Beta Phase: Square45 is currently in beta testing. Expect some features or content to be incomplete or missing.
45

Hydrostatic Pressure Formula

Describes the pressure exerted by a fluid at a given depth, where \rho is density, g is acceleration due to gravity, and h is depth.
📜

The statement of the theorem

The hydrostatic pressure P(h)P(h) at a depth hh within a fluid of constant density ρ\rho under gravitational acceleration g⃗\vec{g} is derived from the condition of mechanical equilibrium. Consider a fluid element of height dhdh and cross-sectional area AA. The pressure gradient ∇P\nabla P must balance the body force per unit volume, f⃗b=ρg⃗\vec{f}_b = \rho \vec{g}. Since the fluid is static, the pressure gradient is purely vertical: ∂P∂h=−ρg\frac{\partial P}{\partial h} = -\rho g. Integrating this differential equation from the surface (h=0h=0) to an arbitrary depth hh, and assuming the surface pressure P0P_0 is the reference pressure, yields the scalar relationship for the gauge pressure Pgauge(h)P_{gauge}(h): \n\nPgauge(h)=∫0hρg dh′=ρghP_{gauge}(h) = \int_{0}^{h} \rho g \, d h' = \rho g h
Source: Wikipedia