From AMS Glossary
(Or pressure-gradient force.) The force due to differences of pressure within a fluid mass.
The (vector) force per unit volume is equal to the pressure gradient, -∇p, and the force per unit mass (specific force) is equal to the product of the volume force and the specific volume, -α∇p. In the atmosphere, the vertical component of this force is of the order of 104 times the horizontal component; in meteorological literature the term "pressure force" usually refers only to the latter horizontal pressure force.