Engineering & Scientific
Sutherland’s Law for Temperature-Dependent Gas Dynamic Viscosity
Model gas dynamic viscosity mu(T) across wide Kelvin temperature spans using Sutherland’s three-coefficient molecular-potential law for HVAC, flue-gas, and aerodynamic Reynolds numbers.
Why gas viscosity rises with temperature and departs from simple T^0.5 hard-sphere theory
Unlike liquids—whose viscosity drops exponentially as heating overcomes intermolecular cohesion—dilute gas viscosity increases with temperature because faster thermal molecular motion transfers more momentum across shear layers. Elementary hard-sphere kinetic theory predicts mu proportional to T^0.5, which underpredicts real gas viscosity growth because attractive intermolecular forces deflect slow-moving cold molecules into wider collision cross-sections.
William Sutherland’s (1893) kinetic-potential correction adds a gas-specific Sutherland temperature S (120 K for dry air, 111 K for nitrogen, 127 K for oxygen): mu(T) = mu_0 * (T / T_0)^(1.5) * ((T_0 + S) / (T + S)), accurate within ~1–2% from 170 K to 1,500 K.
| Dry Air Parameter | Symbol / Cell | Value | Units |
|---|---|---|---|
| Reference Viscosity | mu_0 (B2) | 18.27 | uPa*s (at 291.15 K) |
| Reference Temperature | T_0 (B3) | 291.15 | Kelvin (18.0 °C) |
| Sutherland Constant (Air) | S (B4) | 120.00 | Kelvin |
| Operating Temperature | T (B5) | 500.00 | Kelvin -> mu = 27.27 uPa*s |
Sutherland’s Dynamic Viscosity Formula
Multiply reference viscosity mu_0 by (T / T_0)^1.5 and the Sutherland collision-cross-section factor (T_0 + S) / (T + S).
=ROUND(B2 * ((B5 / B3) ^ 1.5) * ((B3 + B4) / (B5 + B4)), 2)Kinematic Viscosity nu = mu / rho at Ideal-Gas Density
Convert micro-Pascal-seconds (10^-6 Pa*s) to kinematic viscosity in mm^2/s (centistokes) by dividing by gas density rho (kg/m^3): (mu_uPas * 10^-6 / rho) * 10^6 simplifies cleanly to mu_uPas / rho.
=ROUND(E2 / B6, 2)Try the example
Use the original values or change them to test your understanding.