Fluids

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Fluids

• Honors Physics

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Liquids

• In a liquid, molecules flow freely from position
  to position by sliding over each other
• Have definite volume
• Do not have definite shape conform to their
  container

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Density

• Mass Density
• ? m/V
• Units kg/m3
• Common densities
• Air 1.29 kg/m3
• Fresh water 1.00 x 103 kg/m3
• Ice - 0.917 x103 kg/m3

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Densities of Common Substances
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Buoyancy

• The apparent loss of weight of an object that is
  submerged
• The water exerts an upward force that is opposite
  the direction of gravity called the buoyant force.

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Submerged

• An object placed in water will displace, or push
  aside, some of the water
• The volume of water displaced, is equal to the
  volume of the object
• This method can be used to easily determine the
  volume of irregularly shaped objects

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Archimedes Principle

• An immersed object is buoyed up by a force equal
  to the weight of the fluid it displaces.
• This principle is true for all fluids.

• This means that the apparent weight of an
  immersed object is its weight in air minus the
  weight of the water it displaces
• For floating objects
• FB Fg (object)

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Examples

• A brick with a mass of 2kg weighs 19.6N If it
  displaces 1L of water, what is the buoyant force
  exerted on the brick?

• Buoyant force weight of water displaced
• 1L displaced 9.8N
• Buoyant force 9.8N

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Sink or Float?

• If the buoyant force acting on an object is
  greater than its weight force, the object will
  float
• A submerged objects volume, not mass determines
  buoyant force

• 3 Rules
• An object more dense than the fluid it is
  immersed in will sink
• An object less dense than the fluid it is
  immersed in will float
• An object with equal density to the fluid will
  neither sink nor float.

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Density Buoyant Force

• The buoyant force and apparent weight of an
  object depends on density

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Sample Problem 9A

• A bargain hunter purchases a gold crown at a
  flea market. After she gets home, she hangs the
  crown from a scale and finds its weight to be
  7.84 N. She then weighs the crown while it is
  immersed in water, and the scale reads 6.86 N. Is
  the crown make of pure gold? Explain.

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Floatation

• Why is it possible for a brick of iron to sink,
  but an equal mass of iron shaped into a hull will
  float?
• When the iron is shaped, it takes up more space
  (volume)
• Principle of Flotation A floating object
  displaces a weight of fluid equal to its own
  weight

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Liquid Pressure

• Pressure for solids is determined by the equation
  PF/A
• In this equation, the force is simply the weight
  of the object.
• The same principle can be used for liquids

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Pascals Principle

• Pressure applied to a fluid in a closed container
  is transmitted equally to every point of the
  fluid and to the walls of the container.
• F2 A2 F1
• A1

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Sample Problem 9B

• The small piston of a hydraulic life has an area
  of 0.20 m2. A car weighing 1.20 x 104 N sits on a
  rack mounted on the large piston. The large
  piston has an area of 0.90 m2. How large a force
  must be applied to the small piston to support
  the car?

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Pressure

• More dense liquids will produce more force and,
  therefore, more pressure.
• The higher the column of liquid the more pressure
  also.
• For liquids,
• Pressure density x g x depth
• AKA Gauge Pressure ?gh
• Total pressure density x g x depth
  atmospheric pressure
• P PO ?gh

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Examples

• Is there more water pressure at 3m or at 9m of
  depth?
• Calculate the pressure exerted by a column of
  water 10m deep.

• 9m
• 98000 Pa

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Sample Problem 9C

• Calculate the absolute pressure at an ocean depth
  of 1.00 x 103 m. Assume that the density of the
  water is 1.025 x 103 kg/m3 and that PO1.01 x 105
  Pa.

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Pascals Principle

• Changes in pressure at any point in an enclosed
  fluid at rest are transmitted undiminished to all
  points in the fluid and act in all directions.
• Hydraulic systems operate using this principle.

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Gasses

• Have neither definite volume nor shape
• The atmosphere is a good example of a gas.
• In the atmosphere, the molecules are energized by
  sunlight and kept in continual motion

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Atmosphere

• The density of the atmosphere decreases with
  altitude
• Most of the Earths atmosphere is located close
  to the planets surface.

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Atmospheric Pressure

• The atmosphere all around us exerts pressure just
  as if we were submersed in a liquid
• At sea level, air has a density of about 1.2 kg
  per cubic meter

• A column of air, of 1 sq. meter that extends up
  through the atmosphere weighs about 100,000 N
• The avg atmospheric pressure a sea level is
  101.3 kPa

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Measuring Pressure

• A barometer is used to measure atmospheric
  pressure
• Air pressure forces mercury up the glass tube, to
  display the pressure
• This process is similar to that of drinking out
  of a straw

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Boyles Law

• For a gas, the product of the pressure and the
  volume remain constant as long as the temperature
  does not change.
• P1V1 P2V2

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Examples

• If you squeeze a balloon to 1/3 its original
  volume, what happens to the pressure inside?
• 3x

• A swimmer dives down, until the pressure is twice
  the pressure at the waters surface. By how much
  does the air in the divers lungs contract?
• 2x

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Charles Law

• The volume of a definite quantity of a gas varies
  directly with the temperature, provided the
  pressure remains constant.
• V1T2 V2T1

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Combined Gas Law

• When Boyles and Charles laws are combined the
  equation looks like this.
• P1V1T2 P2V2T1

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Sample Problem 9E

• Pure helium gas is contained in a leakproof
  cylinder containing a movable piston. The initial
  volume pressure and temperature of the gas are 15
  L, 2.0 atm and 310 K, respectively. If the gas is
  rapidly compressed to 12 L and the pressure
  increased to 3.5 atm, find the final temperature
  of the gas.

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Ideal Gas Law

• Compares volume, pressure, and temperature of a
  gas
• PV NkBT
• P pressure, V volume, N of mols of gas
  particles, kB Boltzmans Constant (1.38x10-23
  J/K), T temperature

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Fluid Flow

• Smooth flow is said to be laminar flow
• Particles all follow along a smooth path
• Streamline path
• Streamlines never cross

• Irregular flow is said to be turbulent
• Irregular motion produced are called eddies

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Continuity

• Continuity says that the mass of and ideal fluid
  flowing into a pipe must equal to mass flowing
  out of the pipe.
• Or m1 m2

• Because the mass flowing is determined by the
  cross-sectional area of the pipe and how fast it
  flows, we can also say
• A1v1 A2v2

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Bernoullis Principle

• Pressure in a fluid decreases as the fluids
  velocity increases.
• Bernoullis Principle can be seen in birds in
  flight and airplanes
• Pressure above the wing is less than pressure
  below the wing, creating lift

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Bernoullis Equation

• This is an expression of conservation of energy
  in a fluid.
• P ½?v2 ?gh constant
• Pressure kinetic energy per unit volume
  gravitational potential energy per unit volume
  constant along a given streamline

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Sample Problem 9D

• A water tank has a spigot near its bottom. If the
  top is open to the atmosphere, determine the
  speed at which the water leaves the spigot when
  the water level is 0.500m above the spigot.
• Well use
• (P ½?v2 ?gh)1 (P ½?v2 ?gh)2

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• we assume the water level is dropping slowly, so
  v2, at the top, 0
• Also, since both ends are open to the atmosphere
  P1 P2
• That simplifies the equation to
• P ½?v12 ?gh1 P ?gh2 and subtract P
• ½?v12 ?gh1 ?gh2 ? is the same
  throughout, so
• ½v12 gh1 gh2 solve for v
• v v(2g(h2-h1)) plug chug
• v v(2(9.8 m/s2)(.5m))
• v 3.13 m/s

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Pg. 344 17, 18, 23, 25, 29, 36, 39, 44, 47, 48

• Test on FluidsThursday