# Pressure Gradient Force

The pressure gradient force is the force resulting from differences in pressure across a distance.

The x component of the pressure gradient force per unit mass is:
**Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): F = \frac{-1}{\rho} \frac{dp}{dx}**
.

The y component of the pressure gradient force per unit mass is:
**Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): F = \frac{-1}{\rho} \frac{dp}{dy}**
.

The z component of the pressure gradient force per unit mass is:
**Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): F = \frac{-1}{\rho} \frac{dp}{dz}**
.

We can express the acceleration more precisely, for a general pressure P as,

Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \vec{F} = \frac{-1}{\rho} \vec\nabla P.

The direction of the resulting force (acceleration) is thus in the direction of the most rapid change of pressure.

Note: In atmospheric dynamics, the pressure gradient force always moves mass from the area of higher pressure to the area of lower pressure.