05. fluid mechanics

8/22/2019 05. Fluid Mechanics

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© 2012 Pearson Education, Inc.

Conceptual

PhysicalScience5th Edition

Chapter 5:

FLUID MECHANICS





This lecture will help you

understand:

• Density

• Pressure

• 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

• Equation :

• Units of:

– mass in grams or kilograms

– volume in cm3 or m3

– density in kg/m3 or g/cm3

Example: The density of mercury is 13.6 g/cm3

, so mercury has 13.6times as much mass as an equal volume of water (density

1 g/cm3).

density = massvolume




Density

Weight density

• in equation form:

often expressed in pounds per cubic foot

example:

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

than fresh water (density 62.4 lb/ft3)

weight density = weight volume




Which of these has the greatest density? A. 100 kg of lead

B. 100 kg of water C. Both are the same

D. None of the above

Density

CHECK YOUR NEIGHBOR


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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 different volumes. Any

amount of lead is more dense than any amount of water.

Density

CHECK YOUR ANSWER



Pressure

• force per unit area that one object exerts

on another

• equation:

• depends on area over which force isdistributed

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

pressure =forcearea



Pressure in a Liquid

• Force per unit area that a liquid exerts onsomething

• Depth dependent and not volume dependent

Example: Swim twice as deep and the pressure due tothe weight of water above you is twice asmuch. (For total pressure, add to this theatmospheric pressure acting on the water surface.)




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




• Acts equally in all directions

Examples: • 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

• Equation:

liquid pressure = weight density dept



Water Tower

• Force of gravity acting

on the water in a tall

tower produces

pressure in pipesbelow that supply

many homes with

reliable water

pressure.

P




Suppose water from a tall tower supplies a nearby home. If

water faucets upstairs and downstairs are turned fully on,will more water per second flow from the downstairs or the

upstairs faucet? Or will water flow in each be the same?

A. Downstairs.

B. Upstairs.C. Same.

D. Not enough information in problem.

Pressure

CHECK YOUR NEIGHBOR

P




Suppose water from a tall tower supplies a nearby home. If

water faucets upstairs and downstairs are turned fully on,will more water per second flow from the downstairs or the

upstairs faucet? Or will water flow in each be the same?

A. Downstairs

B. UpstairsC. Same

D. Not enough information in problem.

Explanation:

Water pressure depends on the depth below the free surface.

Downstairs faucets are simply ―deeper‖ and receive greater

pressure, which means greater rate of water flow.

Pressure

CHECK YOUR ANSWER

P




Does a 3-meter deep lake or a 6-meter deep small pondexert more pressure on a dam?

A. The three-meter deep lake.B. The six-meter deep small pond.

C. Same amount of pressure is exerted (atmospheric) so same

force.

D. Not enough information given in the question.

Pressure

CHECK YOUR NEIGHBOR

P




Pressure

CHECK YOUR ANSWER

Does a 3-meter deep lake or a 6-meter deep small pondexert more pressure on a dam?

A. The three-meter deep lake.

B. The six-meter deep small pond.

C. Same amount of pressure is exerted (atmospheric) so same

force.

D. Not enough information given in the question.




Buoyancy in a Liquid

Buoyancy

• apparent loss of weight of a submerged object

• amount equals the weight of water displaced




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‖ 1 kg, then the buoyant force or weight

of water displaced is 2 kg(BF = wt out of water – apparent wt = 3 kg – 1 kg = 2 kg)





• 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





• Buoyant force is equal to

the weight of fluid

displaced. It can also be

understood by pressure

differences.

• The greater pressure

against the bottom of the

box, minus the pressure

on the top, results in anupward force—the

buoyant force.





Buoyant Force• Buoyant force is equal to the

weight of fluid displaced.

•Understood by pressuredifferences

greater pressure againstthe box – pressure on the

top of box





On which of these blocks submerged in water is thebuoyant 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 thebuoyant 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 Principle

CHECK YOUR ANSWER





Flotation• Principle of flotation

– A floating object displaces a weight of fluid equal to its ownweight

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 shapedisplaces 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. a smaller volume of water is displaced.

D. None of the above.


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. a smaller volume of water is displaced.


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 lifepreserver will submerge and displace more water than those of your friends who float at the surface. Although the buoyant forceon you will be greater, the net force downward is greater still!


CHECK YOUR ANSWER




Pressure in a Gas

The Falkirk Wheel in Scotland illustrates Figure 5.17 inyour book. Each of the two caissons weigh the same

regardless of the weights of floating boats they carry.




Pressure in a Gas

• Gas pressure is ameasure of the amount of force per area that a gasexerts against containing

walls.• Here the force is exertedby the motion of molecules bouncingaround.

• Temperature is ameasure of the KE per molecules of the gas.




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 theatmospheric 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 playno 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 P 1V 1 = P 2V 2

Pressure in a Gas




When you squeeze a party balloon to 0.8 its volume, thepressure 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

Pressure in a Gas




When you squeeze a party balloon to 0.8 its volume, thepressure 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-hemispheresdemonstration 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 predictweather conditions





• Pressure exerted against bodies immersed in theatmosphere result from the weight of air pressing fromabove

• At sea level is 101 kilopascals

(101 kPa)• Weight of air pressing down on

1 m2 at sea level ~ 100,000 N,so atmospheric pressureis ~ 105 N/m2





• Pressure at the bottom of a column of air reaching to the

top of the atmosphere is the same as the pressure at thebottom 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




Mechanical Pump

• When the piston is

lifted, the intake valve

opens and air moves

in to fill the emptyspace.

• When the piston is

moved downward, the

outlet valve opensand the air is pushed

out.




Barometers

Barometer

• Device to measure atmospheric pressure

• Also determines elevation

Aneroid barometer • Small portable instrument that measures

atmospheric pressure

• Calibrated for altitude, then an altimeter





Atmospheric pressure is caused by the

A. density of Earth’s atmosphere.

B. weight of Earth’s atmosphere.

C. temperature of the atmosphere.

D. effect of the Sun’s energy on the atmosphere.

p

CHECK YOUR NEIGHBOR





p

CHECK YOUR ANSWER

Atmospheric pressure is caused by the

A. density of Earth’s atmosphere. B. weight of Earth’s atmosphere.

C. temperature of the atmosphere.

D. effect of the Sun’s energy on the atmosphere.





Two people are drinking soda using straws. Do they suck

the soda up? Could they drink a soda this way on the

Moon?

CHECK YOUR NEIGHBOR

A. Yes and yes.

B. No, they suck the air out and theatmospheric pressure pushes the sodaup. Yes, they could do the same thing onthe Moon.

C. No, they reduce air pressure in the strawand the atmospheric pressure pushes

the soda up. No, they could not do thesame thing on the Moon.

D. Yes. No, they could not do the samething on the Moon.





CHECK YOUR ANSWER

Two people are drinking soda using straws. Do they suck

the soda up? Could they drink a soda this way on the

moon?

A. Yes and yes.

B. No, they suck the air out and theatmospheric pressure pushes the sodaup. Yes, they could do the same thing onthe Moon.

C. No, they reduce air pressure in thestraw and the atmospheric pressure

pushes the soda up. No, they couldnot do the same thing on the Moon.

D. Yes. No, they could not do the samething on the Moon.

The Moon does not

have an atmosphere.




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 anenclosed fluid at rest is transmitted undiminished to

all points in the fluid

• Applies to all fluids—gases

and liquids

P l’ P i i l





• 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 kgon large piston (right)





A 10-kg load on the left piston will support a 500-kg load on

the right piston. How does the pressure of fluid against thelower part of the left piston compare with the pressure

against the lower right piston? A. More pressure on the left piston.

B. More pressure on the right piston.

C. Same pressure on each.

D. Same force on each.

CHECK YOUR NEIGHBOR





CHECK YOUR ANSWER A 10-kg load on the left piston will support a 500-kg load on

the right piston. How does the pressure of fluid against thelower part of the left piston compare with the pressure

against the lower right piston?

A. More pressure on the left piston.

B. More pressure on the right piston.

C. Same pressure on each.

D. Same force on each.





• Since the pressure in thefluid is the same at both endsof the tube, one can cleverlychange the force and area to

mechanically multiply each.• This principle underlies a lot!

2

2

1

1

21

A

F

A

F

P P

1 P

2

2

A

F

1

1

A

F

2 P





• Application for gases and liquids – seen in everyday hydraulic devices used inconstruction

– in auto lifts in service stations

• increased air pressure produced by an air compressor is transmitted through the air to thesurface of oil in anunderground reservoir.The oil transmits the

pressure to the piston,which lifts the auto.

(Here surface area of reservoir is irrelevant.)





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.

Explanation:

This illustrates the conservation of energy, a cornerstone of all of science.

CHECK YOUR ANSWER




Buoyancy in a Gas• Archimedes’ principle

applies to fluids—liquidsand gases alike.

• Force of air on bottom of balloon is greater than

force on top.• Net horizontal forces

cancel, but not verticalones, which supplies thebuoyant force.

• And this buoyant forceequals the weight of displaced air!

Buoyant ForceCHECK YOUR NEIGHBOR




Is there a buoyant force acting on your classmates at thismoment? Defend your answer.

A. No. If there were, they would float upward.

B. Yes, but it is insignificant compared with their weights.

C. Only in water, but not in air.

D. None of these.

CHECK YOUR NEIGHBOR

Buoyant ForceCHECK YOUR ANSWER




Is there a buoyant force acting on your classmates at thismoment? Defend your answer.

A. No. If there were, they would float upward.

B. Yes, but it is insignificant compared with their weights.

C. Only in water, but not in air.

D. None of these.

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 thatflowing 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




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 (note the larger bubbles!)

• Wider, flow speed is less and pressure within the fluid is

greater (greater pressure squeezes bubbles smaller)





Laminar flow

• Smooth steady flow of constant density fluid

Turbulent flow

• Flow speed above a critical point becomes

chaotic

Bernoulli’s Principle CHECK YOUR NEIGHBOR




What happens to the internal water pressure in a narrowingpipe of moving water?

A. Pressure is higher.

B. Pressure remains unchanged.

C. Pressure is less.

D. None of these.

CHECK YOUR NEIGHBOR

Bernoulli’s Principle CHECK YOUR ANSWER




CHECK YOUR ANSWER

What happens to the internal water pressure in a narrowingpipe of moving water?

A. Pressure is higher.

B. Pressure remains unchanged.

C. Pressure is less.

D. None of these.

Explanation:This reduction in pressure would be

apparent if air bubbles were in the flowing

water. Note their sizes increase in the

narrow part, due to reduced pressure

there!




Applications of Bernoulli

• Moving air gains speedabove the roof of a

house. This change in air

velocity means reduced

pressure on the roof.• Therefore, air pressure

inside the house is

greater, which can raise

the roof.

Bernoulli ApplicationCHECK YOUR NEIGHBOR




The pressure in a stream of water is reduced as the stream

speeds up. How then can a stream of water from a firehose actually knock a person off his or her feet?

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

B. The pressure due to water’s change in momentum can be much

greater than the water’s internal pressure.

C. Bernoulli’s principle works only for laminar flow, which the stream

is not.


CHECK YOUR NEIGHBOR

Bernoulli ApplicationCHECK YOUR ANSWER




CHECK YOUR ANSWER The pressure in a stream of water is reduced as the stream

speeds up. How then can a stream of water from a firehose actually knock a person off his or her feet?

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

B. The pressure due to water’s change in momentum can be

much greater than the water’s internal pressure.

C. Bernoulli’s principle works only for laminar flow, which the stream

is not.


Explanation:

There’s a basic distinction between 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.




Airplane wing

• The vertical vector

represents the net

upward force (lift) that

results from more air pressure below the

wing than above the

wing.

• The horizontal vector represents the air

drag force.

Bernoulli ApplicationCHECK YOUR NEIGHBOR




Air speeds up as it is blown across the top of the vertical

tube. How does this affect the air pressure in the vertical

tube, and what then occurs? A. The air jet pulls liquid up the tube.

B. Liquid mysteriously rises in the tube.

C. Reduced air pressure in the tube (due to Bernoulli) lets

atmospheric pressure on the liquid surface push liquid up into

the tube where it joins the jet of air in a mist.

D. Liquid in the vessel somehow turns to mist.

CHECK YOUR NEIGHBOR

Bernoulli ApplicationCHECK YOUR ANSWER




CHECK YOUR ANSWER

Air speeds up as it is blown across the top of the vertical

tube. How does this affect the air pressure in the vertical

tube, and what then occurs?

A. The air jet pulls liquid up the tube.

B. Liquid mysteriously rises in the tube.

C. Reduced air pressure in the tube (due to Bernoulli) lets

atmospheric pressure on the liquid surface push liquid

up into the tube where it joins the jet of air in a mist.

D. Liquid in the vessel somehow turns to mist.




Bernoulli Boats

• When the speed of water increases

between boats,

Bernoulli must be

compensated for or

else the boats collide!



Bernoulli Umbrella

• Why does Nellie Newtonblame Bernoulli for her

predicament?

05. fluid mechanics

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