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Archimedes Principle

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Double diameter, pressure does not change. On Mars pressure ... Deriving Lift. Use Bernoulli's equation: pt 1/2rvt2=pb 1/2rvb2. The difference in pressure is: ... – PowerPoint PPT presentation

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Title: Archimedes Principle


1
Archimedes Principle
  • Physics 202
  • Professor Lee Carkner
  • Lecture 2

2
PAL 1 Fluids
  • Column of water to produce 1 atm of pressure
  • P rgh
  • P
  • r 1000 kg/m3
  • g 9.8 m/s2
  • h P/rg
  • Double diameter, pressure does not change
  • On Mars pressure would decrease
  • Mars has smaller value of g

3
Archimedes Principle
  • What happens if you put an object in a fluid?
  • Called the buoyant force
  • If you measure the buoyant force and the weight
    of the displaced fluid, you find
  • An object in a fluid is supported by a buoyant
    force equal to the weight of fluid it displaces
  • Applies to objects both floating and submerged

4
Will it Float?
  • Density
  • An object less dense than the fluid will float
  • A floating object displaces fluid equal to its
    weight
  • A sinking object displaces fluid equal to its
    volume

5
Floating
  • How will an object float?
  • The volume of fluid displaced is proportional to
    the ratio of the densities
  • Example ice floating in water,
  • riVigrwVwg
  • VwVi (ri/rw)
  • rw 1024 kg/m3 and ri 917 kg/m3

6
Ideal Fluids
  • Steady --
  • Incompressible -- density is constant
  • Nonviscous --
  • Irrotational -- constant velocity through a cross
    section
  • The ideal fluid approximation is usually not very
    good

7
Moving Fluids
  • What happens if the pipe narrows?
  • Avr constant
  • If the density is constant then,
  • Av constant R volume flow rate
  • Constricting a flow increases its velocity
  • Because the amount of fluid going in must equal
    the amount of fluid going out
  • Or, a big slow flow moves as much mass as a small
    fast flow

8
Continuity
  • RAvconstant is called the equation of
    continuity
  • You can use it to determine the flow rates of a
    system of pipes
  • Cant lose or gain any material

9
The Prancing Fluids
  • How can we keep track of it all?
  • The laws of physics must be obeyed
  • Neither energy nor matter can be created or
    destroyed

10
Bernoullis Equation
  • Consider a pipe that bends up and gets wider at
    the far end with fluid being forced through it
  • Wg -Dmg(y2-y1) -rgDV(y2-y1)
  • The work of the system due to pressure is,
  • WpFdpAdDpDV-(p2-p1)DV
  • D(1/2mv2)1/2rDV(v22-v12)
  • p1(1/2)rv12rgy1p2(1/2)rv22rgy2

11
Consequences of Bernoullis
  • Fast moving fluids exert less pressure than slow
    moving fluids
  • This is known as Bernoullis principle
  • Energy that goes into velocity cannot go into
    pressure
  • Note that Bernoulli only holds for moving fluids

12
Bernoulli in Action
  • Blowing between two pieces of paper
  • Convertible top bulging out
  • Airplanes taking off into the wind

13
Lift
  • If the velocity of the flow is less on the bottom
    than on top there is a net pressure on the bottom
    and thus a net force pushing up
  • If you can somehow get air to flow over an object
    to produce lift, what happens?

14
Deriving Lift
  • Use Bernoullis equation
  • pt1/2rvt2pb1/2rvb2
  • The difference in pressure is
  • pb-pt1/2rvt2-1/2rvb2
  • (Fb/A)-(Ft/A)1/2r(vt2-vb2)
  • L (½)rA(vt2-vb2)

15
Next Time
  • Read 15.1-15.3
  • Homework Ch 14, P 37, 42, 47, Ch 15, P 6, 7

16
Which of the following would decrease the
pressure you exert on the floor the most?
  • Doubling your mass
  • Doubling the mass of the earth
  • Doubling your height
  • Doubling the size of your shoes
  • Doubling air pressure

17
Which of the following would increase the
pressure of a column of fluid of fixed mass the
most?
  • Doubling the width of the column
  • Halving the density of the fluid
  • Halving the mass of the Earth
  • Halving the speed of the Earths rotation
  • Doubling the height of the column

18
Summary Fluid Basics
  • Density rm/V
  • PressurepF/A
  • On Earth the atmosphere exerts a pressure and
    gravity causes columns of fluid to exert pressure
  • Pressure of column of fluid
  • pp0rgh
  • For fluid of uniform density, pressure only
    depends on height

19
Summary Pascal and Archimedes
  • Pascal -- pressure on one part of fluid is
    transmitted to every other part
  • Hydraulic lever -- A small force applied for a
    large distance can be transformed into a large
    force over a short distance
  • FoFi(Ao/Ai) and dodi(Ai/Ao)
  • Archimedes -- An object is buoyed up by a force
    equal to the weight of the fluid it displaces
  • Must be less dense than fluid to float

20
Summary Moving Fluids
  • Continuity -- the volume flow rate (RAv) is a
    constant
  • fluid moving into a narrower pipe speeds up
  • Bernoulli
  • p11/2rv12rgy1p21/2rv22rgy2
  • Slow moving fluids exert more pressure than fast
    moving fluids
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