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.

CurrensPressureOutside =

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.

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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.

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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.

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PWeight = D*V*g

P + W/Area

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Buoyant Force

The extra pressure from below produces a “buoyant” force which is just enough to keep each volume of fluid in place.

Fb = Dw x V x g.– e.g. The buoyant force on 10 m3 of water is:

Fb = Dw x V x g = 1000 kg/m3 x 10 m3 x 9.8 m/s2

Fb = 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.

Fnet = W – Fb. – If Fnet is positive, gravity wins, and it sinks.– If Fnet is negative, buoyancy wins, and it floats.

Density

Ice is less dense than liquid water.– Dice = 917 kg/m3

– So, the weight of a 10m3 chunk of ICE is just W = 917 x 10 x 9.8 = 89,900 N.

Fnet = W – Fb = 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/m3), 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. D2 = 273/373 (1.3 kg/m3) = .94 kg/m3 Hot air is less dense, and it rises!

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