Hot air, floating

1
Hot air, floating
Liquids (and gases) and why stuff
floats Balloons and hot air balloons
From Goldeneye
The Rio Grande Gorge-ous
2
Science fiction?

• In 1976, Vonnegut published Slapstick, a story
  where the earths gravity suddenly "increased
  tremendously, " so that "...elevator cables were
  snapping, ships were sinking, bridges were
  collapsing, and on and on."

g normal
g bigger?
Anyway Slaughterhouse Five was a better book
3
When does metal float?

• Why does a 10,000,000 gram ship float
• when a 10 gram penny sinks?!

4
Scientist stronger than 24 Horses!

• In 1663, Otto von Guericke sealed two hollow
  shells together and put nothing inside them.
• Two teams comprising 24 horses could not pull the
  two shells apart!

When choosing between brains and brawn, .
5
Fluids push uniformly

• Forces in fluids spread out instead of acting
  at only one point
• Solid supplies a force pushing down at the CoM
• Fluid pushes up on the whole platform
• Ffluid pressure ? area (P)(A)
• P F/A (e.g. N/m2)

6
Hydraulic lifts

• Fluid pushed with
• small force small area
• can create
• large force on a large area

7
Gases and Liquids

• Fluid stuff that flows
• Gas compressible fluid (can you squeeze it?
  YES, think of balloons, etc)
• Liquid incompressible fluid (NO, thats why you
  can lift a car)
• So dont make a hydraulic jack based on air
  instead of oil
• unless you only want to lift mosquitos and such

8
One more weird thing

• The water at the top of the barrel spews out more
  slowly than the water at the bottom.
• Theres more force pushing the water out from the
  bottom.
• Whats doing the pushing?
• The water in the barrel.
• So Pbottom Ptop

9
The block weighs less in the water

• T mg - Fbuoyancy
• Measured tension T is less so water must
• be pushing up on the whole
• Even though its submerged

10
Why it weighs less in the water
Ftop

• Imagine the cube of water shown
• Block doesnt move,
• Weight of block sum of forces
• 2. Equal pressure on inside and outside
• wall of the block (it does not collapse)
• Ftop pushing down is weight of water above the
  top surface
• Fbot pushing up is the weight of water above the
  bottom surface
• and Fbot Ftop Wblock Ftop
• 3. Buoyancy force weight of block of water

Fbot
11
Nope just fiction
Vonnegut (Slapstick) the earths gravity
suddenly "increased tremendously, " "...elevator
cables were snapping, ships were sinking, ."
g normal
g bigger?
Fbuoy mgnorm
Fbuoy mgbig
12
Buoyancy questions

• Which boat below is heavier?
• Which boat has a larger volume?
• Which boat displaces more water?
• Which boat is supported by the greater buoyant
  force?

13
If its more dense it sinks

• r (mass)/(volume)
• Stuff floats if rstuff
• mstuff g

But! The ships made of steel
raverage
r 1
14
More challenging question

• Ball sinks in yellow oil, but floats
• in blue oil.
• So rair
• What if we pour yellow oil on top of blue?
• Does the ball change its height? Up or down?

15
Hunh?

• In both cases,
• ball displaces its own weight.

16
How much pressure?
17
Ideal gas

• Gas creates pressure on container
• walls by transfer of momentum
• from individual atoms
• Pressure (number of atoms hitting an area) ?
  (how hard they hit)
• (number of atoms/volume) ? (energy of
  atoms)
• P (N/V) kT (density) ? (Boltzmann const) ?
  (temperature)
• P rN kT
• T has to be in Kelvin !!!!
• (not Centigrade or Fahrenheit)

18
Two ways to make higher pressure

• If you started with a certain
• number density and temperature,
• You could
• 1) Add more atoms with
• the same energy per atom
• T is const, but rN increases
• 2) Add more energy
• to each individual atom
• rN is const, but T increases

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What does Kelvin mean?
Gas pressure shrinks to 0 when gas atoms stop
moving. T 0 means no more motion

• P k rN T
• (rN constant)

173K
373K
473K
73 K
273K
T (K)
20
Altitude sickness

• Gases compress under their own weight
• Above 10,000ft (2 miles)
• many need help breathing
• Air is less dense and so O2
• is in short supply

21
Hot air balloons

• Perfect silence,
• but how?
• Why do they have to
• be hot?
• How do they stay aloft?

22
Buoyancy vs weight

• P r k T
• If we heat, T increases and tries to
• make P increase, but
• theres a hole in the bottom, so
• Poutside Pinside.
• So gas in hot balloon is less dense
• (molecules leave more often
• than they enter through the hole)
• So mhotg
• and the balloon floats

mairg mhotg
23
Dirigibles and such

• Helium atoms weigh 3-4 times less than air atoms
• and hydrogen weighs even less.
• So a balloon filled with the same number density
  of light gas atoms floats in air.

24
Take home messages

• Fluids lead to pressure (and hence to force)
• Buoyant force equals weight of displaced fluid
• Mass density r and particle number density rN
• Ideal gas law P rN kT
• Physics class T only makes sense on an absolute
  scale
• T measures atoms energy (all have about the same
  energy)