Chapter 9 Fluids and Buoyant Force

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Chapter 9 Fluids and Buoyant Force

• In Physics, liquids and gases are collectively
  called fluids.

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Fluids and Buoyant Force
A fluid is a nonsolid state of matter in which
the atoms or molecules are free to move past each
other, as in a gas or a liquid.
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Fluids and Buoyant Force
Liquids differ from gases in that liquids have a
definite volume, gases do not.
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Fluids and Buoyant Force
Recall, volume is the amount of space that an
object occupies.
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Fluids and Buoyant Force
Of course, whether an object floats or sinks has
little to do with size. It is the objects mass
density that matters.
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Fluids and Buoyant Force
Mass density (or just density) is the mass per
unit volume of a substance.
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Fluids and Buoyant Force
The Mass density of fresh water at 4oC and 1 atm
of pressure is 1.00 g/cm3 or 1.00X103kg/m3
Recall, 1 ml 1 cm3
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Fluids and Buoyant Force
That means that one liter (1000 ml) of fresh
water at 4oC and 1 atm of pressure has a mass of
one kilogram (1000 g).
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Fluids and Buoyant Force
Scuba divers, submarines and many types of fish
control their density to sink or rise in the
water.
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Fluids and Buoyant Force
Formula for Mass Density
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Fluids and Buoyant Force
Example 1. If gold has a mass density of 19.3
g/cm3 at STP (standard temperature and
pressure), how large would a 3.75 g sample of
pure gold be?
r 19.3 g/cm3 m 3.75 g
Given
Find
V
Solution
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Fluids and Buoyant Force
You may have noticed that objects feel lighter in
the water than they do in the air.
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Fluids and Buoyant Force
This is because the water exerts a buoyant force
in the opposite direction as gravity.
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Fluids and Buoyant Force
Buoyant Force is a force that acts upward on an
object submerged in a liquid or floating on a
liquids surface.
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Fluids and Buoyant Force
Do you know the story of Archimedes, and how he
discovered what has come to be known as
Archimedes Principle?
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Fluids and Buoyant Force
Archimedes (287-212 BC) is considered to be one
of the greatest mathematicians of all times, and
he is sometimes called the father of
mathematical physics.
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Fluids and Buoyant Force
Hiero, the king of Syracuse, commissioned a
craftsman to fashion a crown, and provided he
with an exact amount of gold to make it.
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Fluids and Buoyant Force
The crown that Heiro received weighed the same
amount as the gold he had provided, but he
suspected the craftsman had used some silver
instead of pure gold, and he asked Archimedes to
prove it.
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Fluids and Buoyant Force
Archimedes was contemplating the problem while in
the bath. He realized that by getting in the
bath, he displaced an amount of water that was
proportional to the part of his body that he
submerged.
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Fluids and Buoyant Force
He is said to have become so excited that he ran
naked through the streets, shouting Eureka!
Eureka! (this translates to, I have found
it!)
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Fluids and Buoyant Force
He formulated what is now known as Archimedes
principle, and a way to test the composition of
the crown.
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Fluids and Buoyant Force
Archimedes Principle any object that is
completely or partially submerged in a fluid
experiences an upward buoyant force equal in
magnitude to the weight of the fluid displaced by
the object.
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Fluids and Buoyant Force
Formula for Buoyant Force
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Fluids and Buoyant Force
Example 2. A piece of an unknown mineral that is
dropped into mercury displaces 0.057 m3 of Hg.
Find the buoyant force on the mineral. (note, r
of Hg 13.6 x 103 kg/m3 at STP.)
r 13.6 x 103 kg/m3 V 0.057 m3
Given
Find
FB
so
Hint
so
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Fluids and Buoyant Force
Example 2. A piece of an unknown mineral that is
dropped into mercury displaces 0.057 m3 of Hg.
Find the buoyant force on the mineral. (note, r
of Hg 13.6 x 103 kg/m3 at STP.)
r 13.6 x 103 kg/m3 V 0.057 m3
Given
Find
Solution
FB
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Fluids and Buoyant Force
If the buoyant force on an object is greater than
the weight of the object, the object will bob to
the surface.
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Fluids and Buoyant Force
For an object that is floating, the buoyant force
is equal and opposite to the weight of the object.
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Fluids and Buoyant Force
In other words, if an object is less dense than
the fluid that it rests in, it will float.
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Fluids and Buoyant Force
The density of the object determines how much of
the objects volume will be submerged below the
surface.
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Fluids and Buoyant Force
Formula for Determining what Portion of a
Floating Object will Submerge
Subsubmerged VVolume of entire object
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Fluids and Buoyant Force
KEEP GOING!!
Example 3. A 2.00 m3 block of wood has a density
of 0.500 x 103 kg/m3. If this object is placed
in fresh water at 4oC and 1 atm of pressure, what
volume will be below the surface of the water?
robject 0.500 x 103 kg/m3 V 2.00
m3 rfluid 1. 00 x 103 kg/m3
Given
Find
Vsub
Solution
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Fluids and Buoyant Force
Notice, if an object is ½ as dense as water, then
½ of it will be under the water.
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Fluids and Buoyant Force
If an object is 90 as dense as water, than 90
of the object will be below the surface (AS IN AN
ICEBERG).
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Fluids and Buoyant Force
If the density of the object is greater than the
density of the fluid, it will continue to sink.
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Fluids and Buoyant Force
The apparent weight of a submerged object depends
upon its density.
This, so called apparent weight is really just
the net force (Fnet) in the y-axis.
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Fluids and Buoyant Force
Formulas for Determining the FNet of a Submerged
Object
Other
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Fluids and Buoyant Force
Example 4. Gold has a density of 19.3 x 103
kg/m3. If a piece of gold with a volume of 0.450
m3 is completely submerged in water, how much
will it seem to weigh?
Hint The Volume of the water is the same as the
volume of the object.
robject 19.3 x 103 kg/m3 Vo 0.450
m3 rfluid 1.00 x 103 kg/m3 Vf 0.450 m3
Given
Find
FNet
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Fluids and Buoyant Force
robject 19.3 x 103 kg/m3 Vo 0.450
m3 rfluid 1.00 x 103 kg/m3 Vf 0.450 m3
Given
Find
FNet
Solution
Because Vo Vf, we can rewrite our equation.
DOWN (it will sink, not float!)
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• Another useful formula is
• Apparent weight Fg FB
• RememberFW and Fg are the same

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Chapter 9 Section 9-1Fluids and Buoyant Force

• Summary of Formulas

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Chapter 9 Section 9-1Fluids and Buoyant Force

• Summary of Formulas
• .
• Apparent weight Fg FB

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Fluid Pressure and Temperature
An object that is submerged in water, or any
other fluid, experiences pressure on all sides.
You have likely noticed the effects of this
pressure while swimming.
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Fluid Pressure and Temperature
Gases also exert pressure. Your body feels the
weight of the atmosphere on it. Your ears also
pop when you change altitude quickly.
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Fluid Pressure and Temperature
Pressure is the magnitude of the force on a
surface per unit area.
Movie Clip ?
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Fluid Pressure and Temperature
Formula for Pressure
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Fluid Pressure and Temperature
Can you explain why a finger does not pop a
balloon even when you exert more force on the
balloon than you do with a needle?
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Fluid Pressure and Temperature
The SI unit of pressure is the pascal (Pa), which
is equal to 1 N/m2.
Conversion Factor 1 Pa 1 N/m2
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Fluid Pressure and Temperature
Example 1. A cylinder-shaped column with a
height of 2.0 m and a base radius of 0.50 m has a
mass of 1250 kg. Find the pressure it exerts on
the ground.
Given
m 1250 kg h 2.0 m r 0.50 m
Find
P
Solution
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Fluid Pressure and Temperature
There are many other common units of pressure,
including the atmosphere (atm) and millimeters of
mercury (mm of Hg).
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Fluid Pressure and Temperature
Important Conversion Factors
1 atm 760 mm of Hg 760 torr 1.013 x 105 Pa
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Fluid Pressure and Temperature
Example 2. Convert 2.30 atm to Pa.
2.30 atm
Pa

2.33 x 105
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Fluid Pressure and Temperature
A barometer is an instrument that is used to
measure atmospheric pressure.
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Fluid Pressure and Temperature
You have probably noticed that when you squeeze a
balloon, it will bulge outwards in a different
area. This can be explained by Pascals
Principle.
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Fluid Pressure and Temperature
Pascals Principle Pressure applied to a fluid
in a closed container is transmitted equally to
every point of the fluid and to the walls of the
container.
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Fluid Pressure and Temperature
Formula for Pascals Principle
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Fluid Pressure and Temperature
Example 3. In a hydraulic car lift, the
compressed air exerts a force on a piston with a
base radius of 5.00 cm. The pressure is
transmitted to a second piston with a base radius
of 35.0 cm. How much force must be exerted on
the first piston to lift a car with a mass of
1.40 x 103 kg on the second piston?
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Fluid Pressure and Temperature
Example 4. In a hydraulic car lift, the
compressed air exerts a force on a piston with a
base radius of 5.00 cm. The pressure is
transmitted to a second piston with a base radius
of 35.0 cm. How much force must be exerted on
the first piston to lift a car with a mass of
1.40 x 103 kg on the second piston?
Given
r1 5.00 cm r2 35.0 cm m2 1.40 x 103
kg
Find
F1
Equation
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Fluid Pressure and Temperature
Given
r1 5.00 cm r2 35.0 cm m2 1.40 x 103
kg
Find
F1
Equation
Solution
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Lesson 9-2Fluid Pressure and Temperature
Pressure varies with depth in a fluid. That is
why your ears pop when you go up in an airplane
or down in the water.
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Lesson 9-2Fluid Pressure and Temperature
Atmospheric pressure (patm) is the pressure
exerted by the atmosphere. It varies from day to
day and from location to location.
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Lesson 9-2Fluid Pressure and Temperature
Standard atmospheric pressure is equal to 1.0 atm
or approximately 1.013 x 105 Pa.
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Lesson 9-2Fluid Pressure and Temperature
Gauge pressure (pgauge rgh) is the pressure
exerted by just the water, or other fluid. When
calculating gauge pressure, leave the atmospheric
pressure out of the calculation.
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Lesson 9-2Fluid Pressure and Temperature
Gauge Pressure as a Function of Depth
Where r density of fluid, g acceleration due
to gravity and h depth
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Lesson 9-2Fluid Pressure and Temperature
Example 5. Calculate the gauge pressure at a
point 10.0 m below the surface of the ocean.
(note, rsea water 1.025 x 103 kg/m3)
Given
r 1.025 x 103 kg/m3 h 10.0 m g 9.81
m/s2
Find
pgauge
Solution
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Lesson 9-2Fluid Pressure and Temperature
Absolute pressure (p) is the total pressure
exerted by the water (or other fluid) and the
atmosphere above the water.
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Lesson 9-2Fluid Pressure and Temperature
Absolute Pressure as a Function of Depth
Where p absolute pressure, p0 pressure at
point of comparison (usually atmospheric
pressure), r density of fluid, g acceleration
due to gravity and h depth
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Lesson 9-2Fluid Pressure and Temperature
Example 6. Calculate the absolute pressure
experienced by a scuba diver 20.0 m below the sea
(r 1.025 x 103 kg/m3). Assume patm 1.0 x 105
Pa
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Lesson 9-2Fluid Pressure and Temperature
Example 6. Calculate the absolute pressure
experienced by a scuba diver 20.0 m below the sea
(r 1.025 x 103 kg/m3). Assume patm 1.0 x 105
Pa
Given
p0 1.0 x 105 Pa h 20.0 m r 1.025 x 103
kg/m3
Find
Solution
p
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Lesson 9-2Fluid Pressure and Temperature

• Summary of Formulas

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Lesson 9-2Fluid Pressure and Temperature

• Summary of Formulas

1 atm 760 mm of Hg 760 torr 1.013 x 105 Pa
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Fluids in Motion

• The motion of a fluid can be described as either
  laminar (smooth) or turbulent (irregular).

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Fluids in Motion

• When studying fluids, is helps to consider the
  behaviors of an ideal fluid.

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Fluids in Motion
An ideal fluid is an imaginary fluid that has no
internal friction or viscosity, and is
incompressible.
The viscosity of a fluid is a measure of its
internal resistance, or its resistance to flow.
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Fluids in Motion

• Fluids with high viscosity, like molasses, flow
  slowly, due to internal friction.

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Fluids in Motion

• The law of conservation of mass explains that the
  mass entering a section of pipe or tube must be
  the same as the mass that leaves.

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Fluids in Motion
The Continuity Equation
area x speed in region 1 area x speed in region
2
The Continuity Equation is an expression of the
conservation of mass.
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Fluids in Motion
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Fluids in Motion
Example 1. An ideal fluid is moving at 3.0 m/s
through a section of pipe with a radius of 0.35
m. How fast will it flow through another section
of the pipe with a radius of 0.20 m?
HINT A pr2
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Fluids in Motion
Example 1. An ideal fluid is moving at 3.0 m/s
through a section of pipe with a radius of 0.35
m. How fast will it flow through another section
of the pipe with a radius of 0.20 m?
n1 3.0 m/s r1 0.35 m r2 0.20 m
Given
Find
n2
Formula
A1
A2
Solution
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Fluids in Motion

• From example 1, we see that as the area of the
  pipe decreases, the velocity of the fluid becomes
  much greater.

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Fluids in Motion

• Another property of fluids explains how the wings
  of an airplane produce lift.

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Fluids in Motion

• To demonstrate Bernoullis principle for
  yourself, try blowing air over the top of a piece
  of paper.

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Fluids in Motion

• Bernoullis Principle The pressure in a fluid
  decreases as the fluids velocity increases.

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Fluids in Motion

• The wings of an airplane are designed to allow
  air to flow quicker over the top than the bottom,
  resulting in lower pressure above the wings.

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Fluids in Motion

• Bernoullis Equation

pressure kinetic energy per unit volume
gravitational potential energy per unit volume
constant along a given streamline.
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Fluids in Motion

• Bernoullis Equation for Comparing a Fluid at Two
  Different Points

pressure kinetic energy per unit volume
gravitational potential energy per unit volume
pressure kinetic energy per unit volume
gravitational potential energy per unit volume .
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Important to know!!!!!

• IF there is no height difference, you can
  eliminate the
• If there is no area change, velocity stays the
  same
• IF there is no pressure change, P1 P2

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Fluids in Motion
Example 2. Water is circulated through a system.
If the water is pumped with a speed of 0.45 m/s
under a pressure of 2.2 x 105 Pa from the first
floor through a 6.0-cm diameter pipe, what will
the pressure be on the next floor 4.0 m above?
HINT The key to this question is that the
diameter of the pipe doesnt change and,
therefore, the velocity of the water remains
constant.
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Fluids in Motion
If n1 n2 , then we can simplify our equation.
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Fluids in Motion
Example 2. Water is circulated through a system.
If the water is pumped with a speed of 0.45 m/s
under a pressure of 2.2 x 105 Pa from the first
floor through a 6.0-cm diameter pipe, what will
the pressure be on the next floor 4.0 m above?
P1 2.2 x 105 Pa h1- h2 -4.0 m rwater
1000 kg/m3 g 9.81 m/s2
Given
Find
Formula
P2
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Fluids in Motion
Example 3. A water tank has a water level of 1.2
m. The spigot is located 0.40 m above the
ground. If the spigot is opened fully, how fast
will water come out of the spigot?
HINT The container is open to the atmosphere,
so the pressure will be the same in both spots.
We can assume that the velocity of the water at
the top (v2) is essentially zero.
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Fluids in Motion
The pressure of the fluid in both areas is the
same, P1 P2 so they cancel out. Also, the
velocity at the top (n2) is zero, so we cross out
that expression.
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Fluids in Motion
Now, we can divide all expressions by r (the
fluid doesnt change, so density is the same
throughout) and continue to isolate n1, the
unknown.
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Fluids in Motion
Example 3. A water tank has a water level of 1.2
m. The spigot is located 0.40 m above the
ground. If the spigot is opened fully, how fast
will water come out of the spigot?
Given
h1 0.40 m h2 1.2 m g 9.81 m/s2
Find
Formula
n2
Solution
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Fluids in Motion

• Summary of Formulas

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Lesson 9-2Fluid Pressure and Temperature
The Kinetic Molecular Theory (KMT) of Gases also
relates the temperature of a gas to the motion of
its particles.
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Lesson 9-2Fluid Pressure and Temperature
Temperature is a measure of the average kinetic
energy of the particles of a substance.
The SI unit of temperature is the Kelvin (K).
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Lesson 9-2Fluid Pressure and Temperature
Converting between Celsius and Kelvin
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Lesson 9-2Fluid Pressure and Temperature
Example 7. Convert 22.0 oC to Kelvin.