4.3.3—Derive, from the definitions of pressure and density, the equation

For a static fluid, the pressure increase caused by a depth h is p=ρgh, from weight per unit area of the fluid column.

Derive it using ρ=m/V and p=F/A; state whether the pressure is gauge pressure or includes atmospheric pressure.

Water 3.0 m below the surface adds about 2.94×10⁴ Pa gauge pressure when ρ=1000 kg m⁻³ and g=9.8 m s⁻².

Depth, not container shape, sets the pressure in a connected static fluid; the equation is not valid when density varies without adjustment.