Atmospheric Stability

1. Atmospheric Stability Hot air and buoyancy

2. Outline • Pressure in fluids • Pascal’s principle • Buoyancy • Archimedes’ principle • Density and Temperature • Adiabatic lapse rate and atmospheric stability

3. 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

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

5. 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.

6. Seeking Horizontal Equilibrium

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

8. 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. Metal Wood ?

9. 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 Weight = D*V*g P P P + W/Area

10. 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.

11. 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.

12. 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.

13. 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

14. 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!