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Air - Prandtl Number

Figures and table showing changes in Prandtl number for air with changes in temperature and pressure

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The Prandtl Number - Pr - is a dimensionless number approximating the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity - and is often used in heat transfer and free and forced convection calculations.

The Prandtl number can for calculations be expressed as

Pr =  μ cp / k                           (1)

where
μ = absolute or dynamic viscosity [kg/(m s)], [lbm/(ft h)]
cp = specific heat [J/(kg K)], [Btu/(lbm oF)]
k = thermal conductivity [W/(m K)], [Btu/(h ft2 oF/ft)]

Below, Prandtl numbers for air at varying temperatures and pressures are given in figures and tables.

See also other properties of Air at varying temperature and pressure: Density and specific weight at varying temperature, Density at varying pressure, Diffusion Coefficients for Gases in Air, Specific heat at varying temperature and Specific heat at varying pressureThermal ConductivityThermal Diffusivity, Properties at gas-liquid equilibrium conditions and Air thermophysical properties at standard conditions and Composition and molecular weight,
as well as Prandtl number of Ammonia, Carbon dioxide, Methane, Nitrogen, Propane and Water.

Air Prandtl number at 1 bara pressure, temperature given as °C or °F:


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Air Prandtl number at varying temperatures and constant pressures, SI and Imperial units:


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Air Prandtl number at 1 bara pressure, temperature given as °C or °F:

Temperature Pr Temperature Pr
[°C] [-] [°F] [-]
-100 0.734 -150 0.733
-50 0.720 -50 0.719
0 0.711 0 0.714
25 0.707 60 0.709
50 0.705 75 0.708
100 0.701 100 0.706
150 0.699 200 0.701
200 0.698 300 0.699
250 0.699 400 0.698
300 0.702 500 0.700

Air Prandtl number at given temperatures and 1, 5 10 and 20 bara presure:

Temperature Prandtl number at given pressures
[K] [°C] [°F] 1 bara,
14.5 psia
5 bara,
72.5 psia
10 bara,
145 psia
20 bara,
725 psia
60 -213.2 -351.7 4.138 4.153 4.170 4.187
80 -193.2 -315.7 1.7 2.252 2.259 2.269
100 -173.2 -279.7 0.780 0.898 1.783 1.770
120 -153.2 -243.7 0.759 0.806 0.890 1.360
140 -133.2 -207.7 0.747 0.773 0.812 0.923
180 -93.2 -135.7 0.731 0.743 0.759 0.792
200 -73.2 -99.7 0.726 0.735 0.745 0.769
220 -53.2 -63.7 0.721 0.728 0.736 0.754
240 -33.2 -27.7 0.717 0.722 0.729 0.742
260 -13.2 8.3 0.713 0.718 0.723 0.734
273 0.0 32.0 0.711 0.715 0.720 0.729
280 6.9 44.3 0.710 0.714 0.718 0.727
289 15.6 60.0 0.709 0.713 0.716 0.073
300 26.9 80.3 0.707 0.711 0.714 0.722
320 46.9 116.3 0.705 0.708 0.711 0.717
340 66.9 152.3 0.703 0.705 0.708 0.714
360 86.9 188.3 0.701 0.703 0.706 0.711
380 106.9 224.3 0.700 0.702 0.704 0.709
400 126.9 260.3 0.699 0.701 0.703 0.706
500 226.9 440.3 0.698 0.700 0.701 0.703
600 326.9 620.3 0.703 0.704 0.704 0.706
700 426.9 800.3 0.710 0.710 0.711 0.712
800 526.9 980.3 0.717 0.718 0.718 0.719
900 626.9 1160.3 0.724 0.725 0.725 0.725
1000 726.9 1340.3 0.730 0.730 0.730 0.731
1100 826.9 1520.3 0.734 0.735
1500 1226.9 2240.3 0.743 0.743
1900 1626.9 2960.3 0.742 0.742

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