Fluids

1
AP Physics

• Fluids Thermodynamics

2
Fluids

• Fluids are substances that can flow, such as
  liquids and gases, and even some solids
• Well just talk about the liquids gases
• Review of Density (remember this from chem?)
• ? m/V
• ? density
• m mass (kg)
• V volume (m3)
• density units kg/m3

3
Pressure

• P F/A
• P pressure (Pa)
• F force (N)
• A area (m2)
• Units for pressure Pascals
• 1 Pa 1 N/m2
• Pressure is always applied as a normal force on a
  surface. Fluid pressure is exerted in all
  directions and is perpendicular to every surface
  at every location.

4
Pressure Practice 1

• Calculate the net force on an airplane window if
  cabin pressure is 90 of the pressure at sea
  level and the external pressure is only 50 of
  the pressure at sea level. Assume the window is
  0.43 m tall and 0.30 m wide.

5
Atmospheric pressure

• Atmospheric pressure is normally about 100,000
  Pascals.
• Differences in atmospheric pressure cause winds
  to blow

6
Pressure of a Liquid

• The pressure of a liquid is sometimes called
  gauge pressure
• If the liquid is water, it is called hydrostatic
  pressure
• P ?gh
• P pressure (Pa)
• ? density (kg/m3)
• g 9.81 m/s2
• h height of liquid column (m)

7
Absolute Pressure

• Absolute pressure is obtained by adding the
  atmospheric pressure to the hydrostatic pressure
• Patm ?gh Pabs

• 2. The depth of Lake Mead at the Hoover Dam is
  600 ft.
• What is the hydrostatic pressure at the base of
  the dam?
• What is the absolute pressure at the base of the
  dam?

8
Buoyancy Force

• Floating is a type of equilibrium An upward
  force counteracts the force of gravity for
  floating objects
• The upward force is called the buoyant force
• Archimedes Principle a body immersed in a fluid
  is buoyed up by a force that is equal to the
  weight of the fluid it displaces

9
Calculating Buoyant Force

• Fbuoy ?Vg
• Fbuoy buoyant force exerted on a submerged or
  partially submerged object
• V volume of displaced fluid
• ? density of displaced fluid
• When an object floats, the upward buoyant force
  equals the downward pull of gravity
• The buoyant force can float very heavy objects,
  and acts upon objects in the fluid whether they
  are floating, submerged, or even resting on the
  bottom

10
Buoyant force on submerged objects

• A sharks body is not neutrally buoyant, so a
  shark must swim continuously or it will sink
  deeper

• Scuba divers use a buoyancy control system to
  maintain neutral buoyancy (equilibrium)
• If the diver wants to rise, he inflates his vest,
  which increases his volume, or the water he
  displaces, and he accelerates upward

11
Buoyant Force on Floating Objects

• If the object floats on the surface, we know that
  Fbuoy Fg! The volume of displaced water equals
  the volume of the submerged portion of the object

12
3

• Assume a wooden raft has 80.0 of the density of
  water. The dimensions of the raft are 6.0 m long
  by 3.0 m wide by 0.10 m tall. How much of the
  raft rises above the level of the water when it
  floats?

13
Buoyant Force Labs

• Determine the density of water by using the
  buoyant force.
• Equipment
• Beakers
• String
• Pulleys
• Weights/Masses
• Graduated cylinder
• (NO BALANCES!)

• 2. Balloon Race
• Determine the buoyant force on your balloon with
  the balloon, masses a balance
• Without using the balloon, design an apparatus
  so that when released, your balloon will hit the
  ceiling LAST.

14
Moving Fluids

• When a fluid flows, mass is conserved
• Provided there are no inlets or outlets in a
  stream of flowing fluid, the same mass per unit
  time must flow everywhere in the stream

• The volume per unit time of a liquid flowing in a
  pipe is constant throughout the pipe
• We can say this because liquids are generally not
  compressible, so mass conservation is also volume
  conservation for a liquid

15
Fluid Flow Continuity

• V Avt
• V volume of fluid (m3)
• A cross sectional areas at a point in the pipe
  (m2)
• v the speed of fluid flow at a point in the pipe
  (m/s)
• t time (s)

• Comparing two points in a pipe
• A1v1 A2v2
• A1, A2 cross sectional areas at points 1 and 2
• v1, v2 speeds of fluid flow at points 1 and 2

16
Practice 4 5

• 4. A pipe of diameter 6.0 cm has fluid flowing
  through it at 1.6 m/s. How fast is the fluid
  flowing in an area of the pipe in which the
  diameter is 3.0 cm? How much water per second
  flows through the pipe?

• 5. The water in a canal flows 0.10 m/s where the
  canal is 12 meters deep and 10 meters across. If
  the depth of the canal is reduced to 6.5 m at an
  area where the canal narrows to 5.0 m, how fast
  will the water be moving through the narrower
  region?

17
Bernoullis Theorem

• The sum of the pressure, the potential energy per
  unit volume, and kinetic energy per unit volume
  at any one location in the fluid is equal to the
  sum of the pressure, the potential energy per
  unit volume, and the kinetic energy per unit
  volume at any other location in the fluid for a
  non-viscous incompressible fluid in streamline
  flow
• All other considerations being equal, when fluid
  moves faster, pressure drops

18
Bernoullis Theorem

• P ?gh ½ ?v2 constant
• P pressure (Pa)
• ? density of fluid (kg/m3)
• g grav. accel. constant (9.81 m/s2)
• h height above lowest point
• v speed of fluid flow at a point in the pipe
  (m/s)

• 6. Knowing what you know about Bernoullis
  principle, design an airplane wing that you think
  will keep an airplane aloft. Draw a cross
  section of the wing.

19
Thermodynamics

• Thermodynamics is the study of heat and thermal
  energy
• Thermal properties (heat temperature) are based
  on the motion of individual molecules, so
  thermodynamics overlaps with chemistry

• Total Energy
• E U K Eint
• U potential energy
• K kinetic energy
• Eint internal or thermal energy

20
Total Energy

• Potential and kinetic energies are specifically
  for big objects, and represent mechanical
  energy
• Thermal energy is related to the kinetic energy
  of the molecules of a substance

21
Temperature Heat

• Temperature is a measure of the average kinetic
  energy of the molecules of a substance. (like
  how fast the molecules are moving) The unit is C
  or K. Temperature is NOT heat!
• Heat is the internal energy that is transferred
  between bodies in contact. The unit is Joules
  (J) or sometimes calories (cal)
• A difference in temperature will cause heat
  energy to be exchanged between bodies in contact.
  When two bodies are the same temp, they are in
  thermal equilibrium and no heat is transferred.

22
Ideal Gas Law

• P initial final pressure (any unit)
• V initial final volume (any unit)
• T initial final temperature (K)
• T in Kelvins T in C 273

23
7

• 7. Suppose an ideal gas occupies 4.0 L at 23C
  and 2.3 atm. What will be the volume of the gas
  if the temperature is lowered to 0C and the
  pressure is increased to 3.1 atm?

24
Ideal Gas Equation

• If you dont remember this from chem, you
  shouldnt have passed!
• P pressure (Pa)
• V volume (m3)
• n number of moles
• R gas law constant 8.31 J/(mol K)
• T temp (K)

25
8

• 8. Determine the number of moles of an ideal gas
  that occupy 10.0 m3 at atmospheric pressure and
  25C.

26
Ideal Gas Equation

• P pressure (Pa)
• V volume (m3)
• N number of molecules
• kB Boltzmanns constant
• 1.38 x 10-23J/K
• T temperature (K)

• 9. Suppose a near vacuum contains 25,000
  molecules of helium in one cubic meter at 0C.
  What is the pressure?

27
Kinetic Theory of Gases

1. Gases consist of a large number of molecules that
   make elastic collisions with each other and the
   walls of their container
2. Molecules are separated, on average, by large
   distances and exert no forces on each other
   except when they collide
3. There is no preferred position for a molecule in
   the container, and no preferred direction for the
   velocity

28
Average Kinetic Energy of a Gas

• Kave 3/2 kBT
• Kave average kinetic energy (J)
• kB Boltzmanns constant (1.38 x 10-23J/K)
• T Temperature (K)
• The molecules have a range of kinetic energies,
  so we take the Kave

29
10 11

• 10. What is the average kinetic energy and
  average speed of oxygen molecules in a gas sample
  at 0C?

• 11. Suppose nitrogen and oxygen are in a sample
  of gas at 100C
• a) What is the ratio of the average kinetic
  energies for the two molecules?
• b) What is the ratio of their average speeds?

30
Thermodynamics

• The system boundary controls how the environment
  affects the system (for our purposes, the system
  will almost always be an ideal gas)

• If the boundary is closed to mass, that means
  mass cant get in or out
• If the boundary is closed to energy, that means
  energy cant get in or out
• What type of boundary does the earth have?

31
First Law of Thermodynamics

• The work done on a system the heat transferred
  to the system the change in internal energy of
  the system.
• ?U W Q
• ?U Eint thermal energy (NOT potential energy
  how stupid is that?)
• W work done on the system (related to change in
  volume)
• Q heat added to the system (J) driven by
  temperature difference Q flows from hot to cold

32
First Law of Thermodynamics
33
More about U

• U is the sum of the kinetic energies of all the
  molecules in a system (or gas)
• U NKave
• U N(3/2 kBT)
• U n(3/2 RT)
• since kB R/NA

34
12 13

• 12. A system absorbs 200 J of heat energy from
  the environment and does 100 J of work on the
  environment. What is its change in internal
  energy?

• 13. How much work does the environment do on a
  system if its internal energy changes from 40,000
  J to 45,000 J without the addition of heat?

35
Gas Process

• The thermodynamic state of a gas is defined by
  pressure, volume, and temperature.
• A gas process describes how gas gets from one
  state to another state
• Processes depend on the behavior of the boundary
  and the environment more than they depend on the
  behavior of the gas

36
Isothermal Process(Constant Temperature)
37
Isobaric Process(Constant Pressure)
38
Isometric Process(Constant Volume)
39
Adiabatic Process(Insulated)
40
Work

• Calculation of work done on a system (or by a
  system) is an important part of thermodynamic
  calculations
• Work depends upon volume change
• Work also depends upon the pressure at which the
  volume change occurs

41
Work

• Done BY a gas

• Done ON a gas

42
14 15

• 14. Calculate the work done by a gas that expands
  from 0.020 m3 to 0.80 m3 at constant atmospheric
  pressure.
• How much work is done by the environment when the
  gas expands this much?

• 15. What is the change in volume of a cylinder
  operating at atmospheric pressure if its thermal
  energy decreases by 230 J when 120 J of heat are
  removed from it?

43
Work (Isobaric)
44
Work is Path Dependent
45
16 17

• 16. One mole of a gas goes from state A (200 kPa
  and 0.5 m3) to state B (150 kPa and 1.5 m3).
  What is the change in temperature of the gas
  during this process?

• 17. One mole of a gas goes from state A (200 kPa
  and 0.5 m3) to state B (150 kPa and 1.5 m3).
• Draw this process assuming the smoothest possible
  transition (straight line)
• Estimate the work done by the gas
• Estimate the work done by the environment

46
Work Done by a Cycle

• When a gas undergoes a complete cycle, it starts
  and ends in the same state. the gas is identical
  before and after the cycle, so there is no
  identifiable change in the gas.
• ?U 0 for a complete cycle
• The environment, however, has been changed

47
Work Done By Cycle

• Work done by the gas is equal to the area
  circumscribed by the cycle
• Work done by the gas is positive for clockwise
  cycles, and negative for counterclockwise cycles.
  Work done by the environment is opposite that of
  the gas

48
18

• Consider the cycle ABCDA, where
• State A 200 kPa, 1.0 m3
• State B 200 kPa, 1.5 m3
• State C 100 kPa, 1.5 m3
• State D 100 kPa, 1.0 m3
• Sketch the cycle
• Graphically estimate the work done by the gas in
  one cycle
• Estimate the work done by the environment in one
  cycle

49
19

• Calculate the heat necessary to change the
  temperature of one mole of an ideal gas from 600
  K to 500 K
• At constant volume
• At constant pressure (assume 1 atm)

50
Second Law of Thermodynamics

• No process is possible whose sole result is the
  complete conversion of heat from a hot reservoir
  into mechanical work (Kelvin-Planck statement)
• No process is possible whose sole result is the
  transfer of heat from a cooler to a hotter body
  (Clausius statement)
• Basically, heat cant be completely converted
  into useful energy

51
Heat Engines

• Heat engines can convert heat into useful work
• According to the 2nd Law of Thermodynamics, Heat
  engines always produce some waste heat
• Efficiency can be used to tell how much heat is
  needed to produce a given amount of work

52
Heat Transfer
53
Heat Engines
54
Adiabatic vs. Isothermal Expansion
55
Carnot Cycle
56
Work and Heat Engines

• QH W QC
• QH Heat that is put into the system and comes
  from the hot reservoir in the environment
• W Work that is done by the system on the
  environment
• QC Waste heat that is dumped into the cold
  reservoir in the environment

57
20

• 20. A piston absorbs 3600 J of heat and dumps
  1500 J of heat during a complete cycle. How much
  work does it do during the cycle?

58
Efficiency of Heat Engine

• In general, efficiency is related to what
  fraction of the energy put into a system is
  converted to useful work
• In the case of a heat engine, the energy that is
  put in is the heat that flows into the system
  from the hot reservoir
• Only some of the heat that flows in is converted
  to work. The rest is waste heat that is dumped
  into the cold reservoir

59
Efficiency of Heat Engine

• Efficiency W/QH (QH QC) / QH
• W Work done by the engine on the environment
• QH Heat absorbed from hot reservoir
• QC Waste heat dumped into cold reservoir
• Efficiency is often given as percent efficiency
• YOUR TASK find the efficiency of your hair dryer

60
21

• A coal-fired stream plant is operating with 33
  thermodynamic efficiency. If this is a 120 MW
  plant, at what rate is heat energy used?

61
Carnot Engine Cycle
62
Efficiency of Carnot Cycle

• For a Carnot engine, the efficiency can be
  calculated from the temperatures of the hot and
  cold reservoirs.
• Carnot Efficiency (TH TC) / TH
• TH temperature of hot reservoir (K)
• TC temperature of cold reservoir (K)

63
22 23

• 22. Calculate the Carnot efficiency of a heat
  engine operating between the temperature of 60
  and 1500C.

• 23. For 22, how much work is produced when 15 kJ
  of waste heat is generated?

64
Entropy

• Entropy is disorder, or randomness
• The entropy of the universe is increasing.
  Ultimately, this will lead to what is
  affectionately known as Heat Death of the
  Universe.

65
Entropy

• ?S Q/T
• ?S change in entropy (J/K)
• Q heat going into the system (J)
• T temperature (K)
• If change in entropy is positive, randomness or
  disorder has increased
• Spontaneous changes involve an increase in
  entropy
• Generally, entropy can go down only when energy
  is put into the system