Archimedes Principle Boyle s Law Bernoulli s Principle

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Fluid Technology

• Archimedes Principle
• Boyles Law
• Bernoullis Principle
• Newtons Laws of Motion

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• The ball and the boat weigh the same WHY DOES
  THE BALL SINK, BUT THE BOAT FLOAT?

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Oi math

• What determines whether it will sink or float?
• MASS
• The amount of matter contained in an object
• VOLUME
• The amount of 3-dimensional space an object
  occupies
• DENSITY
• The ratio of mass-to-volume of an object
• Mass divided by Volume
• M/V D

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EUREKA!!!!!!!

• To a king, a crown
• Is the crown real or fake, though?
• Density of Gold appx. 1206 lbs/ft3
• We can weigh the crown
• (place it on a scale!)
• How to find the volume of the crown?

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Standard volumes

• Cube l3
• Rectangular Prism lwh
• Cylinder (Circular Prism) pir2l
• Triangular Prism ½ bhl
• Sphere 4/3pir3

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Archimedes Principle

• Any floating object displaces its own weight of
  fluid.
• Any object, wholly or partially immersed in a
  fluid, is buoyed up by a force equal to the
  weight of the fluid displaced by the object.
• Buoyancy weight of displaced fluid.
• Buoyancy is an upward force by a fluid acting on
  an object immersed in that fluid.
• Archimedes' principle does not consider the
  surface tension (capillarity) acting on the body.
• The weight of the displaced fluid is directly
  proportional to the volume of the displaced fluid
  (if the surrounding fluid is of uniform density).

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What the heck?

• Hydro water
• Phobos fear
• Philius love
• Hydrophilic water-loving
• Hydrophobic water-fearing
• The fluid doesnt necessarily push up on the
  object, but rather is pulled down by gravity,
  more than is the object, and, since two objects
  cannot occupy the same space at the same time,
  the object is lifted by the surrounding fluid.
  Ah gravity.
• ltltponos workgtgt

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Standard Densities

• Approximate average density of a human body
  64.7283 lbs/ft3
• Density of Pure Water at Sea-Level at 4 degrees
  Celcius 62.4264 lbs/ft3
• Approximate density of air at sea level 0.09485
  lbs/ft3

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Or we could use a table!

• http//www.coolmagnetman.com/magconda.htm
• http//www.coolmagnetman.com/magconda.htm

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• Suppose a 7-lb weight is lowered into water,
  displacing 3 lbs worth of that water.
• Then, the weight would SEEM to weigh 4 lbs.

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Sink or Swim?

• To calculate net-buoyancy, you need to know a
  number of things
• Mass and volume of the Object
• Mass and volume of the DISPLACED FLUID
• The difference between the two
• Mass of Fluid Mass of the Object Net-Buoyancy
• Net-Buoyancy means resulting buoyancy
• MF MO B
• B gt 0 means the object will rise
• B 0 means the object will float
• B lt 0 means the object will sink

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What else?

• Archimedes Principle also explains why balloons
  float in the air.
• Here, if the AIR displaced equals (or exceeds)
  the weight of the balloon, the balloon will
  float.
• THIS IS NOT THE REASON AIRPLANES FLY!! Well
  talk about that later, but it has a tiny bit to
  do with Bernoullis Principle and a LOT to do
  with conservation of momentum.

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Conversions (yes, Ill give these again!)

• 1 ft3 121212 in3 1 728 in3
• 1 in3 1/1 728 ft3 0.000 578 7 ft3
• 1 lb 0.4545 kg
• 1 kg 2.2 lbs
• 1 in 2.54 cm
• 1 cm 0.3937 in
• 1 in 0.0254 m
• 1 m 39.37 in

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Now for some examples

• What is the weight of a cube of aluminum, with
  edge-length of 1ft? (The density of aluminum is
  about 169 lb/ft3.)
• What is the weight of water for the same volume?
• What is the NET-BUOYANCY?
• WILL THE CUBE SINK, FLOAT, OR RISE IN WATER?

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Now for some examples

• What is the weight of a ball of air, with radius
  1ft? (The density of air is about 0.095 lb/ft3.)
• What is the weight of water for the same volume?
• What is the NET-BUOYANCY?
• WILL THE BALL SINK, FLOAT, OR RISE IN WATER?

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Now for some examples

• What is the weight of a rectangular bar of GOLD,
  with a length of 1ft, width of 0.5 ft, and height
  of 0.25 ft? (The density of gold is about 1206
  lb/ft3.)
• What is the weight of water for the same volume?
• What is the NET-BUOYANCY?
• WILL THE CUBE SINK, FLOAT, OR RISE IN WATER?

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I aint sayin she a gold digga

• Btw- a standard gold bar is approximately
  632, so has a volume of about 0.02087 ft3.
  and weighs just about 25.17525 lbs. This is
  approximately 402.804 oz., the unit by which the
  value of Gold is measured. (Of course, there are
  different kinds of ounces, Troy and Avoirdupois,
  with vary with respect to the number of grams to
  which each is equivalent, but never mind all
  that.)
• The morning of 8 April 2010, the price of gold
  was 1146.85 per Troy oz.
• That means the above gold bar would be worth
  about
• 461 955.77!!

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Okay, additional example

• Suppose you took that gold (from the last
  example) and pounded it into a hemisphere (thats
  half of a hollow ball, by the way) with a radius
  of say 3 ft.
• Let pi equal 22/7
• What is the weight of the gold?
• What is the weight of the water DISPLACED BY THE
  GOLD HEMISPHERE??
• What is the net buoyancy?
• Will the gold semi-sphere sink, float, or rise?

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Well what really happens?

• If an object is lighter than air i.e., the
  density is less than that of the surrounding air,
  it will rise in the air. If it is heavier than
  water i.e., the density is greater than that of
  water, it will sink in the water.
• BUT, when the density of the object is between
  that of air and that of water, it will be
  partially submerged and partially exposed.
• We can calculate HOW MUCH OF THE OBJECT is
  submerged!!

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Heres where it gets tricky

• The hemisphere in the previous example weighed
  150.75 lbs (the same as the gold brick), but had
  a volume of 56.5487 ft3. That same volume of
  water would weigh 3530.1318 lbs.
• That means BN 3379.3818 lbs!
• MOST of the hemisphere would be out of the water.
  The only part of the hemisphere IN the water
  will be the 150.75 lbs-worth of water.
• That volume (150.75 / 62.4264) 2.4148 ft3
• In other words, a little bit of the hemisphere
  would be below the water, the rest would be above.

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Lets try a simpler example

• Imagine a cube, with volume of 1 ft3, of a
  certain density, say 62.4264 lb/ft3, for example.
  If placed in water, what would happen?
• Float JUST below the surface
• Suppose we have a cube of the same volume, but
  with a density of 64.7283 lb/ft3. Now what
  happens?
• Sinks.
• What if the density is 60?
• Mf 62.4264, Mo 60, BN 2.4264
• What is the volume of 60lbs of water?
• 0.9611 ft3, so thats how much of the box would
  be under water.

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Gold Balloon!

• What would need to be the volume of a balloon
  made from that 0.125 ft3 of gold, if it were to
  float in air?
• It weighs 150.75 lbs.
• The density of air is 0.09485 lb/ft3
• 1589.3416 ft3!!
• It would need, for example, a sphere with radius
  of 7.2395 feet AND it would need to be filled
  with a vacuum

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Next Steps

• Definitions Mass, Volume, Density, Buoyancy,
  Archimedes Principle
• Be able to state the definitions and principles
• Be able to calculate, given two of M, V, or D,
  the missing value
• Be able to determine whether a given object will
  sink, float, or rise in a given fluid
• Please complete the Archimedess
  Principle/Buoyancy Worksheet for homework.

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Boyles Law

• Imagine Bubble-Wrap.
• As you squeeze the bubbles, what happens?

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What had happened was

• The bubbles are sealed, so have a constant MASS
  of air
• As you squeeze the bubble, you decrease the
  VOLUME of the bubble
• This, in turn, increases the PRESSURE of the air
  inside the bubble
• The pressure, pushing in all directions from each
  point of gas inside, acts on the walls of the
  bubble
• When the pressure is great enough, the bubble
  pops!
• Boyles Law concerns the relationship of a
  constant mass of a fluid under changing VOLUME
  and PRESSURE conditions

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Under Pressure

• Force per unit area, where the force is Normal
  (perpendicular) to the surface.
• A ratio of the force to the unit area, where the
  force is Normal to the surface
• Pounds-per-Square-Inch (psi) is the CMS standard
  unit for pressure.
• lbs / in2

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Pressure Drop

• Consider a rectangular-prism filled with a fluid
  the prism is 12 long x 8 wide x 4 tall.
• Suppose the fluid exerts 10 psi.
• How many pounds of FORCE is exerted in each
  direction?
• Calculate the AREA of each face
• 128 96, 84 32, 412 48
• Multiply by the PRESSURE, psi
• 9610 960, 3210 320, 4810 480
• The top could lift 960 lbs, the sides can resist
  320 lbs, and the front can resist 480 lbs!

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Boyles Law

• Assuming the temperature is held constant, the
  volume of a constant mass of a fluid varies
  inversely with its pressure.
• P1 V1 P2 V2
• As the volume decreases, pressure increases
• As the volume increases, pressure decreases

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Lift Kit

• Boyles Law explains hydraulics and pneumatics
• Hydraulics- machines and tools which use a liquid
  to do work, especially actuators and turbines
• Pneumatics- machines and tools which use gasses
  to do work, especially actuators and turbines
• LIQUIDS ARE HARDER TO COMPRESS THAN GASSES!
• That is why hydraulics are used in many
  applications as actuators, where pneumatics are
  not.

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Two examples
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Example 1

• Suppose a sample of Oxygen gas occupies a volume
  of 1 ft3 at a pressure of 14.5 psi. What volume
  will it occupy at a pressure of 20 psi?
• 14.5 1 20 V2
• 14.5 / 20 V2 0.725 ft3
• http//www.unit-conversion.info/pressure.html
• http//www.unit-conversion.info/pressure.html

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Example 2

• A sample of Carbon Dioxide occupies a volume of
  3.5 ft3 at 18.125 psi. What pressure would the
  gas exert if the volume was decreased to 2 ft3?
• 18.125 3.5 P2 2
• 63.4375 / 2 P2 31.71875 psi

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Next Step

• Homework!
• Please complete the Boyles Law worksheet for
  homework, due at the beginning of class tomorrow

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BERNOULLIS PRINCIPLE

• Take a piece of paper and hold with two hands,
  just below your mouth.
• Now exhale strongly. (You might need to
  angle-down a little and/or blow very hard to get
  the desired result.)
• What are your observations?

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In a nutshell

• Bernoulli states that a faster-moving body of air
  will exert less pressure.
• In other words, if a fluid is accelerated, the
  pressure will be lower for that accelerated
  section of fluid.
• Similarly, if a fluid is decelerated, the
  pressure will be higher for that decelerated
  section of fluid.
• http//hyperphysics.phy-astr.gsu.edu/hbase/pber.ht
  ml
• http//hyperphysics.phy-astr.gsu.edu/hbase/pber.ht
  ml