Fluid Mechanics

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Chapter 15 Fluid Mechanics
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• Fluids
• Fluids (Ch. 5) substances that can flow
  (gases, liquids)
• Fluids conform with the boundaries of any
  container in which they are placed
• Fluids lack orderly long-range arrangement of
  atoms and molecules they consist of
• Fluids can be compressible and incompressible

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• Density and pressure
• Density
• SI unit of density kg/m3
• Pressure (cf. Ch. 14)
• SI unit of pressure N/m2 Pa (pascal)
• Pressure is a scalar at a given point in a
  fluid the measured force is the same in all
  directions
• For a uniform force on a flat area

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• Atmospheric pressure
• Atmospheric pressure
• P0 1.00 atm 1.013 x 105 Pa

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• Fluids at rest
• For a fluid at rest (static equilibrium) the
  pressure is called hydrostatic
• For a horizontal-base cylindrical water sample
  in a container

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• Fluids at rest
• The hydrostatic pressure at a point in a fluid
  depends on the depth of that point but not on any
  horizontal dimension of the fluid or its
  container
• Difference between an absolute pressure and an
  atmospheric pressure is called the gauge pressure

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Chapter 15 Problem 28
Barometric pressure in the eye of a hurricane is
0.91 atm (27.2 in. of mercury). How does the
level of the ocean surface under the eye compare
with the level under a distant fair-weather
region where the pressure is 1.0 atm?
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• Measuring pressure
• Mercury barometer
• Open-tube manometer

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• Pascals principle
• Pascals principle A change in the pressure
  applied to an enclosed incompressible fluid is
  transmitted undiminished to every portion of the
  fluid and to the walls of its container
• Hydraulic lever
• With a hydraulic lever, a given force applied
  over a given distance can be transformed to a
  greater force applied over a smaller distance

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• Archimedes principle
• Buoyant force
• For imaginary void in a fluid
• p at the bottom gt p at the top
• Archimedes principle when a body is submerged
  in a fluid, a buoyant force from the surrounding
  fluid acts on the body. The force is directed
  upward and has a magnitude equal to the weight of
  the fluid that has been displaced by the body

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• Archimedes principle
• Sinking
• Floating
• Apparent weight
• If the object is floating at the surface of a
  fluid, the magnitude of the buoyant force (equal
  to the weight of the fluid displaced by the body)
  is equal to the magnitude of the gravitational
  force on the body

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Chapter 15 Problem 29
On land, the most massive concrete block you can
carry is 25 kg. Given concretes 2200-kg/m3
density, how massive a block could you carry
underwater?
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• Motion of ideal fluids
• Flow of an ideal fluid
• Steady (laminar) the velocity of the moving
  fluid at any fixed point does not change with
  time (either in magnitude or direction)
• Incompressible density is constant and uniform
• Nonviscous the fluid experiences no drag force
• Irrotational in this flow the test body will
  not rotate about its center of mass

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• Equation of continuity
• For a steady flow of an ideal fluid through a
  tube with varying cross-section

Equation of continuity
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• Bernoullis equation
• For a steady flow of an ideal fluid
• Kinetic energy
• Gravitational potential energy
• Internal (pressure) energy

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• Bernoullis equation
• Total energy

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Chapter 15 Problem 33
Water flows through a 2.5-cm-diameter pipe at 1.8
m/s. If the pipe narrows to 2.0-cm diameter,
whats the flow speed in the constriction?
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Questions?
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Answers to the even-numbered problems Chapter 15
Problem 16 10-14
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Answers to the even-numbered problems Chapter 15
Problem 24 5.0 km
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Answers to the even-numbered problems Chapter 15
Problem 36 (a) 1.9 m/s (b) 31 m/s