• id: JME-09-N01
• title: Pressure in Fluids
• tags: pressure, fluid-statics, pascal

Pressure at a point in a fluid is defined as the normal force per unit area: $P = F/A$. SI unit: Pa (N m$^{-2}$). Pressure is a scalar — at any point in a fluid at rest, it acts equally in all directions. This is the essence of Pascal's law for static fluids. The pressure at depth $h$ below the surface: $P = P_0 + \rho gh$, where $P_0$ is atmospheric pressure. Key insight: pressure depends only on depth, not on the shape of the container. This is the hydrostatic paradox — a wide container and a narrow tube with the same depth of fluid have the same pressure at the bottom.