text: 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 opposite direction of the most rapid increase of pressure.