Airflow and ducts
Straight duct pressure drop (Darcy–Weisbach with Colebrook)
- where
- mean air velocity (m/s)
- air volume flow rate (m³/s)
- internal or equivalent duct diameter (mm)
- Reynolds number
- air density (kg/m³)
- dynamic viscosity of air (µPa·s)
- Darcy friction factor (Colebrook–White, solved by iteration; 64/Re if laminar)
- absolute roughness of the duct surface (mm)
- pressure loss per metre (Pa/m)
- pressure loss over the length (Pa)
- straight duct length (m)
Explain this equation
Works out the friction pressure loss along straight round ductwork. Use it to build up the index-run pressure for fan selection.
v is the mean velocity from flow and area. Re, the Reynolds number, compares the air's momentum with its viscosity; above about 4000 the flow is turbulent. f, the friction factor, depends on Re and on the roughness k relative to the diameter, and is found from the Colebrook–White equation by trial until both sides agree. R is the loss per metre and Δp the loss over length L.
Darcy–Weisbach says friction loss is proportional to velocity pressure (ρv²/2) and to length over diameter. The 1000 factors convert millimetres to metres.
Sense check: 0.2 m³/s in a 200 mm galvanised duct is about 2.6 Pa/m; a 500 mm duct at 3 m/s is about 0.2 Pa/m. Doubling the velocity roughly quadruples the loss.
Watch out: fittings often add more than the straight duct; add them separately.
Friction pressure loss along a straight run of round duct, using the Darcy–Weisbach equation with the Colebrook–White friction factor that underlies CIBSE and ASHRAE duct friction charts.
Enter your values to see the result.
Good to know
k = 0.15 mm is the usual value for galvanised sheet steel ductwork. Smoother plastic ducts are nearer 0.01 mm; flexible ducts are much rougher and should be kept short. Air at 20 °C has ρ ≈ 1.2 kg/m³ and µ ≈ 18.1 µPa·s. Low-velocity systems are often designed around 1 Pa/m. Add fitting losses (ζ × 0.6 v²) separately.
Common mistake
Forgetting fittings: bends, tees, dampers and terminals often account for more pressure loss than the straight duct.
Limits
Fully developed turbulent flow in straight duct. Fittings, filters, coils and terminals are not included. For rectangular ducts enter the Huebscher equivalent diameter with the actual flow.
Sources
- CIBSE Guide C: Reference data (2007), chapter 1 (properties of humid air) and chapter 4 (flow of fluids in pipes and ducts)
- P. Koch, “Chapter and verse”, Building (CIBSE Guide C chapter 4 revision: Colebrook–White friction for pipes and ducts)
- CIBSE Journal CPD Module 31: Airflow pressure drop in HVAC ductwork (air density 1.2 kg/m³, viscosity about 18 × 10⁻⁶ kg/m s; 0.50 m duct at 3 m/s: Re = 1 × 10⁵, about 0.21 Pa/m)
- 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: Surface roughness of ventilation ducts (galvanised steel k = 0.15 mm)
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.