Physics 151: Lecture 30 Today

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Physics 151 Lecture 30 Todays Agenda

• Todays Topic
• Fluids in Motion
• Bernoullis Equation and applications

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Example / Fluid Statics

• A beaker of mass mbeaker containing oil of mass
  moil (density roil) rests on a scale. A block
  of iron of mass miron is suspended from a spring
  scale and completely submerged in the oil as in
  Figure on the right.
• Determine the equilibrium readings of both scales.

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Fluids in Motion
See text 14.5

• Up to now we have described fluids in terms of
  their static properties
• density r
• pressure p
• To describe fluid motion, we need something that
  can describe flow
• velocity v

• There are different kinds of fluid flow of
  varying complexity
• non-steady / steady
• compressible / incompressible
• rotational / irrotational
• viscous / ideal

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Ideal Fluids
See text 14.5

• Fluid dynamics is very complicated in general
  (turbulence, vortices, etc.)
• Consider the simplest case first the Ideal Fluid
• no viscosity - no flow resistance (no internal
  friction)
• incompressible - density constant in space and
  time

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Ideal Fluids
See text 14.6

• streamlines do not meet or cross
• velocity vector is tangent to streamline
• volume of fluid follows a tube of flow bounded by
  streamlines

streamline

• Flow obeys continuity equation
• volume flow rate Q Av is constant
  along flow tube.

A1v1 A2v2

• follows from mass conservation if flow is
  incompressible.

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Conservation of Energy for Ideal Fluid
See text 14.7

• Recall the standard work-energy relation
• Apply the principle to a section of flowing fluid
  with volume dV and mass dm r dV (here W is work
  done on fluid)

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Lecture 30 Act 1Continuity

• A housing contractor saves some money by reducing
  the size of a pipe from 1 diameter to 1/2
  diameter at some point in your house.

v1
v1/2
1) Assuming the water moving in the pipe is an
ideal fluid, relative to its speed in the 1
diameter pipe, how fast is the water going in the
1/2 pipe?
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Lecture 30 Act 2Bernoullis Principle

• A housing contractor saves some money by reducing
  the size of a pipe from 1 diameter to 1/2
  diameter at some point in your house.

v1
v1/2
2) What is the pressure in the 1/2 pipe relative
to the 1 pipe?
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DEMO SLIDE

• The smaller the diameter the lower is the pressure

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Example

• A Pitot tube (see Fig. below) can be used to
  determine the velocity of air flow by measuring
  the difference between the total pressure and the
  static pressure. If the fluid in the tube is
  mercury, density rHg 13 600 kg/m3, and h 5.00
  cm, find the speed of air flow. (Assume that the
  air is stagnant at point A and take rair 1.25
  kg/m3.)

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Venturi Meter
v ? Can we know what is v from what we can
measure ? h rHg rair
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Example

• A tank containing a liquid of density r has a
  hole in its side at a distance h below the
  surface of the liquid. The hole is open to the
  atmosphere and its diameter is much smaller than
  the diameter of the tank.
• What is the speed with of the liquid as it leaves
  the tank.

h
r
v?
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Example

• Figure on the right shows a stream of water in
  steady flow from a kitchen faucet. At the faucet
  the diameter of the stream is 0.960 cm. The
  stream fills a 125-cm3 container in 16.3 s. Find
  the diameter of the stream 13.0 cm below the
  opening of the faucet.

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Example

• Water is forced out of a fire extinguisher by air
  pressure, as shown in Figure below. How much
  gauge air pressure in the tank (above
  atmospheric) is required for the water jet to
  have a speed of 30.0 m/s when the water level in
  the tank is 0.500 m below the nozzle?

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Recap of todays lecture

• 14.4-7
• Streamlines
• Bernoullis Equation and applications