Kinematic Viscosity of Air Calculator

Background.

Water is about 55 times more viscous than air at 20 °C, yet by the measure that matters for most flow problems the order flips: air's kinematic viscosity, about 1.5 × 10⁻⁵ m²/s, is fifteen times water's. The reason is density. Kinematic viscosity divides a fluid's resistance to shearing, its dynamic viscosity μ, by how much mass there is to move, its density ρ. Air is very light, so the little viscosity it has goes a long way.

That quotient, ν = μ ⁄ ρ, is the number that sits in the denominator of a Reynolds number, Re = vL ⁄ ν, and so it decides whether the air over a wing, through a duct or around a chimney flows smoothly or turns turbulent. It is also not a constant. It rises steeply with temperature and is inversely proportional to pressure, so a value copied from a sea-level table can be badly off for a hot exhaust, a pressurised line or air at altitude.

The calculator builds ν from two textbook models. Sutherland's 1893 formula gives the dynamic viscosity of air from its absolute temperature alone, and the ideal-gas law gives its density from temperature and pressure. Enter the absolute temperature in kelvin and the absolute pressure in pascals, and it returns the kinematic viscosity in square metres per second, together with a note on what the model covers.

The model describes dry air behaving as an ideal gas. It does not adjust for humidity, for the departures from ideal behaviour that appear at high pressure, for changes in composition at extreme temperatures, or for gas so thin that it stops acting as a continuous fluid. Within ordinary engineering conditions, from cold winter air to hot ducts, at pressures from high altitude up to a few atmospheres, it is the standard way to get the value a Reynolds number needs.

What is kinematic viscosity of air calculator?

Kinematic viscosity ν is dynamic viscosity divided by density. Dynamic viscosity, in pascal-seconds, measures the shear stress needed to keep neighbouring layers of fluid sliding past each other at a given rate. Dividing by density, in kilograms per cubic metre, gives a quantity in square metres per second, the same units as a diffusion coefficient, and that is the best way to picture it: ν is how quickly momentum spreads sideways through the fluid, just as heat or a dissolved dye would. Where ν is large, a disturbance in velocity is smoothed out quickly; where it is small, inertia dominates and flows break up into turbulence more easily. The older unit is the stokes, 1 cm²/s or 10⁻⁴ m²/s, and lubricant data often use the centistokes, 10⁻⁶ m²/s. For air near room temperature ν is about 15 to 16 centistokes; at 15 °C and standard sea-level pressure it is about 1.4607 × 10⁻⁵ m²/s.

Which of the two viscosities a calculation needs depends on the question. Forces and stresses use the dynamic viscosity: the shear stress on a surface, the drag on a slowly settling particle, the pressure drop that Hagen and Poiseuille's law gives for laminar pipe flow. Questions about flow regime, how far momentum diffuses and when inertia overwhelms friction, use the kinematic viscosity, which is why it is the one inside the Reynolds number.

How to use this calculator.

1. 01Enter the absolute temperature in kelvin: add 273.15 to a Celsius reading, so a 25 °C room is 298.15 K. For Fahrenheit, add 459.67 and multiply by 5 ⁄ 9.
2. 02Enter the absolute pressure in pascals. Standard sea level is 101,325 Pa. A gauge reading must have atmospheric pressure added, so a line at 2 bar gauge holds about 301,325 Pa absolute.
3. 03For a site at altitude, use the actual local pressure, not the sea-level-corrected figure a weather report gives. At the 11,000 m of the standard atmosphere's tropopause, pressure is about 22,632 Pa and temperature 216.65 K.
4. 04Read ν in m²/s. Multiply by 10⁶ for centistokes or by 10.7639 for square feet per second.
5. 05Use the value in Re = vL ⁄ ν, with the velocity in m/s and the characteristic length in metres, both measured for the same flow.

The formula.

ν = μ₀ × (T ⁄ T₀)^1.5 × (T₀ + S) ⁄ (T + S) × R × T ⁄ p

The first part is Sutherland's law for the dynamic viscosity μ. Simple kinetic theory treats gas molecules as hard spheres and predicts that viscosity grows with the square root of temperature, because faster molecules carry momentum between layers more quickly. Real molecules also attract each other weakly, which makes slow, cold molecules behave as if they were larger. William Sutherland captured that with a single extra constant, S. The constants used here are μ₀ = 1.716 × 10⁻⁵ Pa·s at the reference temperature T₀ = 273.15 K and S = 110.4 K, the same S that NASA's Glenn Research Center gives in imperial form as 198.72 °R.

Pressure does not appear in μ. Compressing a dilute gas puts more molecules in each layer to carry momentum, but each travels a proportionally shorter distance between collisions, and the two effects cancel. Maxwell predicted this from kinetic theory, and experiment bore it out over a wide range of ordinary pressures.

The second part is the ideal-gas density, ρ = p ⁄ (R × T), with the specific gas constant for dry air R = 287.058 J ⁄ (kg·K). Dividing μ by ρ is the same as multiplying by R × T ⁄ p, which is how both pieces end up in one line.

The result scales exactly as 1 ⁄ p: halve the pressure and ν doubles. Temperature acts twice, raising μ and lowering ρ together, so near room temperature ν grows roughly as T^1.77. Between 300 K and 600 K at one atmosphere, μ rises by a factor of about 1.63 while ν rises by about 3.27.

The equation will return a number for any positive temperature and pressure, including values far outside what it describes. It has no meaning near or below the temperatures at which air's nitrogen and oxygen liquefy, about 77 K and 90 K at atmospheric pressure; at pressures high enough for air to depart from ideal-gas behaviour; at the very high temperatures where molecules start to dissociate; or in gas so rarefied that molecules travel distances comparable to the object in the flow.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NASA Glenn Research Center, Viscosity.
2. [2]NIST Chemistry WebBook, Thermophysical Properties of Fluid Systems.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.
4. [4]NIST Special Publication 811, Guide for the Use of the International System of Units, 2008 edition.
5. [5]NASA Glenn Research Center, Equation of State.