Solids

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Solids Fluids

• Relating Pressure to Solid Fluid systems

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What is a FLUID?

• A fluid is a nonsolid state of matter in which
  the atoms or molecules are free to move past each
  other, as in a gas or a liquid.
• Both liquids and gases are considered fluids
  because they can flow and change shape.
• Liquids have a definite volume gases do not.

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Recall the definition of Density

• How much matter there is in an amount of space.
• In other words
• Density Mass / Volume
• or ?m/V (Greek letter rho is given for
  density)

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Buoyancywhat is it and how is it applied?

• The buoyant force is the upward force exerted by
  a liquid on an object immersed in or floating on
  the liquid.
• Buoyant forces can keep objects afloat if they
  are great enough. It really depends on the
  density of the object and the density of the
  fluid it is in.
• Exs ice in liquid water, helium balloon in air,
  brick in air, stone in pool water, etc.

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Archimedes Principle

• Archimedes principle describes the magnitude of
  a buoyant force.
• Archimedes principle Any object completely or
• partially submerged in a fluid experiences an
• upward buoyant force equal in magnitude to the
• weight of the fluid displaced by the object.
• FB Fg (displaced fluid) mfg
• magnitude of buoyant force weight of fluid
  displaced

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For example
The Brick, when added, will cause the water to be
displaced and fill the smaller container. What
will the volume be inside the smaller container?
The same volume as the brick!
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Another example
The raft and cargo are floating because
their weight and buoyant force are balanced.
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Another example
Now imagine a small hole is put in the raft.
The raft and cargo sink because their overall
density is now greater than the density of the
water.
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More about Buoyancy

• For a floating object, the buoyant force equals
  the objects weight (they would be BALANCED).
• The apparent weight (actual weight minus buoyant
  force experienced) of a submerged object depends
  on the density of the object.

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More about Buoyancy

• For an object with density ?o which is submerged
  in a fluid ?f, the following relationship is
  true
• Weight / Buoyant Force Objects Density /
  Fluids Density
• Or

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Example
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Example
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Example
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Pressure

• The SI unit for pressure is the pascal, Pa.
• It is the same as a N/m2.
• The pressure at sea level is about 101,000 Pa.
• This gives us another unit for pressure, the
• atmosphere, where 1 atm 101,000 N/m2

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Definition of Pressure
Pressure force / area
A womans high heels sink into the soft ground,
but the larger shoes of the much bigger man do
not.
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Solid Applications

• We often relate this Force-to-Area ratio to the
  idea of stress felt by an object.
• In 1-Dimension, the change in Length due to
  stress is determined by Youngs Modulus.
• In 2-Dimensions, the change in Area due to stress
  is determined by the Shear Modulus.
• In 3-Dimensions, the change in Volume due to
  stress is determined by the Bulk Modulus.

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Solid Applications

• strain is defined as the measure of the amount
  of deformation (the EFFECT of the STRESS on the
  material)
• Examples tension on a suspension bridge cable,
  applying a horizontal force to the top of a
  textbook, submerging a block of plastic in a tank
  of water.

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NOW for some FLUID applications Pascals
Principle Any change in the pressure of a fluid
is transmitted uniformly in all directions
throughout the fluid.
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Some visuals
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Heres a common application
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Heres a common application
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Heres a common application
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A small force F1 applied to a piston with a small
area produces a much larger force F2 on the
larger piston. This allows a hydraulic jack to
lift heavy objects.
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Example
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Example
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More on Pressure
Pressure varies with depth in a fluid. The
pressure in a fluid increases with depth. It is
also important to know that Absolute Pressure
takes fluid Atmospheric Pressure into account
ALONG with Fluid Pressure.
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Fluid FLOW

• Viscosity is related to the thickness (internal
  resistance) of a fluid. The higher the
  viscosity, the slower a fluid will flow.
• There is a Continuity Equation which is important
  for ideal fluids

Think Pinching a water-hose
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Bernoullis Principle

• The speed of fluid flow depends on
  cross-sectional area.
• Bernoullis principle states that the pressure in
  a fluid decreases as the fluids velocity
  increases.

Think Is this true? Whats happening inside
of a DRINKING STRAW, for instance?
Think How does this relate to Lift?
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To Sum it all Up

• TOTAL ENERGY is ________
• Because of this, we can show that the following
  is valid for these fluid-flow systems
• The sum of the Pressure, Kinetic Energy per unit
  Volume, and the Potential Energy per unit Volume
  has the same value at all points along a
  streamline.

Think Can you tell from where each term comes?
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The END!
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