Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Conceptual Physics...

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley

Conceptual Physics Fundamentals

Chapter 7:

FLUID MECHANICS

1


This lecture will help you understand:

Density Pressure Pressure in a Liquid Buoyancy in a Liquid Archimedes’ Principle Pressure in a Gas Atmospheric Pressure Pascal’s Principle Buoyancy in a Gas Bernoulli’s Principle

2


Fluid Mechanics

“Men never do evil so cheerfully and completely as when they do so from religious conviction.”

—Blaise Pascal

3


Density

Density importantproperty of materials (solids, liquids,

gases) measure of compactness of how much mass an

object occupies “lightness” or “heaviness” of materials of the

same size

4


Density

in equation form:

units: grams or kilograms

volume: cm3 or m3

example: density of mercury is 13.6 g/cm3, so mercury has 13.6 times as much mass as an equal volume of water (density 1 g/cm3)

density = massvolume

5


The volume of 1000 kg of water is _______________.

A. 1 liter

B. slightly less than 1 liter

C. more than 1 liter

D. None of the above

DensityCHECK YOUR NEIGHBOR

6


The volume of 1000 kg of water is _______________.

A. 1 liter

B. slightly less than 1 liter

C. more than 1 liter


DensityCHECK YOUR ANSWER

7


Density

Weight density in equation form:

example: density of salt water is 64 lb/ft3, more dense

than fresh water (density 62.4 lb/ft3)

weight density = weightvolume

8


Which of these has the greatest density?

A. 100 kg of lead

B. 100 kg of water

C. Both are the same



9


Which of these has the greatest density?

A. 100 kg of lead

B. 100 kg of water

C. Both are the same


Explanation:

They have the same mass and weight, but any amount of lead is more dense than any amount of water.


10


When water freezes, it expands. This tells us that the density of ice is _______________.

A. less than the density of water

B. equal to the density of water

C. more than the density of water



11


When water freezes, it expands. This tells us that the density of ice is _______________

A. less than the density of water

B. equal to the density of water

C. more than the density of water



12


Compared with the weight of water, the weight of a liter of ice is _______________.

A. more

B. less

C. the same



13


Compared with the weight of water, the weight of a liter of ice is _______________.

A. more

B. less

C. the same


Explanation

When a liter of water freezes, its volume increases. To get a liter of ice you’d have to shave part of it off to be the same size. So there is less water in a liter of ice.


14


Pressure

the force per unit area that one object exerts on another

in equation form: depends on area over which force is

distributed

units: N/m2, lb/ft2, or Pa (Pascals)

pressure = forcearea

15


Pressure

example: The teacher between nails is unharmed because force is applied over many nails. Combined surface area of the nails results in a tolerable pressure that does not puncture the skin.

16


When you stand on one foot instead of two, the force you exert on the floor is __________.

A. less

B. the same

C. more


PressureCHECK YOUR NEIGHBOR

17


When you stand on one foot instead of two, the force you exert on the floor is ___________.

A. less

B. the same

C. more


Explanation:

Distinguish between force and pressure!

PressureCHECK YOUR ANSWER

18


When you stand on one foot instead of two, the pressure you exert on the floor is _____________.

A. less

B. the same

C. more


PressureCHECK YOUR NEIGHBOR

19


When you stand on one foot instead of two, the pressure you exert on the floor is _____________.

A. less

B. the same

C. more


Explanation:

Twice as much, in fact!

PressureCHECK YOUR ANSWER

20


Pressure in a Liquid force per unit area that a liquid exerts on an

object depth dependent and not volume dependent

example: swim twice as deep, then twice as much weight of water above you produces as much pressure on you

21


Pressure in a Liquid

acts equally in all directions

example: o your ears feel the same amount of pressure under

water no matter how you tip your heado bottom of a boat is pushed upward by water pressureo pressure acts upward when pushing a beach ball

under water

22



independent of shape of container

whatever the shape of a container, pressure at any particular depth is the same

in equation form:

liquid pressure = weight density depth

23


Water pressure provided by a water tower is greater if the tower __________.

A. is taller

B. holds more water

C. Both A and B


Pressure in a LiquidCHECK YOUR NEIGHBOR

24


Water pressure provided by a water tower is greater if the tower ____________.

A. is taller

B. holds more water

C. Both A and B


Explanation:

Only depth, not amount of water, contributes to pressure.

Pressure in a LiquidCHECK YOUR ANSWER

25



Effects of water pressure acts perpendicular to surfaces

of a container

liquid spurts at right angles from a hole in the surface curving downward– The greater the depth, the greater

the exiting speed

26


Buoyancy in a Liquid

Buoyancy apparent loss of weight of a submerged object amount equals the weight of water displaced

27



Displacement rule: A completely submerged object always displaces a volume of liquid equal to its own volume.

example: Place a stone in a container that is brim- full of water, and the amount of water overflow equals the volume of the stone

28


A cook who measures a specific amount of butter by placing it in a measuring cup with water in it is using the ___________.

A. principle of buoyancy

B. displacement rule

C. concept of density

D. All of the above

Buoyancy in a LiquidCHECK YOUR NEIGHBOR

29


A cook who measures a specific amount of butter by placing it in a measuring cup with water in it is using the __________.

A. principle of buoyancy

B. displacement rule

C. concept of density

D. All of the above

Buoyancy in a LiquidCHECK YOUR ANSWER

30



Buoyant force net upward force that a fluid

exerts on an immersed object = weight of water displaced

example: the difference in the upward and downward

forces acting on the submerged block is the same at any depth

31


How many forces act on a submerged body at rest in a fluid?

A. One—buoyancy

B. Two—buoyancy and the force due to gravity

C. None—in accord with the equilibrium rule, F = 0


Buoyancy in a LiquidCHECK YOUR NEIGHBOR

32


How many forces act on a submerged body at rest in a fluid?

A. One—buoyancy

B. Two—buoyancy and the force due to gravity

C. None—in accord with the equilibrium rule, F = 0


Buoyancy in a LiquidCHECK YOUR ANSWER

33



Sink or float? sink when weight of submerged object is greater

than the buoyant force neither sink nor float when weight of a

submerged object is equal to buoyant force—object will remain at any level

float when weight of submerged object is less than the buoyant force it would have when submerged—when floating, buoyant force = weight of floating object

34


Archimedes’ Principle

Archimedes’ Principle discovered by Greek scientist Archimedes relates buoyancy to displaced liquid states that an immersed body (completely or

partially) is buoyed up by a force equal to the weight of the fluid it displaces

applies to gases and liquids

35


Archimedes’ PrincipleApparent weight of a submerged object weight out of water—buoyant force

example: If a 3-kg block submerged in water apparently “weighs” 2 kg, then the buoyant force or weight of water displaced is 1 kg.

36


On which of these blocks submerged in water is the buoyant force greatest?

A. 1 kg of lead

B. 1 kg of aluminum

C. 1 kg of uranium

D. All the same

Archimedes’ PrincipleCHECK YOUR NEIGHBOR

37


On which of these blocks submerged in water is the buoyant force greatest?

A. 1 kg of lead

B. 1 kg of aluminum

C. 1 kg of uranium

D. all the same

Explanation:

The largest block is the aluminum one. It displaces more water and therefore experiences the greatest buoyant force.

Archimedes’ PrincipleCHECK YOUR ANSWER

38


When a fish expands its air bladder, the density of the fish ________________.

A. decreases

B. increases

C. remains the same



39


When a fish expands its air bladder, the density of the fish _____________.

A. decreases

B. increases

C. remains the same



40


When a fish makes itself less dense, the buoyant force on it ______________.

A. decreases

B. increases

C. remains the same



41


When a fish makes itself less dense, the buoyant force on it ______________.

A. decreases

B. increases

C. remains the same



42


When a fish decreases the size of its air bladder, the density of the fish ___________.

A. decreases

B. increases

C. remains the same



43


When a fish decreases the size of its air bladder, the density of the fish _____________.

A. decreases

B. increases

C. remains the same



44


When a submarine takes water into its ballast tanks, its density __________.

A. decreases

B. increases

C. remains the same



45


When a submarine takes water into its ballast tanks, its density ______________.

A. decreases

B. increases

C. remains the same



46


When a submerged submarine expels water from its ballast tanks, its density __________.

A. decreases

B. increases

C. remains the same



47


When a submerged submarine expels water from its ballast tanks, its density __________.

A. decreases

B. increases

C. remains the same


Explanation:

This is how a submerged submarine is able to surface.


48


Archimedes’ PrincipleFlotation Principle of flotation

o a floating object displaces a weight of fluid equal to its own weightexample: A solid iron 1-ton block may displace 1/8 ton of water

and sink. The same 1 ton of iron in a bowl shape displaces a greater volume of water—the

greater buoyant force allows it to float.

49


The reason a person finds it easier to float in salt water, compared with fresh water, is that in salt water __________.

A. the buoyant force is greater

B. a person feels less heavy

C. Neither of these


50


The reason a person finds it easier to float in salt water, compared with fresh water, is that in salt water __________.

A. the buoyant force is greater

B. a person feels less heavy

C. Neither of these

Explanation:

A floating person has the same buoyant force whatever the density of water. A person floats higher because a smaller volume of the denser salt water is displaced.


51


On a boat ride, the skipper gives you a life preserver filled with lead pellets. When he sees the skeptical look on your face, he says that you’ll experience a greater buoyant force if you fall overboard than your friends who wear Styrofoam-filled preservers.

A. He apparently doesn’t know his physics.

B. He is correct.


52


On a boat ride, the skipper gives you a life preserver filled with lead pellets. When he sees the skeptical look on your face, he says that you’ll experience a greater buoyant force if you fall overboard than your friends who wear Styrofoam-filled preservers.

A. He apparently doesn’t know his physics.B. He is correct.

Explanation:He’s correct, but what he doesn’t tell you is you’ll drown! Your life preserver will submerge and displace more water than those of your friends who float at the surface. Although the buoyant force on you will be greater, the net force downward is greater still!


53



Denser fluids will exert a greater buoyant force on a body than less dense fluids of the same volume.

example: ship will float higher in salt water (density = 1.03 g/cm3) than in fresh water (density = 1.00 g/cm3)

54



applies in airo The more air an object displaces, the greater the

buoyant force on it.o If an object displaces its weight, it

hovers at a constant altitude,o If an object displaces less air, it

descends,

55


As you sit in class, is there a buoyant force acting on you?

A. No, as evidenced by an absence of lift

B. Yes, due to displacement of air


56


As you sit in class, is there a buoyant force acting on you?

A. No, as evidenced by an absence of lift

B. Yes, due to displacement of air

Explanation:

There is a buoyant force on you due to air displacement, but much less than your weight.


57


Pressure in a Gas

greater distance between molecules in a gas than in a liquid

molecules in a gas are free from the cohesive forces

Molecular motion of gas exerts pressure against a container.

For large volumes of gas, gravitational forces limit size and determine shape.

58


Pressure in a GasRelationship between pressure and density gas pressure is proportional to density

example: o Air pressure and air density inside

an inflated tire are greater than the atmospheric pressure and density outside.

o twice as many molecules in the same volume air density doubled

o for molecules moving at the same speed (same temperature), collisions are doubled pressure doubled

59


Pressure in a Gas

Double density of air by doubling the amount of air decreasing the volume to half

60


Pressure in a Gas

Boyle’s Law relationship between pressure and volume for ideal

gases an ideal gas is one in which intermolecular forces play

no role states that pressure volume is a constant for a given

mass of confined gas regardless of changes in pressure or volume (with temperature remaining unchanged)

pressure volume = constant means that

P1V1 = P2V2

61


When you squeeze a party balloon to 0.8 its volume, the pressure in the balloon __________.

A. is 0.8 its former pressure

B. remains the same if you squeeze it slowly

C. is 1.25 times greater

D. is 8 times greater

Pressure in a GasCHECK YOUR NEIGHBOR

62


When you squeeze a party balloon to 0.8 its volume, the pressure in the balloon __________.

A. is 0.8 its former pressure

B. remains the same if you squeeze it slowly

C. is 1.25 times greater

D. is 8 times greater

Explanation:

Boyle’s law, sweet and simple: P(1.0 V) = 1.25 P(0.8 V).

Pressure in a GasCHECK YOUR ANSWER

63


Earth’s AtmosphereAtmosphere ocean of air exerts pressure

The Magdeburg-hemispheres demonstration in 1654 by Otto von Guericke showed the large magnitude of atmosphere’s pressure.

64


Atmospheric Pressure

Atmospheric pressure caused by weight of air varies from one locality to

another not uniform measurements are used to

predict weather conditions

65



Pressure exerted against bodies immersed in the atmosphere result from the weight of air pressing from above.

at sea level is 101 kilopascals(101 kPa)

weight of air pressing down on 1 m2 at sea level ~ 100,000 N, so atmospheric pressure is ~ 105 N/m2

66


Atmospheric Pressure Pressure at the bottom of a column of air reaching to the top of

the atmosphere is the same as the pressure at the bottom of a column of water 10.3 m high.

Consequence: The highest the atmosphere can push water up into a vacuum pump is 10.3 m.

Mechanical pumps that don’t depend on atmospheric pressure don’t have the 10.3-m limit.

67



Barometer device to measure atmospheric pressure also determines elevation

Aneroid barometer small portable instrument that measures atmospheric pressure calibrated for altitude, then an altimeter

68


The maximum height to which water can be drunk through a straw __________.

A. is 10.3 mB. is about 76 cm C. has no limitD. None of the above

Atmospheric PressureCHECK YOUR NEIGHBOR

69


The maximum height to which water can be drunk through a straw __________.

A. is 10.3 m

B. is about 76 cm

C. has no limit


Explanation:

However strong your lungs may be, or whatever device you use to make a vacuum in the straw, at sea level, the water could not be pushed up by the atmosphere higher than 10.3 m.

Atmospheric PressureCHECK YOUR ANSWER

70


Pascal’s Principle

Pascal’s principle discovered by Blaise Pascal, a scientist and theologian in

the 17th century states that a change in pressure at any point in an enclosed

fluid at rest is transmitted undiminished to all points in the fluid

applies to all fluids—gasesand liquids

71


Pascal’s Principle application in hydraulic press

example: o pressure applied to the left piston is transmitted to the

right pistono a 10-kg load on small piston (left) lifts a load of 500 kg

on large piston (right)

72


Pascal’s Principle application for gases and liquids

o seen in everyday hydraulic devices used in construction

o in auto lifts in service stations• Increased air pressure produced by an air

compressor is transmitted through the air to the surface of oil in an

underground reservoir.The oil transmits thepressure to the piston,which lifts the auto.

73


In a hydraulic device, it is impossible for the __________.

A. output piston to move farther than the input piston

B. force output to exceed the force input

C. output piston’s speed to exceed the input piston’s speed

D. energy output to exceed energy input

Pascal’s PrincipleCHECK YOUR NEIGHBOR

74


In a hydraulic device, it is impossible for the __________.

A. output piston to move farther than the input piston

B. force output to exceed the force input

C. output piston’s speed to exceed the input piston’s speed

D. energy output to exceed energy input

Pascal’s PrincipleCHECK YOUR ANSWER

75


Buoyancy in a Gas

Archimedes’ principle applies to air as well as liquids.

states that an object surrounded by air is buoyed up by a force equal to the weight of the air displaced

76


A dirigible that hovers in air __________.

A. displaces its volume of air

B. displaces its weight of air

C. Both A and B

D. Neither A nor B

Buoyancy in GasCHECK YOUR NEIGHBOR

77


A dirigible that hovers in air __________.

A. displaces its volume of air

B. displaces its weight of air

C. Both A and B

D. Neither A nor B

Explanation:

Like a fish in water, both volume and weight of a fluid are displaced.

Buoyancy in GasCHECK YOUR ANSWER

78


Buoyancy in Gas

Rule for “lighter-than-air” objects: When the weight of air displaced by an object is

greater than the weight of the object, it rises. When the weight of air displaced by an object

equals the weight of the object, it hovers in air. When the weight of air displaced by an object is

less than the weight of the object, it is not supported by air.

79


Buoyancy in Gas

Gas-filled balloons gas prevents atmosphere from collapsing them best buoyancy with hydrogen, the lightest gas

(flammable, so seldom used) next-best buoyancy with helium heated air used in sports balloons

As balloons rise, atmosphere becomes less dense with altitude.

80


Buoyancy in Gas

Gas-filled balloon will continue to rise until the weight of displaced air equals the total

weight of the balloon the buoyant force on the balloon

equals its weight (which says the same thing)

81


As a balloon rises higher and higher into the atmosphere, its __________.

A. volume decreases

B. density increases

C. weight increases


Buoyancy in GasCHECK YOUR NEIGHBOR

82


As a balloon rises higher and higher into the atmosphere, its __________.

A. volume decreases

B. density increases

C. weight increases


Buoyancy in GasCHECK YOUR ANSWER

83


Fluid Flow

continuous flow Volume of fluid that flows past any cross-section

of a pipe in a given time is the same as that flowing past any other section of the pipe even if the pipe widens or narrows.

Fluid speeds up when it flows from a wide to narrow pipe.

Motion of fluid follows imaginary streamlines.

84


Bernoulli’s Principle

Bernoulli’s Principle discovered by Daniel Bernoulli, a 15th century

Swiss scientist states that where the speed of a fluid increases,

internal pressure in the fluid decreases applies to a smooth, steady flow

85



Streamlines thin lines representing fluid motion closer together, flow speed is greater and

pressure within the fluid is less wider, flow speed is less and pressure within the

fluid is greater

86



Laminar flow smooth steady flow of constant density fluid

Turbulent flow flow speed above a critical point becomes

chaotic

87


The pressure in a stream of water is reduced as the stream speeds up. Can a stream of water from a fire hose actually knock a person off his or her feet?

A. It can’t, as Bernoulli’s principle illustrates.

B. It can, and is consistent with Bernoulli’s principle.

C. Bernoulli’s principle works only for laminar flow, which the stream is not.


Bernoulli’s PrincipleCHECK YOUR NEIGHBOR

88


The pressure in a stream of water is reduced as the stream speeds up. Can a stream of water from a fire hose actually knock a person off his or her feet?

A. It can’t, as Bernoulli’s principle illustrates.

B. It can, and is consistent with Bernoulli’s principle.

C. Bernoulli’s principle works only for laminar flow, which the stream is not.


Explanation:

There’s a difference in the pressure within flowing water and the pressure it can exert when its momentum is changed. The pressure that knocks one off his or her feet is due to the change in the water’s momentum, not the pressure within the water.

Bernoulli’s PrincipleCHECK YOUR ANSWER

89



Applications of Bernoulli’s Principle Blow on the top surface of a paper and the

paper rises. Reason: The pressure of the moving air is less than the atmospheric pressure beneath it.

Convertible car roof puffs upward as air moves over its top surface. Reason: The pressure of air moving on the top surface is less than the atmospheric pressure inside the car.

90



Wind blowing across a peaked roof can lift the roof off the house. Reason: Pressure is reduced as wind gains speed as it flows over the roof. The greater pressure inside the house lifts the roof up.

Perfume atomizer

Reason: Air rushes across the open end of the tube when you squeeze the bulb, reducing pressure in the tube. Atmospheric pressure on the liquid below pushes it up into the tube.

91



Trucks passing closely on a highway are drawn to each other.

Reason: Air pressure between the trucks is less than pressure on their outer sides pushing inward.

Risk of passing ships colliding sideways

Reason: Water pressure between the ships is less than pressure on their outer sides pushing inward.

92


On a windy day, waves in a lake or the ocean are higher than their average height. What factor in Bernoulli’s principle contributes to the increased height?

A. Reduced pressure pulls water upward.

B. Pressure builds up over the crests.

C. Air travels faster over the crests than the troughs.


Bernoulli’s PrincipleCHECK YOUR NEIGHBOR

93


On a windy day, waves in a lake or the ocean are higher than their average height. What factor in Bernoulli’s principle contributes to the increased height?

A. Reduced pressure pulls water upward.

B. Pressure builds up over the crests.

C. Air travels faster over the crests than the troughs.


Explanation:

The troughs of the waves are partially shielded from the wind, so air travels faster over the crests. Pressure there is thus lower than down below in the troughs. The greater pressure in the troughs pushes water into the even higher crests.

Bernoulli’s PrincipleCHECK YOUR ANSWER

94

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Conceptual Physics...

Documents

Transcript of Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley Conceptual Physics...