PROPERTIES OF THE ATMOSPHERE

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1. International Standard Atmosphere

1.1 Sea Level Conditions

Pressure

101.3 kPa

2116.7 lbf/ft2

Density

1.225 Kg/m3

0.002378 slug/ft3

Temperature

15 oC 288.2 K

59 oF 518 oR

Speed of Sound

340.3 m/s

1116.4 ft/s

Viscosity

1.789 x 10-5 Kg/m/s

3.737 x 10-7 slug/ft/s

Kinematic Viscosity

1.460x10-5 m2/s

1.5723x10-4 ft2/s

Thermal Conductivity

0.02596 W/m/K

0.015 BTU/hr/ft/oR

Gas Constant

287.1 J/Kg/K

1715.7 ft lbf/slug/oR

Specific Heat Cp

1005 J/Kg/K

6005 ft lbf/slug/oR

Specific Heat Cv

717.98 J/Kg/K

4289 ft lbf/slug/oR

Ratio of Specific Heats

1.40


Gravitational Acceleration

9.80665 m/s2

32.174 ft/s2

1.2 Variation with Altitude

 

Figure 1 : Atmospheric temperature at different altitudes

Figure 2 : Troposphere and Stratosphere

Pressure, temperature, density, viscosity and speed of sound variation for the international standard atmosphere (ISA) can be calculated for a range of altitudes from sea level upward. This is done using an exact solution to the hydrostatic equation for a column of air. The air is assumed to be a perfect gas. In the lower region, the troposphere, the atmosphere has a lapse rate (L) of 6.5K/Km. At an altitude of 36089 ft the stratosphere starts and the temperature remains constant at 217K. The hydrostatic equation, perfect gas law and the lapse rate equation are



where the variables used are

P -- Pressure (Pa);
T -- Temperature (K);
-- Density (Kg/m3);
g -- Gravitational acceleration (9.8 m/s2);
To -- Standard sea level temperature (288 K);
R -- Gas constant for air (287 m2/s2/K);
h -- Altitude above sea level (m)
and L -- Lapse rate (0.0065 K/m).

Solving the hydrostatic equation with a constant lapse rate gives the resulting pressure variation in the troposphere.


where Po is set at 101.3 kPa.

Solving the hydrostatic equation with a constant temperature gives the resulting pressure variation in the stratosphere.



where conditions with subscript (s) are values of altitude (hs), pressure (Ps) or temperature (Ts) at the tropopause, the start of the stratosphere, the line dividing the two distinct atmospheric regions.

Once pressure has been calculated at a particular altitude, density is then calculated using the perfect gas law. Viscosity and kinematic viscosity are found by applying the Sutherland law



And finally speed of sound is found as



Based on the above equations, an application is available which shows atmospheric properties for a specific altitude. This application can also be used to predict Mach Number, Dynamic Pressure and other altitude dependent properties if an input speed and reference length are given.

2. Correction for Air Density due to Humidity

The density of the air for a given level of humidity can be found by applying a correction factor to the above calculated perfect gas density.


The correction factor, Kh, can be found by using wet and dry bulb temperature measurements to predict relative humidity as shown in the following table.

 

Relative Humidity (%)

Dry Bulb oC

Temperature Difference,oC

TDRY - TWET 

1    2   3   4   5   6   7   8   9  10  11  12
 
0
 
81  64  46  29  13   -   -   -   -   -   -   -
 
2
 
84  68  52  37  22   7   -   -   -   -   -   -
 
4
 
85  71  57  43  29  16   -   -   -   -   -   -
 
6
 
86  73  60  48  35  24  11   -   -   -   -   -
 
8
 
87  75  63  51  40  29  19   8   -   -   -   -
 
10
 
88  77  66  55  44  34  24  15   6   -   -   -
 
12
 
89  78  68  58  48  39  29  21  12   -   -   -
 
14
 
90  79  70  60  51  42  34  26  18  10   -   -
 
16
 
90  81  71  63  54  46  38  30  23  15   8   -
 
18
 
91  82  73  65  57  49  41  34  27  20  14   7
 
20
 
91  83  74  66  59  51  44  37  31  24  18  12
 
22
 
92  83  76  68  61  54  47  40  34  28  22  17
 
24
 
92  84  77  69  62  56  49  43  37  31  26  20
 
26
 
92  85  78  71  64  58  51  46  40  34  29  24
 
28
 
93  85  78  72  65  59  53  48  42  37  32  27
 
30
 
93  86  79  73  67  61  55  50  44  39  35  30
 
32
 
93  86  80  74  68  62  57  51  46  41  37  32
 
34
 
93  87  81  75  69  63  58  53  48  43  39  35
 
36
 
94  87  81  75  70  64  59  54  50  45  41  37

The relative humidity can be used to obtain the density correction factor from the following graph.

Density Correction due to Humidity

Note : Density correction factor assumes approximately sea level pressure in the application of these formulae. 

Reference: "Handbook of Chemistry and Physics" Ed R.C.Weast, The Chemical Rubber Co., Ohio, 1964

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