By balancing these forces, the total force on the fluid is ∑ ∑ F = F bottom + F top + F weight = P bottom A − − P top A − − ρ ρ g A h This sum equals zero if the fluid's velocity is constant. Dividing by A, 0 = P bottom − − P top − − ρ ρ g h Or, P top − − P bottom = − − ρ ρ g h P top − P bottom is a change in pressure, and h is the height of the volume element—a change in the distance above the ground. By saying these changes are infinitesimally small, the equation can be written in differential form. d P = − − ρ ρ g d h Density changes with pressure, and gravity changes with height, so the equation would be: d P = − − ρ ρ ( P ) g ( h ) d h