ISA VARIATION WITH ALTITUDE
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 equations are,
where the variables used are,
P  Pressure (Pa); 
T  Temperature (K); 
g  Gravitational acceleration (9.8 m/ m/s^{2}); 
T_{O}  Standard sea level temperature (288 K); 
R  Gas constant for air (287 m^{2}/s^{2}/K); 
h  Altitude above sea level (m), 
L  Lapse rate (0.0065 K/m) and 
ρ  Air density, ( Kg/m^{3});

Atmospheric Layers and Temperature Variation with Altitude.
Solving the hydrostatic equation with a constant lapse rate gives the resulting pressure variation in the troposphere.
where sea level pressure, Po , is set at the standard 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 (h_{s}), pressure (P_{s}) or temperature (T_{s}) 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 based on the temperature,
where γ is the ratio of specific heats for air (1.4)