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Transcript
Conceptual
Physical
Science
5th Edition
Chapter 5:
FLUID MECHANICS
© 2012 Pearson Education, Inc.
© 2012 Pearson Education, Inc.
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
© 2012 Pearson Education, Inc.
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
© 2012 Pearson Education, Inc.
Density
• Equation :
density = mass
volume
• 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 13.6
times as much mass as an equal volume of water (density
1 g/cm3).
© 2012 Pearson Education, Inc.
Density
Weight density
• in equation form:
weight density = weight
volume

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)
© 2012 Pearson Education, Inc.
Density
CHECK YOUR NEIGHBOR
Which of these has the greatest density?
A.
B.
C.
D.
100 kg of lead
100 kg of water
Both are the same
None of the above
© 2012 Pearson Education, Inc.
Density
CHECK YOUR ANSWER
Which of these has the greatest density?
A.
B.
C.
D.
100 kg of lead
100 kg of water
Both are the same
None of the above
Explanation:
They have the same mass and weight, but different volumes. Any
amount of lead is more dense than any amount of water.
© 2012 Pearson Education, Inc.
Pressure
• force per unit area that one object exerts
on another
• equation:
pressure = force
area
• depends on area over which force is
distributed

• units in lb/ft2, N/m2, or Pa (Pascals)
© 2012 Pearson Education, Inc.
Pressure in a Liquid
• Force per unit area that a liquid exerts on
something
• Depth dependent and not volume dependent
Example: Swim twice as deep and the pressure due to
the weight of water above you is twice as
much. (For total pressure, add to this the
atmospheric pressure acting on the water
surface.)
© 2012 Pearson Education, Inc.
Pressure in a Liquid
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
© 2012 Pearson Education, Inc.
Pressure in a Liquid
• 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
© 2012 Pearson Education, Inc.
Pressure in a Liquid
• Independent of shape of container
whatever the shape of a container, pressure
at any particular depth is the same
• Equation:
liquid pressure = weight density  depth

© 2012 Pearson Education, Inc.
Water Tower
• Force of gravity acting
on the water in a tall
tower produces
pressure in pipes
below that supply
many homes with
reliable water
pressure.
© 2012 Pearson Education, Inc.
Pressure
CHECK YOUR NEIGHBOR
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.
B.
C.
D.
Downstairs.
Upstairs.
Same.
Not enough information in problem.
© 2012 Pearson Education, Inc.
Pressure
CHECK YOUR ANSWER
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.
B.
C.
D.
Downstairs
Upstairs
Same
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.
© 2012 Pearson Education, Inc.
Pressure
CHECK YOUR NEIGHBOR
Does a 3-meter deep lake or a 6-meter deep small pond
exert more pressure on a dam?
A.
B.
C.
D.
The three-meter deep lake.
The six-meter deep small pond.
Same amount of pressure is exerted (atmospheric) so same
force.
Not enough information given in the question.
© 2012 Pearson Education, Inc.
Pressure
CHECK YOUR ANSWER
Does a 3-meter deep lake or a 6-meter deep small pond
exert more pressure on a dam?
A.
B.
C.
D.
The three-meter deep lake.
The six-meter deep small pond.
Same amount of pressure is exerted (atmospheric) so same
force.
Not enough information given in the question.
© 2012 Pearson Education, Inc.
Buoyancy in a Liquid
Buoyancy
• apparent loss of weight of a submerged object
• amount equals the weight of water displaced
© 2012 Pearson Education, Inc.
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
© 2012 Pearson Education, Inc.
Archimedes’ Principle
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)
© 2012 Pearson Education, Inc.
Archimedes’ Principle
• 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
© 2012 Pearson Education, Inc.
Archimedes’ Principle
• 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 an
upward force—the
buoyant force.
© 2012 Pearson Education, Inc.
Archimedes’ Principle
Buoyant Force
• Buoyant force is equal to the
weight of fluid displaced.
• Understood by pressure
differences
greater pressure against
the box – pressure on the
top of box
© 2012 Pearson Education, Inc.
Archimedes’ Principle
CHECK YOUR NEIGHBOR
On which of these blocks submerged in water is the
buoyant force greatest?
A.
B.
C.
D.
1 kg of lead.
1 kg of aluminum.
1 kg of uranium.
All the same.
© 2012 Pearson Education, Inc.
Archimedes’ Principle
CHECK YOUR ANSWER
On which of these blocks submerged in water is the
buoyant force greatest?
A.
B.
C.
D.
1 kg of lead.
1 kg of aluminum.
1 kg of uranium.
All the same.
Explanation:
The largest block is the aluminum one. It displaces more water
and therefore experiences the greatest buoyant force.
© 2012 Pearson Education, Inc.
Archimedes’ Principle
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
© 2012 Pearson Education, Inc.
Archimedes’ Principle
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.
B.
C.
D.
the buoyant force is greater.
a person feels less heavy.
a smaller volume of water is displaced.
None of the above.
© 2012 Pearson Education, Inc.
Archimedes’ Principle
CHECK YOUR ANSWER
The reason a person finds it easier to float in salt water,
compared with fresh water, is that in salt water
A.
B.
C.
D.
the buoyant force is greater.
a person feels less heavy.
a smaller volume of water is displaced.
None of the above.
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.
© 2012 Pearson Education, Inc.
Archimedes’ Principle
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 Styrofoamfilled preservers.
A.
B.
He apparently doesn’t know his physics.
He is correct.
© 2012 Pearson Education, Inc.
Archimedes’ Principle
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 Styrofoamfilled preservers.
A.
B.
He apparently doesn’t know his physics.
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!
© 2012 Pearson Education, Inc.
Pressure in a Gas
The Falkirk Wheel in Scotland illustrates Figure 5.17 in
your book. Each of the two caissons weigh the same
regardless of the weights of floating boats they carry.
© 2012 Pearson Education, Inc.
Pressure in a Gas
• Gas pressure is a
measure of the amount of
force per area that a gas
exerts against containing
walls.
• Here the force is exerted
by the motion of
molecules bouncing
around.
• Temperature is a
measure of the KE per
molecules of the gas.
© 2012 Pearson Education, Inc.
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
© 2012 Pearson Education, Inc.
Pressure in a Gas
Double density of air by
• Doubling the amount of air
• Decreasing the volume to half
© 2012 Pearson Education, Inc.
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
© 2012 Pearson Education, Inc.
Pressure in a Gas
CHECK YOUR NEIGHBOR
When you squeeze a party balloon to 0.8 its volume, the
pressure in the balloon
A.
B.
C.
D.
is 0.8 its former pressure.
remains the same if you squeeze it slowly.
is 1.25 times greater.
is 8 times greater.
© 2012 Pearson Education, Inc.
Pressure in a Gas
CHECK YOUR ANSWER
When you squeeze a party balloon to 0.8 its volume, the
pressure in the balloon
A.
B.
C.
D.
is 0.8 its former pressure.
remains the same if you squeeze it slowly.
is 1.25 times greater.
is 8 times greater.
Explanation:
Boyle’s law, sweet and simple: P(1.0 V) = 1.25 P(0.8 V).
© 2012 Pearson Education, Inc.
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.
© 2012 Pearson Education, Inc.
Atmospheric Pressure
Atmospheric pressure
•
•
•
•
Caused by weight of air
Varies from one locality to another
Not uniform
Measurements are used to predict
weather conditions
© 2012 Pearson Education, Inc.
Atmospheric Pressure
• 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
© 2012 Pearson Education, Inc.
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
© 2012 Pearson Education, Inc.
Mechanical Pump
• When the piston is
lifted, the intake valve
opens and air moves
in to fill the empty
space.
• When the piston is
moved downward, the
outlet valve opens
and the air is pushed
out.
© 2012 Pearson Education, Inc.
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
© 2012 Pearson Education, Inc.
Atmospheric Pressure
CHECK YOUR NEIGHBOR
Atmospheric pressure is caused by the
A.
B.
C.
D.
density of Earth’s atmosphere.
weight of Earth’s atmosphere.
temperature of the atmosphere.
effect of the Sun’s energy on the atmosphere.
© 2012 Pearson Education, Inc.
Atmospheric Pressure
CHECK YOUR ANSWER
Atmospheric pressure is caused by the
A.
B.
C.
D.
density of Earth’s atmosphere.
weight of Earth’s atmosphere.
temperature of the atmosphere.
effect of the Sun’s energy on the atmosphere.
© 2012 Pearson Education, Inc.
Atmospheric Pressure
CHECK YOUR NEIGHBOR
Two people are drinking soda using straws. Do they suck
the soda up? Could they drink a soda this way on the
Moon?
A.
B.
C.
D.
Yes and yes.
No, they suck the air out and the
atmospheric pressure pushes the soda
up. Yes, they could do the same thing on
the Moon.
No, they reduce air pressure in the straw
and the atmospheric pressure pushes
the soda up. No, they could not do the
same thing on the Moon.
Yes. No, they could not do the same
thing on the Moon.
© 2012 Pearson Education, Inc.
Atmospheric Pressure
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.
B.
C.
D.
Yes and yes.
No, they suck the air out and the
atmospheric pressure pushes the soda
up. Yes, they could do the same thing on
the Moon.
No, they reduce air pressure in the
straw and the atmospheric pressure
pushes the soda up. No, they could
not do the same thing on the Moon.
Yes. No, they could not do the same
thing on the Moon.
© 2012 Pearson Education, Inc.
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 an
enclosed fluid at rest is transmitted undiminished to
all points in the fluid
• Applies to all fluids—gases
and liquids
© 2012 Pearson Education, Inc.
Pascal’s Principle
• 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)
© 2012 Pearson Education, Inc.
Pascal’s Principle
CHECK YOUR NEIGHBOR
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 the
lower part of the left piston compare with the pressure
against the lower right piston?
A.
B.
C.
D.
More pressure on the left piston.
More pressure on the right piston.
Same pressure on each.
Same force on each.
© 2012 Pearson Education, Inc.
Pascal’s Principle
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 the
lower part of the left piston compare with the pressure
against the lower right piston?
A.
B.
C.
D.
More pressure on the left piston.
More pressure on the right piston.
Same pressure on each.
Same force on each.
© 2012 Pearson Education, Inc.
Pascal’s Principle
P1  P2
F1 F2

A1 A2
P1
F1
A1
© 2012 Pearson Education, Inc.
• Since the pressure in the
fluid is the same at both ends
of the tube, one can cleverly
change the force and area to
mechanically multiply each.
• This principle underlies a lot!
P2
F2
A2
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.
(Here surface area of
reservoir is irrelevant.)
© 2012 Pearson Education, Inc.
Pascal’s Principle
CHECK YOUR NEIGHBOR
In a hydraulic device, it is impossible for the
A.
B.
C.
D.
output piston to move farther than the
input piston.
force output to exceed the force input.
output piston’s speed to exceed the
input piston’s speed.
energy output to exceed energy input.
© 2012 Pearson Education, Inc.
Pascal’s Principle
CHECK YOUR ANSWER
In a hydraulic device, it is impossible for the
A.
B.
C.
D.
output piston to move farther than the input piston.
force output to exceed the force input.
output piston’s speed to exceed the input piston’s speed.
energy output to exceed energy input.
Explanation:
This illustrates the conservation of energy, a cornerstone of
all of science.
© 2012 Pearson Education, Inc.
Buoyancy in a Gas
• Archimedes’ principle
applies to fluids—liquids
and gases alike.
• Force of air on bottom of
balloon is greater than
force on top.
• Net horizontal forces
cancel, but not vertical
ones, which supplies the
buoyant force.
• And this buoyant force
equals the weight of
displaced air!
© 2012 Pearson Education, Inc.
Buoyant Force
CHECK YOUR NEIGHBOR
Is there a buoyant force acting on your classmates at this
moment? Defend your answer.
A.
B.
C.
D.
No. If there were, they would float upward.
Yes, but it is insignificant compared with their weights.
Only in water, but not in air.
None of these.
© 2012 Pearson Education, Inc.
Buoyant Force
CHECK YOUR ANSWER
Is there a buoyant force acting on your classmates at this
moment? Defend your answer.
A.
B.
C.
D.
No. If there were, they would float upward.
Yes, but it is insignificant compared with their weights.
Only in water, but not in air.
None of these.
© 2012 Pearson Education, Inc.
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
© 2012 Pearson Education, Inc.
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
© 2012 Pearson Education, Inc.
Bernoulli’s Principle
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)
© 2012 Pearson Education, Inc.
Bernoulli’s Principle
Laminar flow
• Smooth steady flow of constant density fluid
Turbulent flow
• Flow speed above a critical point becomes
chaotic
© 2012 Pearson Education, Inc.
Bernoulli’s Principle
CHECK YOUR NEIGHBOR
What happens to the internal water pressure in a narrowing
pipe of moving water?
A.
B.
C.
D.
Pressure is higher.
Pressure remains unchanged.
Pressure is less.
None of these.
© 2012 Pearson Education, Inc.
Bernoulli’s Principle
CHECK YOUR ANSWER
What happens to the internal water pressure in a narrowing
pipe of moving water?
A.
B.
C.
D.
Pressure is higher.
Pressure remains unchanged.
Pressure is less.
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!
© 2012 Pearson Education, Inc.
Applications of Bernoulli
• Moving air gains speed
above 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.
© 2012 Pearson Education, Inc.
Bernoulli Application
CHECK 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 fire
hose actually knock a person off his or her feet?
A.
B.
C.
D.
It can’t, as Bernoulli’s principle illustrates.
The pressure due to water’s change in momentum can be much
greater than the water’s internal pressure.
Bernoulli’s principle works only for laminar flow, which the stream
is not.
None of the above.
© 2012 Pearson Education, Inc.
Bernoulli Application
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 fire
hose actually knock a person off his or her feet?
A.
B.
C.
D.
It can’t, as Bernoulli’s principle illustrates.
The pressure due to water’s change in momentum can be
much greater than the water’s internal pressure.
Bernoulli’s principle works only for laminar flow, which the stream
is not.
None of the above
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.
© 2012 Pearson Education, Inc.
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.
© 2012 Pearson Education, Inc.
Bernoulli Application
CHECK 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.
B.
C.
D.
The air jet pulls liquid up the tube.
Liquid mysteriously rises in the tube.
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.
Liquid in the vessel somehow turns to mist.
© 2012 Pearson Education, Inc.
Bernoulli Application
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.
B.
C.
D.
The air jet pulls liquid up the tube.
Liquid mysteriously rises in the tube.
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.
Liquid in the vessel somehow turns to mist.
© 2012 Pearson Education, Inc.
Bernoulli Boats
• When the speed of
water increases
between boats,
Bernoulli must be
compensated for or
else the boats collide!
© 2012 Pearson Education, Inc.
Bernoulli Umbrella
• Why does Nellie Newton
blame Bernoulli for her
predicament?
© 2012 Pearson Education, Inc.