The three fundamental principles for the variation of static pressure p throughout a body of fluid at rest are (a) the pressure at a point is the same in all directions (Pascal’s law), (b) the pressure is the same at all points on the same horizontal level, and (c) the pressure increases with depth z according to the hydrostatic equation. dp/dz= ρg For a fluid with constant density ρ, the increase in pressure over a depth increase h is ρgh, a result which can be used to analyse the response of simple barometers and manometers to applied pressure changes and differences. In situations where very large changes in pressure occur an equation of state may be required to relate pressure and density together with an assumption about the fluid temperature. The hydrostatic equation is still valid but more difficult to integrate, as illustrated by consideration of the earth’s atmosphere.
Adiabatic Processes Realized with a Trapped Brownian Particle