Fluid Statics Why do your ears hurt when you dive deep into a pool, and how can steel float on water?

Fluid statics: pressure and density  Pressure is Force/Area (N/m 2 = Pascals)  A thumb tack is a good way to feel the difference between Force and pressure.  The atmosphere has a constant nominal pressure of 1.01 x 10 5 Pa (or 1 atm)

Fluid Statics: Pressure and Density  Density ρ = mass/volume  ρ(water) = 1000 kg/m 3  ρ(aluminum) = 2700 kg/m 3  ρ(gold) = kg/m 3

Fluid Statics: change in pressure with increased depth  The deeper you dive into a pool the greater the pressure is.  Increased pressure P gauge = ρgh = pressure due to the weight of the fluid at a given depth h.  The gauge pressure is the amount of increase in pressure compared to the surface (typically the surface pressure is atmosphere)

Hydrostatic pressure   Pressure in a fluid  P gauge = ρgh  P=Pgauge + Psurface  ( Psurface= Patm)

Fluid Pressure increase with depth  The total pressure at a given depth is P=Pgauge + Psurface (where Psurface usually means Patm)  Fluid pressure depends on depth and not on the shape of the container.

Buoyant Forces and Archimedes Principle (280 B.C. Greek scientist)  The buoyant Force pushing up by a fluid = weight of the fluid displaced  To calculate the weight of the fluid multiply the fluid density (ρ) by the displaced Volume and by g  F buoyant = ρVg = weight of the fluid

Archimedes principle  Buoyant force