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Conceptual Physics
Fundamentals
Chapter 7:
FLUID MECHANICS
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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
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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
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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
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Densities
seven-layer-density-column
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Aerogel Density – 0.020 g/cm3 (lightest solid)
Can hold 4000 times it’s own weight
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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
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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 ANSWER
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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
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
D. none of the above
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
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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.
D. none of the above
Density
CHECK YOUR NEIGHBOR
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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.
D. none of the above
Density
CHECK YOUR ANSWER
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Compared with the weight of water, the weight of a liter of ice is
A. more.
B. less.
C. the same.
D. none of the above
Density
CHECK YOUR NEIGHBOR
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Compared with the weight of water, the weight of a liter of ice is
A. more.
B. less.
C. the same.
D. none of the above
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
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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
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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
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When you stand on one foot instead of two, the force you
exert on the floor is
A. less.
B. the same.
C. more.
D. none of the above
Pressure
CHECK YOUR NEIGHBOR
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When you stand on one foot instead of two, the force you
exert on the floor is
A. less.
B. the same.
C. more.
D. none of the above
Explanation:
Distinguish between force and pressure!
Pressure
CHECK YOUR ANSWER
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When you stand on one foot instead of two, the pressure
you exert on the floor is
A. less.
B. the same.
C. more.
D. none of the above
Pressure
CHECK YOUR NEIGHBOR
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When you stand on one foot instead of two, the pressure
you exert on the floor is
A. less.
B. the same.
C. more.
D. none of the above
Explanation:
Twice as much, in fact!
Pressure
CHECK YOUR ANSWER
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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
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Pressure in a Liquid
• 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
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Pressure in a Liquid
• 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
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Water pressure provided by a water tower is greater if the
tower
A. is taller.
B. holds more water.
C. both A and B
D. none of the above
Pressure in a Liquid
CHECK YOUR NEIGHBOR
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Water pressure provided by a water tower is greater if the
tower
A. is taller.
B. holds more water.
C. both A and B
D. none of the above
Explanation:
Only depth, not amount of water, contributes to pressure.
Pressure in a Liquid
CHECK YOUR ANSWER
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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
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Buoyancy in a Liquid
Buoyancy
• apparent loss of weight of a submerged object
• amount equals the weight of water displaced
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Buoyancy in a Liquid
• 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
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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 Liquid
CHECK YOUR NEIGHBOR
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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 Liquid
CHECK YOUR ANSWER
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Buoyancy in a Liquid
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
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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
D. none of the above
Buoyancy in a Liquid
CHECK YOUR NEIGHBOR
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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
D. none of the above
Buoyancy in a Liquid
CHECK YOUR ANSWER
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Buoyancy in a Liquid
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
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Buoyancy in a Liquid
Diving Ketchup
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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
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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” 2 kg, then the buoyant
force or weight of water displaced is 1 kg
Demo
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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’ Principle
CHECK YOUR NEIGHBOR
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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’ Principle
CHECK YOUR ANSWER
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When a fish expands its air bladder, the density of the fish
A. decreases.
B. increases.
C. remains the same.
D. none of the above
Archimedes’ Principle
CHECK YOUR NEIGHBOR
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When a fish expands its air bladder, the density of the fish
A. decreases.
B. increases.
C. remains the same.
D. none of the above
Archimedes’ Principle
CHECK YOUR ANSWER
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When a fish makes itself less dense, the buoyant force on it
A. decreases.
B. increases.
C. remains the same.
D. none of the above
Archimedes’ Principle
CHECK YOUR NEIGHBOR
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When a fish makes itself less dense, the buoyant force on it
A. decreases.
B. increases.
C. remains the same.
D. none of the above
Archimedes’ Principle
CHECK YOUR ANSWER
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When a fish decreases the size of its air bladder, the
density of the fish
A. decreases.
B. increases.
C. remains the same.
D. none of the above
Archimedes’ Principle
CHECK YOUR NEIGHBOR
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When a fish decreases the size of its air bladder, the
density of the fish
A. decreases.
B. increases.
C. remains the same.
D. none of the above
Archimedes’ Principle
CHECK YOUR ANSWER
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When a submarine takes water into its ballast tanks, its
density
A. decreases.
B. increases.
C. remains the same.
D. none of the above
Archimedes’ Principle
CHECK YOUR NEIGHBOR
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When a submarine takes water into its ballast tanks, its
density
A. decreases.
B. increases.
C. remains the same.
D. none of the above
Archimedes’ Principle
CHECK YOUR ANSWER
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When a submerged submarine expels water from its ballast
tanks, its density
A. decreases.
B. increases.
C. remains the same.
D. none of the above
Archimedes’ Principle
CHECK YOUR NEIGHBOR
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When a submerged submarine expels water from its ballast
tanks, its density
A. decreases.
B. increases.
C. remains the same.
D. none of the above
Explanation:
This is how a submerged submarine is able to surface.
Archimedes’ Principle
CHECK YOUR ANSWER
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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
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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
D. none of the above
Archimedes’ Principle
CHECK YOUR NEIGHBOR
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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
D. 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.
Archimedes’ Principle
CHECK YOUR ANSWER
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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.
Archimedes’ Principle
CHECK YOUR NEIGHBOR
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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!
Archimedes’ Principle
CHECK YOUR ANSWER
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Archimedes’ Principle
• 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)
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Archimedes’ Principle
• 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
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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
Archimedes’ Principle
CHECK YOUR NEIGHBOR
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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
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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.
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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
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Pressure in a Gas
Double density of air by
• doubling the amount of air
• decreasing the volume to half
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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
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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
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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
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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.
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Atmospheric Pressure
Atmospheric pressure
• caused by weight of air
• varies from one locality to another
• not uniform
• measurements are used to predict weather conditions
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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
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Atmospheric Pressure
• 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
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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
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Atmospheric Pressure
Barometer
• device to measure atmospheric pressure
• also determines elevation
Aneroid barometer • small portable instrument that measures
atmospheric pressure
• calibrated for altitude, then an altimeter
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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.
D. none of the above
Atmospheric Pressure
CHECK YOUR NEIGHBOR
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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.
D. none of the above
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 Pressure
CHECK YOUR ANSWER
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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
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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)
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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.
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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 Principle
CHECK YOUR NEIGHBOR
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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 Principle
CHECK YOUR ANSWER
Hydraulic Fracturing - Natural gas extraction
Principles of Hydraulics
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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
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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
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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
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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.
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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.
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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)
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As a balloon rises higher and higher into the atmosphere,
its
A. volume decreases.
B. density increases.
C. weight increases.
D. none of the above
Buoyancy in Gas
CHECK YOUR NEIGHBOR
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As a balloon rises higher and higher into the atmosphere,
its
A. volume decreases.
B. density increases.
C. weight increases.
D. none of the above
Buoyancy in Gas
CHECK YOUR ANSWER
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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
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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
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Bernoulli’s Principle
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
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Bernoulli’s Principle
Laminar flow
• smooth steady flow of constant density fluid
Turbulent flow
• flow speed above a critical point becomes
chaotic
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Bernoulli’s Principle
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
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Bernoulli’s Principle
• 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.
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley
Bernoulli’s Principle
• 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
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley
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.
D. none of the above
Bernoulli’s Principle
CHECK YOUR NEIGHBOR
Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley
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.
D. none of the above
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 Principle
CHECK YOUR ANSWER
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