscosity 1.506×10⁻⁵ m²/s. One inch of water is 249.0889 Pa. The search finds the diameter whose loss per 100 ft matches the rate you set.
Δp = f · (L / D) · ρ · V² / 2
De = 1.30 · (a · b)^0.625 / (a + b)^0.25
The rectangular equivalent is Huebscher’s formula (1948), which ASHRAE still prints. A 12×12 square comes out near 13.1 inches round. Velocity is airflow divided by the actual free area, so a rectangle uses its own area, not the equivalent round. Medium-smooth galvanized is taken as 0.09 mm, the chart roughness. Average galvanized is 0.15 mm. Flex is entered as 3.0 mm so the penalty is visible. Standard sizes jump 4 through 10 by the inch, then even sizes through 24.
Worked examples
12 inch round at 0.10 in. wg per 100 ft, roughness 0.09 mm. The airflow is 709 CFM and the velocity is about 900 fpm. A Colebrook chart at the same standard air lists 710 CFM. This page stays inside 2% of that 710, and inside about 1% at this particular point. A different ductulator that prints 678 CFM is not the check.
100 CFM in a 6 inch round. Friction comes out near 0.085 in. wg per 100 ft. The same published table is 0.083. 1,000 CFM in a 12 inch round is near 0.188, against 0.189 on that table.
A 12 by 12 rectangle. Huebscher’s equivalent is 13.1 inches. Size a round first, then read the width that matches it at the height you typed.
Reference
Round capacity at 0.10 in. wg per 100 ft, roughness 0.09 mm, from this page’s equation.
| Round | CFM | Velocity |
|---|---|---|
| 6 in | 110 | 559 fpm |
| 8 in | 238 | 682 fpm |
| 10 in | 434 | 796 fpm |
| 12 in | 709 | 902 fpm |
| 14 in | 1,072 | 1,003 fpm |
Questions
How much air does a 12 inch round carry at 0.10 inch of water per 100 feet?
About 709 CFM on this page, at medium-smooth galvanized roughness of 0.09 mm. A published Colebrook friction chart lists 710 CFM for that point. The two agree within 1 percent. Another online ductulator prints 678 CFM. This page is checked against 710, not 678.
What is a reasonable friction rate?
Residential supply ducts are often planned around 0.08 to 0.10 inch of water per 100 feet. That is a design rate, not a code limit. The page defaults to 0.10.
Is the velocity a safe limit?
No. The page shows the velocity so you can compare it with the band you are designing to. Trunks are often planned near 900 feet per minute and branches near 700. Those are guidance figures. They are not a statement that a velocity is safe.
Sources
- ASHRAE Handbook — Fundamentals, duct design chapter: Altshul–Tsal friction factor, Darcy–Weisbach, standard air at 1.204 kg/m³ and 1.506×10⁻⁵ m²/s, and the roughness table (medium-smooth galvanized near 0.09 mm).
- Huebscher, C. “Friction Equivalents for Round, Square and Rectangular Ducts.” ASHVE Transactions 54 (1948). De = 1.30 (ab)^0.625 / (a+b)^0.25.
- Checked against a published Darcy–Colebrook friction chart that lists 710 CFM for 12 in at 0.10 in. wg per 100 ft (ε = 0.0003 ft, standard air). This page is within 2% of that 710, and within about 1% at 12 in. A chart that prints 678 CFM for the same point was not used.