1. Lecture 6. EPS 5: 23 Sep. 2010 1.Review the concept of the barometric law (hydrostatic balance: each layer of atmosphere must support the weight of the overlying column mass of atmosphere). Discuss the distribution of pressure with altitude in the atmosphere, or depth in the ocean. 2.Introduce buoyancy. Pressure force "upwards" on an object immersed in a fluid. 3.Archimedes principle: the buoyancy force on an object is equal to the weight of the fluid displaced by the object. Role of gravity. 4.The buoyancy of warm air. 5.A brief look at global weather patterns—sea surface temperature and buoyancy.

2. Buoyancy Buoyancy is the tendency for less dense fluids to be forced upwards by more dense fluids under the influence of gravity. Buoyancy arises when the pressure forces on an object are not perfectly balanced. Buoyancy is extremely significant as a driving force for motions in the atmosphere and oceans, and hence we will examine the concept very carefully here. The mass density of air  is given by mn, where m is the mean mass of an air molecule (4.81  10 -26 kg molecule -1 for dry air), and n is the number density of air (n =2.69  10 25 molecules m -3 at T=0 o C, or 273.15 K). Therefore the density of dry air at 0 C is  = 1.29 kg m -3. If we raise the temperature to 10  C (283.15 K), the density is about 4% less, or 1.24 kg m -3. This seemingly small difference in density would cause air to move in the atmosphere, i.e. to cause winds.

3. Buoyancy force: Forces on a solid body immersed in a tank of water. The solid is assumed less dense than water and to have area A (e.g. 1m 2 ) on all sides. P1 is the fluid pressure at level 1, and P1x is the downward pressure exerted by the weight of overlying atmosphere, plus fluid between the top of the tank and level 2, plus the object. The buoyancy force is P1 – P1x (up ↑) per unit area of the submerged block. P1x Net Force (Net pressure forces – Gravity)

4. The buoyancy force and Archimedes principle. 1. Force on the top of the block: P2  A =  water D 2 A g (A = area of top) weight of the water in the volume above the block 2. Upward force on the bottom of the block = P1  A =  water D 1 A g 3. Downward force on the bottom of the block = weight of the water in the volume above block + weight of block =  water D 2 A g +  block (D 1 - D 2 ) A g Unbalanced, Upward force on the block ( [2] – [3] ): F b =  water D 1 A g – [  water D 2 A +  block (D 1 - D 2 ) A ] g =  water g V block –  block g V block = (  water –  block ) (D 1 – D 2 ) A g weight of block BUOYANCY FORCE = weight of the water (fluid) displaced by the block Volume of the block = (D 1 – D 2 ) A

5. Archimedes principle: the buoyancy force on an object is equal to the weight of the fluid displaced by the object object immersed in a fluid weight of fluid displaced for the fluid itself, there will be a net upward force (buoyancy force exceeds object weight) on parcels less dense than the surrounding fluid, a net downward force on a parcel that is more dense. buoyancy can accelerate parcels in the vertical direction (unbalanced force). the derivation of the barometric law assumed that every air parcel experienced completely balanced forces, thus didn't accelerate. Buoyancy exactly balanced the weight of the parcel (“neutrally buoyant”) – this is approximately true even if the acceleration due to unbalanced forces is quite noticeable, because the total forces on an air parcel are really huge (100,000 N/m 2 ), and thus only small imbalances are needed to produce significant accelerations.

6. Write down your answer. We will do this experiment in the next class, and invite a volunteer to explain the result using Archimedes principle.

7. A closer look at the U-tube experiment… compute the density of the paint thinner : U h1h1 h2h2 h3h3  w h 1 =  w h 3 +  p h 2  w (h 1 – h 3 ) =  p h 2 buoyancy force:  w h i g –  p h i g = (  w –  p )h i g Looks a lot like Archimedes' principle 2 h i = h 1 + h 2 + h 3

8. Lecture 6. EPS 5 1.Review the concept of the barometric law (hydrostatic balance: each layer of atmosphere must support the weight of the overlying column mass of atmosphere). Discuss the distribution of pressure with altitude in the atmosphere, or depth in the ocean. 2.Introduce buoyancy. Pressure force "upwards" on an object immersed in a fluid. 3.Archimedes principle: the buoyancy force on an object is equal to the weight of the fluid displaced by the object. Role of gravity. 4.The buoyancy of warm air.

9. Cold, relatively dense air has higher density than adjacent warm air, the warm air is buoyant (the cold air is "negatively buoyant"). The "warm air rises" (is buoyant!). Buoyancy and air temperature. Consider two air parcels at the same pressure, but different temperatures. P =  1 (k/m) T 1 =  2 (k/m) T 2 Then  1 /  2 = T 2 /T 1 ; if T 1 > T 2,  1 <  2. Warmer air, lower density!

10. Lecture 6. EPS 5 1.Review the concept of the barometric law (hydrostatic balance: each layer of atmosphere must support the weight of the overlying column mass of atmosphere). Discuss the distribution of pressure with altitude in the atmosphere, or depth in the ocean. 2.Introduce buoyancy. Pressure force "upwards" on an object immersed in a fluid. 3.Archimedes principle: the buoyancy force on an object is equal to the weight of the fluid displaced by the object. Role of gravity. 4.The buoyancy of warm air.

11. Lecture 6. EPS 5: 23 Sep. 2010 Review the concept of the barometric law (hydrostatic balance: each layer of atmosphere must support the weight of the overlying column mass of atmosphere). Discuss the distribution of pressure with altitude in the atmosphere, or depth in the ocean. 1.Introduce buoyancy. Pressure force "upwards" on an object immersed in a fluid. 2.Archimedes principle: the buoyancy force on an object is equal to the weight of the fluid displaced by the object. Role of gravity. 3.The buoyancy of warm air. 4.A brief look at global weather patterns—sea surface temperature and buoyancy.

12. Global Sea Surface Temperatures February 2002

13. Global Sea Surface Temperature Anomalies, December 2001

14. 10 Feb 2002 GOES ir image

15. 10 Feb 2002 GOES ir image

16. http://www.cira.colostate.edu/Special/CurrWx/g8full40.asp 10 Feb 2003 GOES ir image

17. Global Sea Surface Temperature Anomalies, Dec. 2001, Jan 2003 12-2001 La Niña 01-2003 El Niño

18. Lecture 6. EPS 5: 23 Sep. 2010 Review the concept of the barometric law (hydrostatic balance: each layer of atmosphere must support the weight of the overlying column mass of atmosphere). Discuss the distribution of pressure with altitude in the atmosphere, or depth in the ocean. 1.Introduce buoyancy. Pressure force "upwards" on an object immersed in a fluid. 2.Archimedes principle: the buoyancy force on an object is equal to the weight of the fluid displaced by the object. Role of gravity. 3.The buoyancy of warm air. 4.A brief look at global weather patterns—sea surface temperature and buoyancy.