Conceptual Physics Fundamentals - Chap7.pdf · Archimedes’ Principle Archimedes’ Principle •discovered by Greek scientist Archimedes •relates buoyancy to displaced liquid

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

Conceptual Physics

Fundamentals

Chapter 7:

FLUID MECHANICS


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


Density

Density

• important property of materials (solids, liquids,

gases)

• measure of compactness of how much mass an

object occupies

• “lightness” or “heaviness” of materials of the

same size


Density

• in equation form:

• units:

mass: 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

3g/cm 3cm

grams=density


Densities

seven-layer-density-column

http://www.stevespanglerscience.com/experiment/seven-layer-density-column








Aerogel Density – 0.020 g/cm3 (lightest solid)

Can hold 4000 times it’s own weight


The volume of 1000 g of water is

A. 1 liter.

B. slightly less than 1 liter.

C. more than 1 liter.

D. none of the above

Density

CHECK YOUR NEIGHBOR


The volume of 1000 g of water is

A. 1 liter.

B. slightly less than 1 liter.

C. more than 1 liter.


Density

CHECK YOUR ANSWER


Which of these has the greatest density?

A. 100 kg of lead

B. 100 kg of water

C. both are the same


Density

CHECK YOUR NEIGHBOR


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.

Density

CHECK YOUR ANSWER


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.


Density

CHECK YOUR NEIGHBOR


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.


Density

CHECK YOUR ANSWER


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

A. more.

B. less.

C. the same.


Density

CHECK YOUR NEIGHBOR


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.

Density

CHECK YOUR ANSWER


Pressure

• the force per unit area that one object

exerts on another


• depends on area over which force is

distributed

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

pressure = forcearea


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.

You tube

http://www.youtube.com/watch?v=hG7lGZqWFpM


When you stand on one foot instead of two, the force you

exert on the floor is

A. less.

B. the same.

C. more.


Pressure

CHECK YOUR NEIGHBOR


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!

Pressure

CHECK YOUR ANSWER


When you stand on one foot instead of two, the pressure

you exert on the floor is

A. less.

B. the same.

C. more.


Pressure

CHECK YOUR NEIGHBOR


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!

Pressure

CHECK YOUR ANSWER


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



• acts equally in all directions

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

water no matter how you tip your head

• bottom of a boat is pushed upward by water pressure

• pressure acts upward when pushing a beach ball

under water



• independent of shape of container

whatever the shape of a container, pressure

at any particular depth is the same


liquid pressure = weight density depth


Water pressure provided by a water tower is greater if the

tower

A. is taller.

B. holds more water.

C. both A and B



CHECK YOUR NEIGHBOR


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.


CHECK YOUR ANSWER



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


Buoyancy in a Liquid

Buoyancy

• apparent loss of weight of a submerged object

• amount equals the weight of water displaced



• 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

07_ArchimedesPrincipl_VID.mov


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


CHECK YOUR NEIGHBOR


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


CHECK YOUR ANSWER



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


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



CHECK YOUR NEIGHBOR


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



CHECK YOUR ANSWER



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



Diving Ketchup

http://www.youtube.com/watch?v=OM6iC6N12xY&feature=related


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



Apparent 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

Demo

http://www.youtube.com/watch?v=g6aErhwFXsg


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


CHECK YOUR NEIGHBOR


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.


CHECK YOUR ANSWER


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

A. decreases.

B. increases.

C. remains the same.



CHECK YOUR NEIGHBOR


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

A. decreases.

B. increases.




CHECK YOUR ANSWER


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

A. decreases.

B. increases.




CHECK YOUR NEIGHBOR


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

A. decreases.

B. increases.




CHECK YOUR ANSWER


When a fish decreases the size of its air bladder, the

density of the fish

A. decreases.

B. increases.




CHECK YOUR NEIGHBOR


When a fish decreases the size of its air bladder, the

density of the fish

A. decreases.

B. increases.




CHECK YOUR ANSWER


When a submarine takes water into its ballast tanks, its

density

A. decreases.

B. increases.




CHECK YOUR NEIGHBOR


When a submarine takes water into its ballast tanks, its

density

A. decreases.

B. increases.




CHECK YOUR ANSWER


When a submerged submarine expels water from its ballast

tanks, its density

A. decreases.

B. increases.




CHECK YOUR NEIGHBOR


When a submerged submarine expels water from its ballast

tanks, its density

A. decreases.

B. increases.



Explanation:

This is how a submerged submarine is able to surface.


CHECK YOUR ANSWER



Flotation • Principle of flotation

– a floating object displaces a weight of fluid equal to its own weight

example: 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


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



CHECK YOUR NEIGHBOR


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.


CHECK YOUR ANSWER


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.


CHECK YOUR NEIGHBOR


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!


CHECK YOUR ANSWER



• 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)



• applies in air

– the more air an object displaces, the greater the

buoyant force on it

– if an object displaces its weight, it

hovers at a constant altitude

– if an object displaces less air, it

descends


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


CHECK YOUR NEIGHBOR


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.

Archimedes’ Prinicple

CHECK YOUR ANSWER


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.


Pressure in a Gas

Relationship between pressure and density

• gas pressure is proportional to density

example: – air pressure and air density inside

an inflated tire are greater than the

atmospheric pressure and density

outside

– twice as many molecules in the same

volume air density doubled

– for molecules moving at the same

speed (same temperature), collisions

are doubled pressure doubled


Pressure in a Gas

Double density of air by

• doubling the amount of air

• decreasing the volume to half


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

Breathing and Boyle’s law

http://www.youtube.com/watch?v=q6-oyxnkZC0


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 Gas

CHECK YOUR NEIGHBOR


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 Gas

CHECK YOUR ANSWER


Earth’s Atmosphere

Atmosphere

• ocean of air

• exerts pressure

The Magdeburg-hemispheres

demonstration in 1654 by

Otto von Guericke showed

the large magnitude of

atmosphere’s pressure.


Atmospheric Pressure

Atmospheric pressure

• caused by weight of air

• varies from one locality to another

• not uniform

• measurements are used to predict weather conditions



• 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



• The atmospheric pressure at the earth’s

surface is 14.7 pounds per square inch or

around 100 kPa. A comparable water

pressure occurs at a depth of 10 m (33 ft)

(9.8 m (32 ft) for sea water). Thus, at

about 10 m below the surface, the water

exerts twice the pressure (2 atmospheres

or 200 kPa) on the body as air at surface

level.

Glass of water

http://en.wikipedia.org/wiki/Atmospheric_pressure

http://en.wikipedia.org/wiki/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



Barometer

• device to measure atmospheric pressure

• also determines elevation

Aneroid barometer • small portable instrument that measures

atmospheric pressure

• calibrated for altitude, then an altimeter


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.



CHECK YOUR NEIGHBOR


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.


CHECK YOUR ANSWER


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—gases

and liquids



• application in hydraulic press

example:

– pressure applied to the left piston is transmitted to the

right piston

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

on large piston (right)


Pascal’s Principle • application for gases and liquids

– seen in everyday hydraulic devices used in

construction

– 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 the

pressure to the piston,

which lifts the auto.


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.


CHECK YOUR NEIGHBOR


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.


CHECK YOUR ANSWER

Hydraulic Fracturing - Natural gas extraction

Principles of Hydraulics

http://www.youtube.com/watch?feature=endscreen&NR=1&v=lB3FOJjpy7s




http://www.youtube.com/watch?v=YlmRa-9zDF8


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


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 Gas

CHECK YOUR NEIGHBOR


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 Gas

CHECK YOUR ANSWER


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.


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.


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)


As a balloon rises higher and higher into the atmosphere,

its

A. volume decreases.

B. density increases.

C. weight increases.


Buoyancy in Gas

CHECK YOUR NEIGHBOR


As a balloon rises higher and higher into the atmosphere,

its

A. volume decreases.

B. density increases.

C. weight increases.


Buoyancy in Gas

CHECK YOUR ANSWER


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 pipe widens or narrows.

• fluid speeds up when it flows from a wide to narrow pipe

• motion of fluid follows imaginary streamlines


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



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



Laminar flow

• smooth steady flow of constant density fluid

Turbulent flow

• flow speed above a critical point becomes

chaotic



Applications of Bernoulli’s Principle

• blow on the top surface of a paper and the paper

rises

reason: 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: pressure of air moving on the top surface is

less than the atmospheric pressure inside the car



• 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.



• 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


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.



CHECK YOUR NEIGHBOR


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.


CHECK YOUR ANSWER

You tube video

http://www.youtube.com/watch?v=KCcZyW-6-5o

Documents

Conceptual Physics Fundamentals - Chap7.pdf · Archimedes’ Principle Archimedes’ Principle •discovered by Greek scientist Archimedes •relates buoyancy to displaced liquid