Formalism
Consider a cubic parcel of fluid with a density, a height, and a surface area . The mass of the parcel can be expressed as, . Using Newton's second law, we can then examine a pressure difference (assumed to be only in the -direction) to find the resulting force, .
The acceleration resulting from the pressure gradient is then,
.
The effects of the pressure gradient are usually expressed in this way, in terms of an acceleration, instead of in terms of a force. We can express the acceleration more precisely, for a general pressure as,
.
The direction of the resulting force (acceleration) is thus in the direction of the most rapid change of pressure.
Read more about this topic: Pressure-gradient Force
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