Reynolds Number for Air Calculator
Air Reynolds number is calculated identically to other fluids, but air's viscosity and density depend strongly on temperature (via the Sutherland formula for viscosity and ideal...
Formula
Source: White, F.M. (2016) Fluid Mechanics 8th ed.; Sutherland (1893) | Last reviewed: July 3, 2026
Examples
5 velocity
= 65400 reynolds
- temperature = 20
- pressure = 14.7
- diameter = 200
Air at 5 m/s, 20°C, 1 atm, 200 mm duct → Re = 65,400 (turbulent)
10 velocity
= 55600 reynolds
- temperature = 200
- pressure = 14.7
- diameter = 100
Air at 10 m/s, 200°C, 1 atm, 100 mm duct → Re = 55,600
50 velocity
= 372000 reynolds
- temperature = 800
- pressure = 50
- diameter = 50
Hot air at 50 m/s, 800°C, 50 psia, 50 mm duct → Re = 372,000
Quick Reference Table
| T (°C) | ρ (kg/m³) | μ (Pa·s) | ν (m²/s) |
|---|---|---|---|
| -20 | 1.395 | 0.0000162 | 0.0000116 |
| 0 | 1.293 | 0.0000171 | 0.0000132 |
| 20 | 1.205 | 0.0000181 | 0.000015 |
| 40 | 1.127 | 0.000019 | 0.0000169 |
| 100 | 0.946 | 0.0000218 | 0.000023 |
| 200 | 0.747 | 0.0000261 | 0.000035 |
| 400 | 0.524 | 0.0000336 | 0.0000641 |
| 800 | 0.329 | 0.0000463 | 0.000141 |
Where is this used?
The viscosity of air is much lower than water (about 50x lower), so Re is much higher for the same geometry.
A 4-inch pipe at 100 CFM air has Re ≈ 1,000,000 — extremely turbulent.
This calculator uses the Sutherland formula for accurate viscosity across a wide temperature range, which is critical for high-temperature applications (gas turbine, furnace, engine).
Real-World Usage Scenarios
HVAC Duct Sizing Verification
An office building AHU serves a 12-inch round duct at 4,000 CFM. At 20°C and 1 atm: V = 4000 CFM × 0.000472 m³/s/CFM / (π × (0.305/2)²) = 9.7 m/s. D = 0.305 m. ρ = 1.205 kg/m³, μ = 1.81e-5 Pa·s. Re = 1.205 × 9.7 × 0.305 / 1.81e-5 = 197,000. The flow is highly turbulent, well into the regime where the friction factor is independent of Re (depends only on relative roughness). For galvanized steel duct (ε = 0.00015 m, ε/D = 0.0005), f ≈ 0.019.
Common Mistakes to Avoid
Using water viscosity for air
Water viscosity is 50x higher than air viscosity. A calculation that uses water μ for air gives Re off by 50x — usually over-predicting (claiming laminar flow when actually turbulent). Air flow in pipes is almost always turbulent.
Ignoring temperature effect
Air viscosity increases 2x from -20°C to 200°C. A calculation at 20°C gives Re that's 2x too high if the actual temperature is 200°C. This matters for high-temperature applications (engine intake, gas turbine, furnace). Use Sutherland formula for accurate μ across temperatures.
Industry Standards Referenced
Frequently Asked Questions
What is the Sutherland formula?
Sutherland's formula gives the dynamic viscosity of an ideal gas as a function of temperature: μ = μ₀ × (T/T₀)^1.5 × (T₀ + S) / (T + S). For air: μ₀ = 1.716e-5 Pa·s, T₀ = 273.15 K, S = 110.4 K. The formula is accurate to 1% from 100 K to 1000 K. For non-air gases, different S values apply (e.g., S = 194 K for N2, S = 138 K for CO2).
Is air flow in ducts always turbulent?
Almost always. Air viscosity is very low (1.81e-5 Pa·s at 20°C), so even small ducts with low velocity have Re >> 4,000. A 1-inch duct at 10 ft/min has Re ≈ 800 (laminar), but this is a very rare case. Typical HVAC ducts (Re > 100,000) and pneumatic systems (Re > 10,000) are all turbulent.
What is the Sutherland formula for air?
μ=μ₀×(T/T₀)^1.5×(T₀+S)/(T+S) where μ₀=1.716e-5 Pa·s, T₀=273.15K, S=110.4K. Accurate ±1% from -200°C to 800°C. More precise than lookup tables for specific temperatures.
Reviewed for accuracy
Cross-referenced against White's Fluid Mechanics and ASHRAE Handbook · Last reviewed: July 3, 2026
All calculations are for reference only. Always verify with manufacturer data and a qualified engineer for critical applications. Learn about our editorial process.