Fluid Mechanics

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Fluid Mechanics

• Liquids and gases have the ability to flow
• They are called fluids
• There are a variety of LAWS that fluids obey
• Need some definitions

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Density

• Regardless of form (solid, liquid, gas) we can
  define how much mass is squeezed into a
  particular space

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Pressure

• A measure of the amount of force exerted on a
  surface area

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Pressure in a Fluid

• The pressure is just the weight of all the fluid
  above you
• Atmospheric pressure is just the weight of all
  the air above on area on the surface of the earth
• In a swimming pool the pressure on your body
  surface is just the weight of the water above you
  (plus the air pressure above the water)

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Pressure in a Fluid

• So, the only thing that counts in fluid pressure
  is the gravitational force acting on the mass
  ABOVE you
• The deeper you go, the more weight above you and
  the more pressure
• Go to a mountaintop and the air pressure is lower

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Pressure in a Fluid
Pressure acts perpendicular to the surface and
increases at greater depth.
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Pressure in a Fluid
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Buoyancy
Net upward force is called the buoyant
force!!! Easier to lift a rock in water!!
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Displacement of Water
The amount of water displaced is equal to the
volume of the rock.
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Archimedes Principle

• An immersed body is buoyed up by a force equal to
  the weight of the fluid it displaces.
• If the buoyant force on an object is greater than
  the force of gravity acting on the object, the
  object will float
• The apparent weight of an object in a liquid is
  gravitational force (weight) minus the buoyant
  force

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Flotation

• A floating object displaces a weight of fluid
  equal to its own weight.

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Flotation
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Gases

• The primary difference between a liquid and a gas
  is the distance between the molecules
• In a gas, the molecules are so widely separated,
  that there is little interaction between the
  individual moledules
• IDEAL GAS
• Independent of what the molecules are

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Boyles Law
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Boyles Law

• Pressure depends on density of the gas
• Pressure is just the force per unit area exerted
  by the molecules as they collide with the walls
  of the container
• Double the density, double the number of
  collisions with the wall and this doubles the
  pressure

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Boyles Law
Density is mass divided by volume. Halve the
volume and you double the density and thus the
pressure.
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Boyles Law

• At a given temperature for a given quantity of
  gas, the product of the pressure and the volume
  is a constant

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Atmospheric Pressure

• Just the weight of the air above you
• Unlike water, the density of the air decreases
  with altitude since air is compressible and
  liquids are only very slightly compressible
• Air pressure at sea level is about 105
  newtons/meter2

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Barometers
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Buoyancy in a Gas

• An object surrounded by air is buoyed up by a
  force equal to the weight of the air displace.
• Exactly the same concept as buoyancy in water.
  Just substitute air for water in the statement
• If the buoyant force is greater than the weight
  of the object, it will rise in the air

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Buoyancy in a Gas
Since air gets less dense with altitude, the
buoyant force decreases with altitude. So helium
balloons dont rise forever!!!
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Bernoullis Principle
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Bernoullis Principle

• Flow is faster when the pipe is narrower
• Put your thumb over the end of a garden hose
• Energy conservation requires that the pressure be
  lower in a gas that is moving faster
• Has to do with the work necessary to compress a
  gas (PV is energy, more later)

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Bernoullis Principle

• When the speed of a fluid increases, internal
  pressure in the fluid decreases.

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Bernoullis Principle
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Bernoullis Principle
Why the streamlines are compressed is quite
complicated and relates to the air boundary
layer, friction and turbulence.
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Bernoullis Principle