The Hydrostatic Equation

The Hydrostatic Equation

We now approach the problem of the equilibrium of a bulk of air
at rest under the external force of gravity, g has the dimensions of
an acceleration, L/T*. Its value depends slightly on latitude and
altitude, increasing by 0-5 per cent, from the equator to the poles
and decreasing by 0-5 per cent, from sea-level to 10 miles altitude,
At sea-level and 45 latitude its value is 32173
in ft.-sec. units. The value 32-2 ft./sec.

2 is sufficiently accurate for most purposes.
Since no horizontal component of external force
acts anywhere on the bulk of air, the pressure
in every horizontal plane is constant, as otherwise
motion would ensue. Let h represent altitude, so
that it increases upward. Consider an elementcylinder
of the fluid with axis vertical, of length
SA and cross-sectional area A .