Physics 151: Lecture 29 Today

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Physics 151 Lecture 29 Todays Agenda

• Todays topics
• Fluids under static conditions, Ch. 14.1 through
  14.4
• Pressure
• Pascals Principle (hydraulic lifts etc.)
• Archimedes Principle (floatation)

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Fluids
See text 14.1

• At ordinary temperature, matter exists in one of
  three states
• Solid - has a shape and forms a surface
• Liquid - has no shape but forms a surface
• Gas - has no shape and forms no surface
• What do we mean by fluids?
• Fluids are substances that flow. substances
  that take the shape of the container
• Atoms and molecules are free to move.
• No long range correlation between positions.

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Fluids
See text 14.1

• What parameters do we use to describe fluids?
• Density

units kg/m3 10-3 g/cm3
r(water) 1.000 x103 kg/m3 1.000
g/cm3 r(ice) 0.917 x103 kg/m3
0.917 g/cm3 r(air) 1.29 kg/m3
1.29 x10-3 g/cm3 r(Hg) 13.6
x103 kg/m3 13.6 g/cm3
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Fluids

• What parameters do we use to describe fluids?
• Pressure

units 1 N/m2 1 Pa
(Pascal) 1 bar 105 Pa 1 mbar 102 Pa 1 torr
133.3 Pa
1atm 1.013 x105 Pa 1013 mbar
760 Torr 14.7 lb/m2 (PSI)

• Any force exerted by a fluid is perpendicular to
  a surface of contact, and is proportional to the
  area of that surface.
• Force (a vector) in a fluid can be expressed in
  terms of pressure (a scalar) as

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Pressure vs. DepthIncompressible Fluids
(liquids)
See text 14.2

• When the pressure is much less than the bulk
  modulus of the fluid, we treat the density as
  constant independent of pressure incompressible
  fluid
• For an incompressible fluid, the density is the
  same everywhere, but the pressure is NOT!

• Consider an imaginary fluid volume (a cube, face
  area A)
• The sum of all the forces on this volume must be
  ZERO as it is in equilibrium F2 - F1 - mg 0

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Pressure vs. Depth
See text 14.2

• If the pressures were different, fluid would flow
  in the tube!
• However, if fluid did flow, then the system was
  NOT in equilibrium since no equilibrium system
  will spontaneously leave equilibrium.

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Lecture 29, ACT 1Pressure

• What happens with two fluids?? Consider a U tube
  containing liquids of density r1 and r2 as shown
• Compare the densities of the liquids

dI
r2
r1
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Example

• A U-tube of uniform cross-sectional area, open to
  the atmosphere, is partially filled with mercury.
  Water is then poured into both arms. If the
  equilibrium configuration of the tube is as shown
  in Figure on the right, with h2 1.00 cm.
• Determine the value of h1.

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Example

• Figure on the right shows Superman attempting to
  drink water through a very long straw. With his
  great strength he achieves maximum possible
  suction. The walls of the tubular straw do not
  collapse.
• (a) Find the maximum height through which he can
  lift the water.

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Pascals Principle
See text 14.2

• So far we have discovered (using Newtons Laws)
• Pressure depends on depth Dp rgDy
• Pascals Principle addresses how a change in
  pressure is transmitted through a fluid.

• Pascals Principle explains the working of
  hydraulic lifts
• i.e. the application of a small force at one
  place can result in the creation of a large force
  in another.
• Does this hydraulic lever violate conservation
  of energy?
• Certainly hope not.. Lets calculate.

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Pascals Principle
See text 14.2

• Consider the system shown
• A downward force F1 is applied to the piston of
  area A1.
• This force is transmitted through the liquid to
  create an upward force F2.
• Pascals Principle says that increased pressure
  from F1 (F1/A1) is transmitted throughout the
  liquid.

• F2 gt F1 Have we violated conservation of
  energy??

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Pascals Principle
See text 14.2

• Consider F1 moving through a distance d1.
• How large is the volume of the liquid displaced?

• This volume determines the displacement of the
  large piston.

• Therefore the work done by F1 equals the work
  done by F2 We have NOT obtained something for
  nothing.

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Lecture 29, ACT 2aHydraulics

• Consider the systems shown to the right.
• In each case, a block of mass M is placed on the
  piston of the large cylinder, resulting in a
  difference dI in the liquid levels.
• If A2 2A1, compare dA and dB.

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Lecture 29, ACT 2bHydraulics

• Consider the systems shown to the right.
• In each case, a block of mass M is placed on the
  piston of the large cylinder, resulting in a
  difference dI in the liquid levels.
• If A10 2A20, compare dA and dC.

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Archimedes Principle
See text 14.4

• Suppose we weigh an object in air (1) and in
  water (2).
• How do these weights compare?

• Why?
• Since the pressure at the bottom of the object is
  greater than that at the top of the object, the
  water exerts a net upward force, the buoyant
  force, on the object.

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Archimedes Principle
See text 14.4

• The buoyant force is equal to the difference in
  the pressures times the area.

• The buoyant force determines whether an object
  will sink or float. How does this work?

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Sink or Float?
See text 14.4

• The buoyant force is equal to the weight of the
  liquid that is displaced.
• If the buoyant force is larger than the weight of
  the object, it will float otherwise it will sink.

• We can calculate how much of a floating object
  will be submerged in the liquid

• Object is in equilibrium

Animation
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The Tip of the Iceberg
See text 14.4

• What fraction of an iceberg is submerged?

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Lecture 29, ACT 3Buoyancy

• A lead weight is fastened to a large styrofoam
  block and the combination floats on water with
  the water level with the top of the styrofoam
  block as shown.
• If you turn the styrofoamPb upside down, what
  happens?

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ACT 3-AMore Fun With Buoyancy
See text 14.4

• Two cups are filled to the same level with water.
  One of the two cups has plastic balls floating
  in it.
• Which cup weighs more?

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ACT 3-BEven More Fun With Buoyancy
See text 14.4

• A plastic ball floats in a cup of water with half
  of its volume submerged. Next some oil (roil lt
  rball lt rwater) is slowly added to the container
  until it just covers the ball.
• Relative to the water level, the ball will

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Recap of todays lecture

• Chapter 14.1-4
• Pressure
• Pascals Principle
• Archimedes Principle