Statics
of the Atmosphere
The vertical variations of parameters such as pressure are studied.
The Hydrostatic Equation:
The pressure variation in a "motionless" atmosphere is given by:
where, the left hand side term is the vertical pressure gradient per unit
mass, and the right hand side term represents gravitational force per unit
mass.
If the atmosphere is not "motionless", Newton's second law can be
used to write the general equation as:
The hydrostatic equation can be used to derive a relationship between
pressure and elevation of the air parcel. The hydrostatic equation and
the equation of state can be rewritten as:
Integration of the equation yields:
The initial conditions used in the integration are: z = 0, p = 0
Thus the variation of pressure depends on the vertical profile of temperature.
For an isothermal atmosphere, one can integrate the left hand side term
of the above equation as:
Where, To is the temperature of isothermal atmosphere.
Simple calculation using the equation show that the pressure decreases
exponentially with height at a ratio of 12.24 mb per 100 meter.