In general, a pressure is a force per unit area across a surface.
A difference in pressure across a surface then implies a difference in force, which can result in an acceleration according to Newton's second law of motion, if there is no additional force to balance it.
When a fluid is in an equilibrium state (i.e. there are no net forces, and no acceleration), the system is referred to as being in hydrostatic equilibrium.
In the case of atmospheres, the pressure-gradient force is balanced by the gravitational force, maintaining hydrostatic equilibrium.
In Earth's atmosphere, for example, air pressure decreases at altitudes above Earth's surface, thus providing a pressure-gradient force which counteracts the force of gravity on the atmosphere.
The Magnus effect is an observable phenomenon that is commonly associated with a spinning object moving through a fluid.
The deflection can be explained by the difference in pressure of the fluid on opposite sides of the spinning object.
The Magnus effect is dependent on the speed of rotation.
Consider a cubic parcel of fluid with a density
The acceleration resulting from the pressure gradient is then,
We can express the acceleration more precisely, for a general pressure
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