Buoyancy and Archimedes Principle Lecturer: Professor Stephen T. Thornton

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Buoyancy and Archimedes Principle Lecturer
Professor Stephen T. Thornton
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Reading Quiz
A) diminish B) stop altogether C) go out in a
straight line D) curve upwards

• When a hole is made in the side of a Coke can
  holding water, water flows out and follows a
  parabolic trajectory. If the container is
  dropped in free fall, the water flow will

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Reading Quiz
A) diminish B) stop altogether C) go out in a
straight line D) curve upwards

• When a hole is made in the side of a Coke can
  holding water, water flows out and follows a
  parabolic trajectory. If the container is
  dropped in free fall, the water flow will

Water flows out of the hole because the water
pressure inside is larger than the air pressure
outside. The water pressure is due to the weight
of the water. When the can is in free fall, the
water is weightless, so the water pressure is
zero, and hence no water is pushed out of the
hole!
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Last Time

• Density, fluids
• Pressure
• Pressure gauges and barometers

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Today

• More on pressure
• Pascals Principle
• Buoyancy
• Archimedes Principle
• Mass flow equation of continuity
• Today we are studying fluid dynamics after
  Archimedes Principle.

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Measurement of Pressure Gauges and the Barometer
There are a number of different types of pressure
gauges. This one is an open-tube manometer. The
pressure in the open end is atmospheric pressure
the pressure being measured will cause the fluid
to rise until the pressures on both sides at the
same height are equal.
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Tire pressure gauge.
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Pascals PrincipleAn external pressure applied
to an enclosed fluid is transmitted unchanged to
every point within the fluid.
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Do Pascals vases demoDo Cartesian diver demo
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A Hydraulic Lift
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In the hydraulic lift (show demo at end), the
liquid is enclosed, and the pressure is the same
throughout.
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Pascals Principle
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Conceptual Quiz
A) container 1 B) container 2 C) container 3
D) all three are equal

• Three open containers are filled with water to
  the same height and have the same surface area at
  the base, but the total weight of water is
  different for each. Which container has the
  greatest total force acting on its base?

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Conceptual Quiz
A) container 1 B) container 2 C) container 3
D) all three are equal

• Three open containers are filled with water to
  the same height and have the same surface area at
  the base, but the total weight of water is
  different for each. Which container has the
  greatest total force acting on its base?

The pressure at the bottom of each container
depends only on the height of water above it!
This is the same for all the containers. The
total force is the product of the pressure times
the area of the base, but since the base is also
the same for all containers, the total force is
the same.
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Conceptual Quiz
A) water pressure B) gravity C) inertia D)
atmospheric pressure E) mass
When you drink liquid through a straw, which of
the items listed is primarily responsible for
this to function?
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Conceptual Quiz
A) water pressure B) gravity C) inertia D)
atmospheric pressure E) mass
When you drink liquid through a straw, which of
the items listed below is primarily responsible
for this to function?
When you suck on a straw, you expand your lungs,
which reduces the air pressure inside your mouth
to less than atmospheric pressure. Then the
atmospheric pressure pushing on the liquid in the
glass provides a net upward force on the liquid
in the straw sufficient to push the liquid up the
straw.
Follow-up Is it possible to sip liquid through
a straw on the Moon?
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Conceptual Quiz

• You put a straw into a glass of water, place
  your finger over the top so no air can get in or
  out, and then lift the straw from the liquid.
  You find that the straw retains some liquid. How
  does the air pressure P in the upper part compare
  to atmospheric pressure PA?

A) greater than PA B) equal to PA C) less than
PA
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Conceptual Quiz

• You put a straw into a glass of water, place
  your finger over the top so no air can get in or
  out, and then lift the straw from the liquid.
  You find that the straw retains some liquid. How
  does the air pressure P in the upper part compare
  to atmospheric pressure PA?

A) greater than PA B) equal to PA C) less than
PA
Consider the forces acting at the bottom of the
straw PA P r g H 0 This
point is in equilibrium, so net force is zero.
Thus, P PA r g H and so we see
that the pressure P inside the straw must be less
than the outside pressure PA.
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Buoyant Force Due to a Fluid
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The buoyant force is due to the difference in
force at the bottom and the top of the cube of
sides L.
Archimedes principle An object completely
immersed in a fluid experiences an upward buoyant
force equal in magnitude to the weight of fluid
displaced by the object.
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Buoyant force equals the weight of the displaced
liquid, not the weight of the object!
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Buoyancy and Archimedes Principle
Archimedes principle The buoyant force on an
immersed object equals the weight of
displaced fluid. The picture below shows an
object in the air, partially submerged, and
completely submerged.
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Do Archimedes Principle I demo.
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Start Archimedes Principle II demo.
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FlotationAn object floats when it displaces an
amount of fluid equal to its weight.The total
weight of the block equals the weight of the
fluid displaced.
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Floating an Object That Is More Dense than
WaterThe wood and water in (a) have the same
weight, and the metal block and water in (b) have
the same weight.Note in (c) that bowl made of
the metal floats, because the bowl is hollow.
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is water density
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Conceptual QuizWhat happens to
the water level when the ice melts? A)
Water overflows. B) Water level decreases. C)
Water level stays the same.
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Answer C

• Water level stays the same. Because the ice cube
  is floating, it displaces a volume of water equal
  to its weight. When it melts it becomes water
  and displaces the same volume of water it
  displaced. Remember the density of ice is less
  than that of water.

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Conceptual QuizTwo identical glasses are filled
to the same level with water. One of the two
glasses has ice cubes floating in it. Which
weighs more? A)    The glass without ice
cubes.B)    The glass with ice cubes.C)    The
two weigh the same.
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Answer C

• The ice cubes displace exactly their own weight
  in water, so the two glasses weigh the same
  amount. It is essential that the ice sticks out
  above the level of the water.

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Conceptual QuizNow a
pebble sits on top of the ice, and the water is
filled to the brim of the glass. What happens
when the ice melts?A) The water overflows.B)
The water level decreases.C) The water level
stays the same.D) The pebble explodes.
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Answer B

• The ice makes no difference, but now the pebble
  also displaces an amount of water equal to the
  pebbles weight. When the ice melts, the pebble
  drops to the bottom and displaces a volume of
  water equal to its own volume. Because the
  volume of the pebble is less than the volume of
  the water it displaced originally, there is less
  water displaced afterwards. The water level
  drops.

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Turbulent flow Laminar flow, also known as
streamline flow.
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Consider a mass ?m passing through a particular
point in time ?t. The ratio ?m/ ?t must be
constant at every point or mass will build up.
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(No Transcript)
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Gases are compressible, but liquids are not. For
liquid flow, the density ? is constant. Then
for liquids.Useful equation
for many applications for example, water hoses.
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When using a water hose, we put our thumb over
end to increase water speed.Hose nozzle does the
same thing. Decrease area, increase speed.
A1v1 A2v2 small A, large v
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Conceptual Quiz

• Imagine holding two identical bricks in place
  underwater. Brick 1 is just beneath the surface
  of the water, and brick 2 is held about 2 feet
  down. The force needed to hold brick 2 in place
  is

A) greater B) the same C) smaller
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Conceptual Quiz

• Imagine holding two identical bricks in place
  underwater. Brick 1 is just beneath the surface
  of the water, and brick 2 is held about 2 feet
  down. The force needed to hold brick 2 in place
  is

A) greater B) the same C) smaller
The force needed to hold the brick in place
underwater is W FB. According to
Archimedes Principle, FB is equal to the weight
of the fluid displaced. Because each brick
displaces the same amount of fluid, then FB is
the same in both cases.