Pressure Height Dependence

Consider a horizontal surface of area A submersed in a fluid.  Also, consider increasing the vertical coordinate by the infinitesimal dz.  This will remove the pressure contribution from the weight of an infinitesimal cylinder.  This infinitesimal cylinder has the weight ρgAdz where ρ is the fluid density and g is the freefall acceleration.  Therefore, if dP is the infinitesimal change in pressure:

dP = -ρgdz