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.
Transcript
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.
BuoyancyBuoyancy 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 ρ is given by mn, where m is the mean mass of an air molecule (4.8110-26 kg molecule-1 for dry air), and n is the number density of air (n =2.69 1025 molecules m-3 at T=0o C, or 273.15 K). Therefore the density of dry air at 0 C is ρ = 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.
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. 1m2 ) 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)
The buoyancy force and Archimedes principle.
1. Force on the top of the block: P2 A = ρwater D2 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 = ρwater D1 A g
3. Downward force on the bottom of the block = weight of the water in the volume above block + weight of block = ρwater D2 A g + ρblock (D1 - D2) A g
Unbalanced, Upward force on the block ( [2] – [3] ):
Fb = ρwater D1 A g – [ ρwater D2 A + ρblock (D1 - D2) A ] g
= ρwater g Vblock – ρblock g Vblock = (ρwater – ρblock) (D1 – D2) A g
weight of block
BUOYANCY FORCE = weight of the water (fluid) displaced by the blockVolume of the block = (D1 – D2) A
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/m2), and thus only small imbalances are needed to produce significant accelerations.
Write down your answer. We will do this experiment in the next class, and invite a volunteer to explain the result using Archimedes principle.
A closer look at the U-tube experiment…
compute the density of the paint thinner :
Uh1
h2
h3
ρw h1 =ρw h3 + ρp h2
ρw (h1 – h3) = ρp h2
buoyancy force: ρwhi g – ρphi g = (ρw – ρp )hi g
Looks a lot like Archimedes' principle
2 hi = h1 + h2 + h3
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.
Cold, relatively dense air hashigher density than adjacent warmair, the warm air is buoyant (the coldair 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 = ρ1 (k/m) T1 = ρ2 (k/m) T2
Then ρ1/ρ2 = T2/T1 ; if T1 > T2, ρ1 < ρ2 . Warmer air, lower density!
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.
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.
Global Sea Surface Temperatures February 2002
Global Sea Surface Temperature Anomalies, December 2001
Global Sea Surface Temperature Anomalies, Dec. 2001, Jan 2003
12-2001
La Niña
01-2003
El Niño
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.
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