Pressure

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Pressure
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Fluid Statics

• Static Not Moving

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Stack of Books
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(No Transcript)
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(No Transcript)
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Weight from above F3
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For your notes
Weight Above
Pressure Supports
Weight Above
Pressure Supports
Weight Above
Pressure Supports
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Special property of fluidsForces are transferred
in all direction
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A Difference Between Fluids and Solids.

• Solids exert pressure straight down.
• Fluids exert pressure in all directions.

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Pressure on Objects in Water
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Your Turn
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Vacuums

• Vacuums exert no force
• You cant get sucked out of a space ship.
• But you can get blown out by the air inside the
  ship.
• Vacuums dont suck everything else blows.

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Magdeburg Spheres

• 1 atm 101,000 N/m2
• Calculate the force acting on the spheres if they
  are 0.12m in diameter.

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Buoyancy

• Less dense than water floats
• More dense than water sinks
• Why?
• Weight and buoyancy are involved, but how?
• What gives an object its buoyancy?
• Do objects that sink still have a buoyant force
  on them?

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Eureka!

• The Story of Archimedes and a Crooked Crown

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A Dilemma

• King Hieron II of Syracuse (in Greece)
  commissioned a crown and give the craftsman a
  kilogram of gold.
• The finished crown weighed a kilogram, but the
  king suspected that the smith kept some of the
  gold and substituted some filler material.
• The king wanted to know if he had been cheated,
  but didnt want to damage the exquisite crown in
  the process.

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Archimedes to the Rescue

• The king set Archimedes to the task of figuring
  out if the crown was made of pure gold.
• The density of gold was well known, and
  Archimedes knew the mass of the crown was 1 kg,
  but finding the volume of such a complex shape
  would be mathematically intractable, even for an
  expert at geometry

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Eureka!

• One day at a bath house, Archimedes lowered
  himself into a brimming-full tub and noticed that
  as his body became submerged, water flowed over
  the edge. If he lifted himself up, the tub was no
  longer full of water.
• He realized that the volume of water that was
  displaced out of the tub would be very easy to
  measure, and that it had a volume equal to his
  body.
• In his excitement, he ran down the street to his
  workshop (still naked) shouting Eureka! or
  Ive found it!

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Archimedes Principle

• For an object that is partially or completely
  submerged in a fluid (air counts), an upward
  buoyant force acts upon the object and is equal
  to the weight of the displaced fluid.

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FBDs of Water
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Bunch o Water
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What weight is this force holding up?
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Water
SF 0
Buoyant Force
Weight
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Styrofoam
Water
Steel
Buoyant Force
Buoyant Force
Buoyant Force
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Water
SF 0
Buoyant Force
Weight
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Take-Away Lesson

• Buoyancy happens because pressure is always
  greater on the bottom of the object that on the
  top
• Because pressure increases with depth.
• Buoyancy is the difference between the fluid
  pressure on the top and bottom of the object.
• Floating vs sinking is determined by comparing
  the downward force of gravity and the upward
  force of buoyancy.

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Hydraulics
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Balloon and PistonFluids transfer forces around
any bend
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Hydraulics - Pressure
The fluid exerts Equal Pressure Unequal Forces
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Remember Levers

• Big force moves small distance.
• Little force moves large distance.

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Hydraulics - Work
Work is transfer of Energy I loose GPE, Elephant
gains GPE
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Hydraulics - Work
GPEgained mg?h
GPElost mg ?h
Work is transfer of Energy I loose GPE, Elephant
gains GPE
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Hydraulics - Work
Work is transfer of Energy I gain GPE, Elephant
looses GPE
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Hydraulics - Work
GPElost mg?h
GPEgained mg?h
Work is transfer of Energy I gain GPE, Elephant
looses GPE
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Pressure on large area
Pressure on small area
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Distributed Forces
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• Weve been representing forces as single arrows.
  This works fine when we care about the total
  force on an object.
• If we care how a force is spread out over a
  surface, we use a distributed force

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Water on a Dam
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Equal Pressure at Equal DepthRegardless of shape
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Equal Depth Equal PressureRegardless of shape
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Equal Depth Equal PressureRegardless of shape
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• Towers store equal volume.
• Start with equal pressure.
• Remove 50

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Scraps
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Blades and Points

• Back of knife.
• Edge of knife.

Note materials break / split / cut /etc. because
of pressure, not force. It is called the yield
stress (pressure) of the material.
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Calculate the pressure at the bottom of the
Hoover Dam
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Calculate the pressure at the bottom of the
Hoover Dam

• ?water 1000 kg/m3
• Height of Hoover 221 m high (726 ft)
• 1 PSI 6895 pascal (Pa)

Approximate Car Tire Pressure Metric 100,000
pascals (Pa) English 30 PSI Both 2
Atmospheres (Atm)
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A Little History

• In 1654 Otto Von Guericke gave the citizens of
  Magdeburg a remarkable lesson in the force of the
  atmosphere. He machined two hollow hemispheres,
  twenty inches in diameter, so they fit snuggly
  into a sealed sphere. He pumped the air out of
  it. Then he put sixteen horses, eight on each
  side, to the task of pulling the halves apart.
  The horses couldn't, of course. It would've taken
  a force of over two tons to separate the halves.
• That may look more like showmanship than science.
  But it served its purpose. Von Guericke showed
  the world that seemingly insubstantial gases
  could exert astonishing forces -- forces that
  could probably be harnessed.

http//www.uh.edu/engines/epi1553.htm