 # Atmospheric Stability Hot air and buoyancy. Outline  Pressure in fluids –Pascal’s principle  Buoyancy –Archimedes’ principle –Density and Temperature.

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Atmospheric Stability Hot air and buoyancy

Outline  Pressure in fluids –Pascal’s principle  Buoyancy –Archimedes’ principle –Density and Temperature –Adiabatic lapse rate and atmospheric stability

Atmospheric Pressure  Pressure in a fluid increases with depth because of the weight of the fluid above. –Demonstration (water in column).  Air pressure is a result of the weight of air above us. That pressure is strong enough to: –Hold up water in a cup –Hold together evacuated spheres –Crush cans

Pascal’s principle  Pressure that is applied at one point in an enclosed fluid is communicated to all other points in the fluid. Currens Pressure Outside = P inside

Atmospheric Stability: Part I  A stable atmosphere is one in which the pressure at the same height is the same, everywhere.  The sun’s heating and the earth’s cooling make that an unreachable goal.  Winds and the jet stream are all evidence that the earth’s atmosphere is seeking horizontal stability, but never finding it.  This is the basic reason for all air movements and weather systems.

Seeking Horizontal Equilibrium

Hydraulic systems  An important application of Pascal’s principle is in hydraulic controls. P P A 5A

Archimedes’ Principle  An object submerged in a fluid experiences an upward, “buoyant” force. –Objects which are denser than the fluid SINK. –Objects less dense than the fluid FLOAT. ? Wood Metal

Vertical equilibrium in fluids  The pressure below must be greater than the pressure above, to keep the fluid in place.  The difference is just equal to the weight of the fluid in between, per area. P P Weight = D*V*g P + W/Area P

Buoyant Force  The extra pressure from below produces a “buoyant” force which is just enough to keep each volume of fluid in place.  F b = D w x V x g. – e.g. The buoyant force on 10 m 3 of water is: F b = D w x V x g = 1000 kg/m 3 x 10 m 3 x 9.8 m/s 2 F b = 98,000 N.  This force balances that of gravity and maintains vertical equilibrium.

Floating or Sinking?  I take an object of the same volume V as the water from the previous problem, only having a different density, and submerge it. –The buoyant force would be exactly the same! –But the weight of the object would be different.  F net = W – F b. –If F net is positive, gravity wins, and it sinks. –If F net is negative, buoyancy wins, and it floats.

Density  Ice is less dense than liquid water. –D ice = 917 kg/m 3 –So, the weight of a 10m 3 chunk of ICE is just W = 917 x 10 x 9.8 = 89,900 N.  F net = W – F b = 89,900 – 98,000 = -8,100 N  The water pushes the ice up out of the water, until the volume of water displaced corresponds to a buoyant force of 89,900N.  Salt water is more dense, so actually, about 20% of an iceberg is above the ocean surface.

Buoyancy in air  The density of air is quite low (1.3 kg/m 3 ), so most things sink.  What can float in air? –Helium, –Hydrogen, –Hot Air

Gas law  In a gas, Density is both temperature and pressure dependent. When pressure is constant (at a constant height) Density is inversely related to temperature.  e.g. D 2 = 273/373 (1.3 kg/m 3 ) =.94 kg/m 3  Hot air is less dense, and it rises!

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