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

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

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Fluid Statics: Pressure and Density Density ρ = mass/volume Density ρ = mass/volume ρ(water) = 1000 kg/m 3 ρ(water) = 1000 kg/m 3 ρ(aluminum) = 2700 kg/m 3 ρ(aluminum) = 2700 kg/m 3 ρ(gold) = 19300 kg/m 3 ρ(gold) = 19300 kg/m 3

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Fluid Statics: change in pressure with increased depth The deeper you dive into a pool the greater the pressure is. 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. 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) The gauge pressure is the amount of increase in pressure compared to the surface (typically the surface pressure is atmosphere)

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

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Buoyant Forces and Archimedes Principle (280 B.C. Greek scientist) The buoyant Force pushing up by a fluid = weight of the fluid displaced 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 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 F buoyant = ρVg = weight of the fluid

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