Fluid Flow and Continuity

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Fluid Flow and Continuity
Imagine that a fluid flows with a speed v1
through a cylindrical pip of cross-sectional
area A1.
If the pipe narrows to a cross-sectional area A2,
as in the right-hand portion of the Figure, the
fluid will flow with a new speed, v2.
Any amount of fluid that passes point 1 in a
given time , ?t, must also flow past the point 2
in the same time. To find the mass of fluid
passing point 1 in the time ?t, note that the
fluid moves through a distance v1 ?t in this
time. As a result, the volume of fluid going past
point 1 is
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Fluid Flow and Continuity
the volume of fluid going past point 1 is
Hence, the mass of fluid passing point 1 is
Similarly, the mass passing point 2 in the same
time,
Equation of Continuity
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Example 7 Spray I Water travels through a 9.6 cm
diameter fire hose with a speed of 1.3 m/s. At
the end of the hoe, the water flows out through
nozzle whose diameter is 2.5 cm. What is the
speed of the water coming out of the nozzle?
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Physics 102 Part IIThermal Physics
Temperature and Heat Lecture 13

• Moza M. Al-Rabban
• Professor of Physics
• mmr_at_qu.edu.qa

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Temperature and the Zeroth Law of Thermodynamics

• Heat is the energy transferred between objects
  because of a temperature difference.
• Therefore, when we say that there is a transfer
  of heat or a heat flow from object A to
  object B, it means that the total energy of
  object A decreases and the total energy of object
  B increases.

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Heat

• Definition Flow of energy between two objects
  due to difference in temperature
• Note similar to WORK
• Object does not have heat (it has energy)

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• Temperature
• How hot or cold an objects feels?
• Thermal Contact
• ?? Two objects are in thermal contact if
  they can exchange energy by
• Heat (includes conduction)
• Electromagnetic radiation
• ?? Energy is exchanged when there is a
  temperature difference
• ?? Thermal contact does not have to also
  be physical contact
• Thermal Equilibrium
• ?? Thermal equilibrium is a when two
  objects would not exchange energy
• by heat or electromagnetic radiation if
  they were placed in thermal
• contact. The transfer of heat ceases.
• ?? Two objects in thermal equilibrium are
  at the same temperature
• ?? Objects at different temperatures are
  not in thermal equilibrium
• They will exchange energy if
  brought into thermal contact
• Zeroth Law of Thermodynamics

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Thermometers

• Make use of physical properties that change with
  temperature
• Many physical properties can be used
• volume of a liquid
• length of a solid
• pressure of a gas held at constant volume
• volume of a gas held at constant pressure
• electric resistance of a conductor
• color of a very hot object

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Temperature scales
Celsius Scale

• Temperature of an ice-water mixture is defined as
  0º C
• This is the freezing point of water
• Temperature of a water-steam mixture is defined
  as 100º C
• This is the boiling point of water
• Distance between these points is divided into 100
  segments
• There is no upper limit to the value a
  temperature may have.
• There is a lower limit, however. For the Celsius
  scale, it is -273.15 ?C.

A temperature of five degrees is 5 ?C (five
degrees Celsius) A temperature change of five
degrees is 5 C ? ( five Celsius degrees)
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The Fahrenheit Scale

• Temperature of an ice-water mixture is defined as
  32º F
• This is the freezing point of water
• Temperature of a water-steam mixture is defined
  as 212º C
• This is the boiling point of water
• Distance between these points is divided into 180
  segments

• Note that the Fahrenheit scale has
• Different zero than the Celsius scale
• Different size for its degree.
• The Fahrenheit degrees are smaller by factor of
  100/180 5/9

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Conversion between Degrees Celsius and Degrees
Fahrenheit
Conversion between Degrees Fahrenheit and Degrees
Celsius
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• Example1 Temperature Conversions
• On a fine spring day you notice that temperature
  is 75 F. What is the corresponding temperature on
  the Celsius scale?
• If the temperature on a brisk winter morning is
  2.0 C, what is the corresponding Fahrenheit
  temperature?

Part (a)
Part (b)
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Absolute Zero

• Temperature readings are nearly independent of
  the gas
• Pressure varies with temperature when maintaining
  a constant volume

• All gases extrapolate to the same temperature at
  0 pressure
• This temperature is absolute zero

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Example 2 Its a Gas The gas in a
constant-volume gas thermometer has a pressure of
80.0 kPa at 0.00 C. Assuming ideal behavior, as
in the Figure, what is the pressure of this gas
at 105 C?

1. Calculate the rate at which pressure increases
   for this gas

2. Multiply this rate by the temperature change
from -273.15 C to 105 C
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Kelvin Scale

• When the pressure of a gas goes to zero, its
  temperature is 273.15º C
• This temperature is called absolute zero

This is the zero point of the Kelvin
scale 273.15º C 0 K To convert
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Modern Definition of Kelvin Scale

• Defined in terms of two points
• Agreed upon by International Committee on Weights
  and Measures in 1954
• First point is absolute zero
• Second point is the triple point of water
• Triple point is the single point where water can
  exist as solid, liquid, and gas
• Same temperature and pressure
• Occurs at 0.01º C and P 4.58 mm Hg

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A comparison of temperature scales
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Question
You measure your body temperature with a
thermometer calibrated in degrees Kelvin, 98 F.
Convert it to Kelvin temperature scale 1.
307 K 2. 310 K 3. 313 K 4.
317 K
98oF 37oC 310oK
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Thermal Expansion

• The thermal expansion of an object is a
  consequence of the change in the average
  separation between its constituent atoms or
  molecules
• At ordinary temperatures, molecules vibrate with
  a small amplitude
• As temperature increases, the amplitude increases
• This causes the overall object as a whole to
  expand

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Linear Expansion
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Linear Expansion

• For small changes in temperature
• The coefficient of linear expansion, ??, depends
  on the material
• SI unit for ?
• These are average coefficients, they can vary
  somewhat with temperature

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ApplicationsA bimetallic strip
Thermometer
Thermostat
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Thermal Expansion joints
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Area Expansion

• Two dimensions expand

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Question

• You are given a 4.000-cm diameter steel ball
  bearing and a brass plate with a 3.994-cm
  diameter hole at room temperature (20C). You are
  asked to squeeze the steel ball through the brass
  plate. You are allowed to increase or decrease
  the temperature of the two objects. However, they
  should both be at equal temperature at all times.
  What can you do to succeed?
• (? brass 2 x 10-5 /C, ? steel 1 x 10-5 /C)
• Cool the ball and the plate.
• Heat the ball and the plate.
• You can never succeed.

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Volume Expansion

• Three dimensions expand
• For liquids, only coefficient of volume expansion
  exists

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Example 3 Oil Spill A copper flask with a
volume of 150 cm3 is filled to the brim with
olive oil. If the temperature of the system is
increased from 6.0 C to 31 C, how much oil spills
from the flask?
1. Calculate the change in volume of the oil
2. Calculate the change in volume of the flask
3. Find the difference in volume expansions. This
is the volume of oil that spills out
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Special Properties of Water
The unusual behavior of water near 4 C.
The density of water actually increases as the
water is heated between 0 C and 4 C. Maximum
density occurs near 4 C.
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End Of Lecture 13