The prandtl number of air is around 0.7 as many other gases at 1 atm.
The Prandtl Number is a dimensionless number approaching the proportion of momentum diffusivity and thermal diffusivity.
Prandtl number equation is defined as:
where:
ν is the kinematic viscosity, ν = μ / ρ.
μ is dynamic viscosity, (SI units: Pa s = N s/m2).
ρ is density, (SI units: kg/m3).
α is the thermal diffusivity, α = k / (ρ cp).
k is thermal conductivity, (SI units: W/m·K)
cp is specific heat, (SI units: J/kg·K)
ρ is density, (SI units: kg/m3).
The values of μ, cp and k are acknowledged to change with temperature consequently the Prandtl number will change with temperature.
The values of μ, cp and k are only very weak functions of pressure so the Prandtl number presumed independent of pressure.
Prandtl Number of Air
Prandtl Number of Dry air at 1 atm pressure:
Temp, C | Temp, F | Temp, K | Prandtl Number, Pr |
---|---|---|---|
-193.15 | -315.67 | 80 | mix |
-183.15 | -297.67 | 90 | 0.7960 |
-173.15 | -279.67 | 100 | 0.7860 |
-153.15 | -243.67 | 120 | 0.7730 |
-133.15 | -207.67 | 140 | 0.7630 |
-113.15 | -171.67 | 160 | 0.7540 |
-93.15 | -135.67 | 180 | 0.7450 |
-73.15 | -99.67 | 200 | 0.7380 |
-33.15 | -27.67 | 240 | 0.7240 |
6.85 | 44.33 | 280 | 0.7100 |
26.85 | 80.33 | 300 | 0.7050 |
76.85 | 170.33 | 350 | 0.6990 |
126.85 | 260.33 | 400 | 0.6940 |
176.85 | 350.33 | 450 | 0.6910 |
226.85 | 440.33 | 500 | 0.6890 |
326.85 | 620.33 | 600 | 0.6900 |
426.85 | 800.33 | 700 | 0.6960 |
526.85 | 980.33 | 800 | 0.7050 |
626.85 | 1160.33 | 900 | 0.7090 |
726.85 | 1340.33 | 1000 | 0.7110 |
Note: For ideal gases, the properties cp, k, m, and Pr are independent of pressure.
Prandtl number of air (dry Air) Table at temperature between 70 deg C and 2000 deg C :
Temp, C | Temp, F | Temp, K | Prandtl |
---|---|---|---|
Number, Pr | |||
70 | 158 | 343.15 | 0.7177 |
80 | 176 | 353.15 | 0.7154 |
90 | 194 | 363.15 | 0.7132 |
100 | 212 | 373.15 | 0.7111 |
120 | 248 | 393.15 | 0.7073 |
140 | 284 | 413.15 | 0.7041 |
160 | 320 | 433.15 | 0.7014 |
180 | 356 | 453.15 | 0.6992 |
200 | 392 | 473.15 | 0.6974 |
250 | 482 | 523.15 | 0.6946 |
300 | 572 | 573.15 | 0.6935 |
350 | 662 | 623.15 | 0.6937 |
400 | 752 | 673.15 | 0.6948 |
450 | 842 | 723.15 | 0.6965 |
500 | 932 | 773.15 | 0.6986 |
600 | 1112 | 873.15 | 0.7037 |
700 | 1292 | 973.15 | 0.7092 |
800 | 1472 | 1073.15 | 0.7149 |
900 | 1652 | 1173.15 | 0.7206 |
1000 | 1832 | 1273.15 | 0.7260 |
1500 | 2732 | 1773.15 | 0.7478 |
2000 | 3632 | 2273.15 | 0.7539 |
Note: For ideal gases, the properties cp, k, m, and Pr are independent of pressure.
Prandtl Number of Air @ Different Pressure
Temp, C | Temp, F | 10 bar | 30 bar | 50 bar | 70 bar | 100 bar |
---|---|---|---|---|---|---|
-193.15 | -315.67 | 2.32 | 2.37 | 2.42 | 2.48 | 2.57 |
-183.15 | -297.67 | 1.77 | 1.79 | 1.82 | 1.85 | 1.91 |
-173.15 | -279.67 | 1.54 | 1.53 | 1.53 | 1.53 | 1.55 |
-153.15 | -243.67 | 0.89 | 1.65 | 1.48 | 1.4 | 1.34 |
-133.15 | -207.67 | 0.82 | 1.2 | 2.14 | 2.07 | 1.52 |
-113.15 | -171.67 | 0.78 | 0.92 | 1.13 | 1.37 | 1.72 |
-93.15 | -135.67 | 0.763 | 0.83 | 0.932 | 1.07 | 1.25 |
-73.15 | -99.67 | 0.749 | 0.788 | 0.841 | 0.9 | 1 |
-33.15 | -27.67 | 0.729 | 0.746 | 0.767 | 0.8 | 0.82 |
6.85 | 44.33 | 0.713 | 0.721 | 0.731 | 0.742 | 0.76 |
26.85 | 80.33 | 0.708 | 0.715 | 0.721 | 0.728 | 0.742 |
76.85 | 170.33 | 0.699 | 0.703 | 0.707 | 0.711 | 0.716 |
126.85 | 260.33 | 0.694 | 0.696 | 0.698 | 0.7 | 0.704 |
176.85 | 350.33 | 0.691 | 0.692 | 0.693 | 0.694 | 0.696 |
226.85 | 440.33 | 0.689 | 0.689 | 0.69 | 0.69 | 0.691 |
326.85 | 620.33 | 0.69 | 0.689 | 0.689 | 0.689 | 0.69 |
426.85 | 800.33 | 0.695 | 0.695 | 0.695 | 0.695 | 0.695 |
526.85 | 980.33 | 0.704 | 0.704 | 0.703 | 0.703 | 0.702 |
626.85 | 1160.33 | 0.708 | 0.708 | 0.708 | 0.708 | 0.708 |
726.85 | 1340.33 | 0.711 | 0.711 | 0.71 | 0.71 | 0.709 |
Prandtl Number of Air @ Different Temperature
280 K | 300K | 500K | 1000 K | |
---|---|---|---|---|
1 | 0.71 | 0.705 | 0.689 | 0.711 |
5 | 0.711 | 0.707 | 0.689 | 0.711 |
10 | 0.713 | 0.708 | 0.689 | 0.711 |
20 | 0.717 | 0.712 | 0.689 | 0.711 |
30 | 0.721 | 0.715 | 0.689 | 0.711 |
40 | 0.726 | 0.717 | 0.69 | 0.71 |
50 | 0.731 | 0.721 | 0.69 | 0.71 |
60 | 0.737 | 0.725 | 0.69 | 0.71 |
70 | 0.742 | 0.728 | 0.69 | 0.71 |
80 | 0.75 | 0.732 | 0.691 | 0.709 |
90 | 0.75 | 0.737 | 0.691 | 0.709 |
100 | 0.76 | 0.742 | 0.691 | 0.709 |
Prandtl number of Humid air
Prandtl number of moist air with a relative humidity (RH) varying between 0% and 100%
References:
Thermophysical and transport properties of humid air at temperature range between 0 and 100 C P.T. Tsilingiris *
https://www.researchgate.net/profile/Ingo_Riess/post/What_should_be_the_viscosity_of_Air_Water_Mixture/attachment/5acb4c45b53d2f63c3c4b633/AS%3A613464624070664%401523272772980/download/2007_Properties+of+humid+air.pdf