# Hydrostatic Balance

The Hydrostatic Balance is when in the absence of atmospheric motions the gravity force must be exactly balanced by the vertical component of the pressure gradient force.

**Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \frac{dp}{dz} = -\rho g**

This condition of hydrostatic balance provides an excellent approximation for the vertical dependence of the pressure field in the real atmosphere. Only for intense small-scale systems such as squall lines and tornadoes is it necessary to consider departures from hydrostatic balance.

Integrating from a height z to the top of the atmosphere we find that:

**Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): p(z) = \int_z^\infty {\rho g dz}**

so that the pressure at any point is simply equal to the weight of the unit cross section column of air overlying the point. Thus, mean sea level pressure p(0) = 1013.25 hPa is simply the average weight per square meter of the total atmospheric column.

Note that **Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): d\Phi = g dz **
and that **Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \alpha = \frac{RT}{p} **

So we can also express the hydrostatic equation as:

**Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): g dz = d\Phi = -\frac{RT}{p} dp = -RT d \ln p **

To continue with integration, see Hypsometric Equation