1. Professor Stephen Thornton October 27, 2016
PHYS 1425
Professor Stephen Thornton
October 27, 2016

2. Reading Quiz: While snorkeling in the ocean you exhale air that forms bubbles. As the bubbles rise towards the surface, does the diameter of the bubbles A) increase? B) decrease? C) stay the same?

3. Answer: A
As the bubble rises, the pressure in the water decreases, which allows the air to expand and occupy a larger volume. LOOK AT THE PICTURE!

4. Today Begin Chapter 13 Density, fluids Pressure
Pressure gauges and barometers
Pascal’s Principle
Buoyancy
Archimedes Principle
Mass flow – equation of continuity

5. Roman Arch
Look at simple demo of Roman arch and notice how the surfaces push against each other. The stones can handle considerable compression forces on the ends. But eventually we need to deal with horizontal forces. That is why large cathedrals like Notre Dame in Paris have the large buttresses on the sides.

6. States of Matter
Matter has three states: solid, liquid, and gas
In a solid, the molecules are very close together, and the form of the solid depends on the details of the forces between them; that form is often a lattice. Solids resist changes in shape.
In a gas, the molecules are far apart and the forces between them are very small.
In a liquid, the molecules are also close together and resist changes in density, but not in shape.

7. Qualitative behavior of the force between a pair of molecules as a function of their separation, r:
A substance with no resistance to shear is called a fluid (it flows) This includes gases and liquids.

8. Fluids take the shape of the container they are in
Fluids take the shape of the container they are in. They are liquids and gases.
Density:
Densities go up to 2,700 kg/m3 for Al, 11, ,000 for heavy metals (iron, gold).

9. What is pressure?
We all understand what pressure means. Imagine three large defensive lineman piling on top. That is pressure! (Studying for physics exams is a different kind of pressure.) Pressure is related to force. In physics, we have to define it (think of force per unit area):

10. 1 Pa  1 N/m2 (pascal) SI unit Patm = 101.3 kPa (kilopascal)
Atmospheric pressure is the pressure of the air around us. It is due to the weight of the air above us, so it is greater at sea level, less on mountains.
Patm = x 105 N/m2
1 Pa  1 N/m2 (pascal) SI unit
Patm = kPa (kilopascal)
Patm = 14.7 lb/in2 common unit in U.S.
1 bar = 105 Pa  1 Patm
Pascal is named after Blaise Pascal, French mathematician and physicist Worked on mechanical calculators, fluids; clarified pressure and vacuum. Was also a Catholic philosopher, who had a mystical experience and abandoned science in favor of philosophy and theology.

11. Gauge pressure is what we use to check the pressure in our tires
Gauge pressure is what we use to check the pressure in our tires. It refers to the pressure above atmospheric pressure.
Show pressure gauges.

12. Bed of Nails demo
Do chair demo.

13. Pressure is the same in every direction in a static fluid at a given depth; if it were not, the fluid would flow.
Figure Pressure is the same in every direction in a nonmoving fluid at a given depth. If this weren’t true, the fluid would be in motion.

14. For a fluid at rest, there is also no component of force parallel to any solid surface—once again, if there were, the fluid would flow.
Figure If there were a component of force parallel to the solid surface of the container, the liquid would move in response to it. For a liquid at rest, F|| = 0.

15. Pressure as a function of depth in liquid

16. Pressure in Fluids
If there is external pressure in addition to the weight of the fluid itself, or if the density of the fluid is not constant, we calculate the pressure at a height y in the fluid; the negative sign indicates that the pressure decreases with height (increases with depth):
Figure Forces on a flat, slablike volume of fluid for determining the pressure P at a height y in the fluid.

17. We then integrate to find the pressure:
Figure Pressure at a depth h = (y2 – y1) in a liquid of density ρ is P = P0 + ρgh, where P0 is the external pressure at the liquid’s top surface.
Easy to integrate for contant density ρ.

18. Pressure Variation with Depth

19. Do some demos. Crush soda can - start early, do later
Do some demos Crush soda can - start early, do later Hydrostatic pressure Magdeburg hemispheres Air has weight
Hydrostatic pressure: vases in water. Air has weight: pump out air, weigh, tare, let in air.

20. A Simple Barometer

21. Hurricane Wilma set record: 26.4 in
Many barometers we use today in meteorology contain mercury, because of its high density. Calculate the height h of a mercury column of the simple barometer we just saw.
Hurricane Wilma was a category 5 storm in 2005 that went west to east from the Gulf of Mexico over Florida. $30 billion damage.
Hurricane Wilma set record: 26.4 in

22. Height of water tower
We just showed that a mercury barometer can at most be 760 mm tall due to atmospheric pressure.
How high can a water barometer be? We still use

23. Vacuum
Vacuum is the absence of matter. There will be no pressure when there is a vacuum. P = 0.
What happens when we have atmospheric pressure and a vacuum across an interface?
Do soda can demo.

24. Lots of demos to do here

25. Tanker car collapse
Workers steam cleaned tanker car, then closed all the valves and left for the night.

26. Conceptual Quiz
When a hole is made in the side of a Coke can holding water, water flows out and follows a parabolic trajectory. If the container is dropped in free fall, the water flow will:
A) diminish
B) stop altogether
C) go out in a straight line
D) curve upwards
Coca-Cola

27. Conceptual Quiz
When a hole is made in the side of a Coke can holding water, water flows out and follows a parabolic trajectory. If the container is dropped in free fall, the water flow will:
A) diminish
B) stop altogether
C) go out in a straight line
D) curve upwards
Water flows out of the hole because the water pressure inside is larger than the air pressure outside. The water pressure is due to the weight of the water. When the can is in free fall, the water is weightless, so the water pressure is zero, and hence no water is pushed out of the hole!
Coca-Cola

28. When we have unequal water levels, the pressure is different at the bottom. Fluid will flow (due to the force) to make the levels equal.

29. Oil and water have different densities. Oil will float on the water
Oil and water have different densities. Oil will float on the water. The pressure at the bottom is equal on both sides.

30. Measurement of Pressure; Gauges and the Barometer
There are a number of different types of pressure gauges. This one is an open-tube manometer. The pressure in the open end is atmospheric pressure; the pressure being measured will cause the fluid to rise until the pressures on both sides at the same height are equal.
Figure 13-10a.

31. Tire pressure gauge.

32. Pascal’s Principle: Pressure is transmitted undiminished in an enclosed static fluid. Any externally applied pressure is transmitted to all parts of the enclosed fluid. Do Pascal’s vases demo Do Cartesian diver demo
Pascal vases has five glass tubes with a common reservoir – all will have fluid at the same height independent of shape and area.

33. Conceptual Quiz
You are walking out on a frozen lake and you begin to hear the ice cracking beneath you. What is your best strategy for getting off the ice safely?
A) stand absolutely still and don’t move a muscle
B) jump up and down to lessen your contact time with the ice
C) try to leap in one bound to the bank of the lake
D) shuffle your feet (without lifting them) to move towards shore
E) lie down flat on the ice and crawl toward shore

34. Conceptual Quiz
You are walking out on a frozen lake and you begin to hear the ice cracking beneath you. What is your best strategy for getting off the ice safely?
A) stand absolutely still and don’t move a muscle
B) jump up and down to lessen your contact time with the ice
C) try to leap in one bound to the bank of the lake
D) shuffle your feet (without lifting them) to move towards shore
E) lie down flat on the ice and crawl toward shore
As long as you are on the ice, your weight is pushing down. What is important is not the net force on the ice, but the force exerted on a given small area of ice (i.e., the pressure!). By lying down flat, you distribute your weight over the widest possible area, thus reducing the force per unit area.

35. Conceptual Quiz
Consider what happens when you push both a pin and the blunt end of a pen against your skin with the same force. What will determine whether your skin will be punctured?
A) the pressure on your skin
B) the net applied force on your skin
C) both pressure and net applied force are equivalent
D) neither pressure nor net applied force are relevant here
Answer: 1

36. Conceptual Quiz
Consider what happens when you push both a pin and the blunt end of a pen against your skin with the same force. What will determine whether your skin will be punctured?
A) the pressure on your skin
B) the net applied force on your skin
C) both pressure and net applied force are equivalent
D) neither pressure nor net applied force are relevant here
The net force is the same in both cases. However, in the case of the pin, that force is concentrated over a much smaller area of contact with the skin, such that the pressure is much greater. Because the force per unit area (i.e., pressure) is greater, the pin is more likely to puncture the skin for that reason.

37. A Hydraulic Lift

38. In the hydraulic lift (show demo), the liquid is enclosed, and the pressure is the same throughout.

39. Pascal’s Principle
Figure Applications of Pascal’s principle: (a) hydraulic lift; (b) hydraulic brakes in a car.

40. Conceptual Quiz 1 2 3 A) container 1 B) container 2 C) container 3
D) all three are equal
Three containers are filled with water to the same height and have the same surface area at the base, but the total weight of water is different for each. Which container has the greatest total force acting on its base? 1 2 3

41. Conceptual Quiz 1 2 3 A) container 1 B) container 2 C) container 3
D) all three are equal
Three containers are filled with water to the same height and have the same surface area at the base, but the total weight of water is different for each. Which container has the greatest total force acting on its base?
The pressure at the bottom of each container depends only on the height of water above it! This is the same for all the containers. The total force is the product of the pressure times the area of the base, but since the base is also the same for all containers, the total force is the same. 1 2 3

42. Conceptual Quiz A) water pressure B) gravity
C) inertia
D) atmospheric pressure
E) mass
When you drink liquid through a straw, which of the items listed is primarily responsible for this to work?
Click to add notes

43. Conceptual Quiz A) water pressure B) gravity
C) inertia
D) atmospheric pressure
E) mass
When you drink liquid through a straw, which of the items listed below is primarily responsible for this to work?
When you suck on a straw, you expand your lungs, which reduces the air pressure inside your mouth to less than atmospheric pressure. Then the atmospheric pressure pushing on the liquid in the glass provides a net upward force on the liquid in the straw sufficient to push the liquid up the straw.
Follow-up: Is it possible to sip liquid through a straw on the Moon?

44. Buoyant Force Due to a Fluid

45. The buoyant force is due to the difference in force at the bottom and the top of the cube of sides L.
Archimedes’ principle:
An object completely immersed in a fluid experiences an upward buoyant force equal in magnitude to the weight of fluid displaced by the object.

46. Buoyant force equals the weight of the displaced liquid, not the weight of the object!

47. Buoyancy and Archimedes’ Principle
Archimedes’ principle: The buoyant force on an immersed object equals the weight of displaced
fluid.
The picture below shows an object in the air, partially submerged, and completely submerged.

48. Do Archimedes’ Principle demo.

49. Flotation An object floats when it displaces an amount of fluid equal to its weight. The total weight of the block equals the weight of the fluid displaced.

50. Flotation An object floats when it displaces an amount of fluid equal to its weight. The total weight of the block equals the weight of the fluid displaced.

51. Floating an Object That Is More Dense than Water The metal block and water in (b) have the same weight. Note in (c) that bowl made of the metal floats, because the bowl is hollow.

52. Conceptual Quiz: Two identical glasses are filled to the same level with water. One of the two glasses has ice cubes floating in it. Which weighs more?   A)    The glass without ice cubes. B)    The glass with ice cubes. C)    The two weigh the same.

53. Answer: C
The ice cubes displace exactly their own weight in water, so the two glasses weigh the same amount. It is essential that the ice sticks out above the level of the water.

54. is water density

55. Conceptual Quiz: What happens to the water level when the ice melts
Conceptual Quiz: What happens to the water level when the ice melts? A) Water overflows. B) Water level decreases. C) Water level stays the same.

56. Answer: C
Because the ice cube is floating, it displaces a volume of water equal to its weight. When it melts it becomes water and displaces the same volume of water it displaced. Remember the density of ice is less than that of water.

57. Conceptual Quiz: Now a pebble sits on top of the ice, and the water is filled to the brim of the glass. What happens when the ice melts? A) The water overflows. B) The water level decreases. C) The water level stays the same. D) The pebble explodes.

58. Answer: B
The ice makes no difference, but now the pebble also displaces an amount of water equal to the pebble’s weight. When the ice melts, the pebble drops to the bottom and displaces a volume of water equal to its own volume. Because the volume of the pebble is less than the volume of the water it displaced originally, there is less water displaced afterwards. The water level drops.

59. Turbulent flow
Laminar flow, also known as streamline flow.

60. Consider a mass m passing through a particular point in time t
Consider a mass m passing through a particular point in time t. The ratio m/ t must be constant at every point or mass will build up.

62. Gases are compressible, but liquids are not
Gases are compressible, but liquids are not. For liquid flow, the density  is constant. Then for liquids. Useful equation for many applications: for example, water hoses.

63. When using a water hose, we put our thumb over end to increase water speed. Hose nozzle does the same thing. Decrease area, increase speed.
A1v1 = A2v2
small A, large v

64. 13-34. A scuba diver and her gear displace a volume of 65
A scuba diver and her gear displace a volume of 65.0 L and have a total mass of 68.0 kg. (a) What is the buoyant force on the diver in seawater? (b) Will the diver sink or float?