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Unformatted text preview: Lecture 19 Fluids: density, pressure, Pascal’s principle and Buoyancy. What is a fluid? Fluids are “substances that flow”…. “substances that take the shape of the container” Atoms and molecules must be free to move .. No long range correlation between positions (e.g., not a crystal). Gas or liquid… or granular materials (like sand) Density, pressure ρ = m V Density: F p A ⊥ = Pressure: Units: Pascal (Pa) = 1 N/m 2 psi (pounds per square inch) atmosphere 1 atm = 1.013 × 10 5 Pa bar 1 bar = 10 5 Pa Pure water: 1000 kg/m 3 Atmospheric pressure DEMO: Piston and weight The atmosphere of Earth is a fluid, so every object in air is subject to some pressure. At the surface of the Earth, the pressure is p atm ~ 1.013 x 10 5 Pa = 1 atm Area of a hand ~ 200 cm 2 = 0.02 m 2 atm ~ 2000 N on your hand due to air! F p A = Pressure vs. depth F bottom F top mg Imaginary box of fluid with density ρ with bases of area A and height h bottom/top bottom/top F P A = bottom top p p gh ρ = + m Ah ρ = h Net force must be zero! bottom top F F mg = + DEMO: Plastic tube with cover Example: How deep under water is p = 2 atm ? h = p bottom − p top ρ g = 1.01 × 10 5 Pa ( 10 3 kg/m 3 )( 9.81 m/s 2 ) = 10.3 m ( i.e. 1 atm is produced by a 10.3 m high column of water ) Fluid in an open container Pressure is the same at a given depth, independent of the shape of the container. p(y) y Fluid level is the same everywhere in a connected container (assuming no surface forces) • A • B If liquid height was higher above A than above B If liquid height was higher above A than above B p...
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 Summer '08
 B
 Buoyancy, net force

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