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Fluids
Fluids
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Pressure
Fluids at rest
Archimedes’ principle
Fluids in motion
Bernoulli’s principle
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Fluids
Demonstration: Cups and Balloons
Fluids
Fluid – Anything that flows
•Water
•Oil
•Air
•Jellybeans?
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Fluids
Fluids can be:
Static
Dynamic
Fluids can not be directly pushed or pulled.
They can only be moved by PRESSURE
Static Fluids
Density (ρ)
m
Mass (kg )
ρ=
⇒
v
Volume(m3 )
ρwater=1000 kg/m3
To convert from g/cm3
to kg/m3 you must
multiply by 1000
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Static Fluids
Pressure=Force/Area
P=
Force( N )
Area (m 2 )
Pascal (Pa) is
the unit of
pressure
The smaller the
area the greater the
pressure
Can you think of
other common units???
Static Fluids
A cube and a spherical ball are made of the same material and have
the same mass. Which exerts the larger pressure on the floor?
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Static Fluids
Describe how a gas exerts pressure on the walls of its container.
Static Fluids
Why does the pressure in a tire increase as you add more air?
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Static Fluids
Demonstration: Dixie Cups
Static Fluids
Some Perspective on Pressure
Air Pressure= 1.01 ⋅105 Pa or 14.7 PSI
Tire Pressure= 3.03 ⋅10 Pa
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Full SCUBA TANK=
or 45PSI
2.06 ⋅107 Pa or 3000 PSI
Ocean Bottom= 1.1 ⋅10 Pa or >16000 PSI
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Static Fluids
Example: The “foot print” of a car tire is approx.
150 cm2. The pressure in each tire is 3.03x105 Pa.
What is the weight of the car?
Static Fluids
Day 1 HW:
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Static Fluids
Demonstration: Vacuum Cannon
Static Fluids
Vacuum Cannon…how it works
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Static Fluids
Demonstrations
•Suction Cups
•Magdeburg Hemispheres
•Balloon in Bell Jar
•Alarm in Bell Jar
Static Fluids
Pascal's Principle
(hydraulic principle)
Any INCREASE (or decrease) in
pressure to a confined fluid is transmitted
undiminished throughout the fluid
Assume the
fluid is
quasistatic
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Static Fluids
Pascal's Principle examples:
•Hydraulic Jacks
•Squeezing Toothpaste
•Bulldozers and Backhoes
•Automotive Breaks
Small Area=
small input force
Large Area=large output force
F = PA
Static Fluids
Pascal's Principle Equation
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Static Fluids
Example: A Hydraulic jack for a car has an output piston
diameter of 5.0 cm and an input piston diameter of 1.0 cm. You
want to lift a 8000 N car. How much force must be applied to
the input piston?
Pressure Measurement
The change in
height relates
directly to the
gauge pressure
using P = ρ hg
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Pressure Measurement
Static Fluids
Q: Which container has the greatest fluid pressure at
the bottom of the container?
h
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Static Fluids
Q: Which container has the greatest fluid pressure at
the bottom of the container?
Static Fluids
Example: You are driving on a rainy day and hydroplane into a
puddle that is barely deep enough to cover the roof of your car
(approx. 1.6 meters). Determine the minimum force necessary to
open your car door. The door has an area of approximately 1
square meter.
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Static Fluids
Homework:
Static Fluids – Buoyant Force
Buoyant Force -An upward pointing force exerted on
a body immersed in a fluid.
-Caused by the increasing pressure
with increasing depth
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Static Fluids – Buoyant Force
Buoyant Force
Static Fluids – Buoyant Force
Example: Determine the apparent weight of a 3000 N
treasure chest filled with gold coin. The chest is
airtight and 40 cm on a side.
Fbuoy
N
Fg
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Static Fluids – Buoyant Force
Example: What volume of helium is needed if a
balloon is to lift a load of 180 kg (including the weight
of the empty balloon)
Fbuoy
FgHe
Fgload
Static Fluids – Archimedes’ Principle
Archimedes’ Principle
The buoyant force is equal to the
weight of the displaced fluid.
If you want something to
float in water you must
make its effective density
less than the density of
water.
Eureka!!
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Static Fluids – Archimedes’ Principle
Archimedes’ Principle
Lab: Buoyant Force w/ force
sensor
Static Fluids – Archimedes’ Principle
Activity – Penny Barge
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Fluids in Motion
Fluid Dynamics
•The study of moving fluids
•Only consider Laminar flow
Laminar – Layers
Turbulent –
Mixing of layers
Equation of Continuity
Av is another way
of expressing
volume/time
The equation of continuity is really a
statement of conservation of matter…what
goes in must come out!
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Equation of Continuity
Moving Fluids – Bernoulli’s Equation
Bernoulli’s Equation is just another
restatement of conservation of energy.
P1 + 12 ρ v12 + ρ gy1 = P2 + 12 ρ v22 + ρ gy2
GPE at
location 1
Kinetic Energy
location 1
Pressure at
location 1
More accurately, work done as
a result of a pressure difference
P1-P2
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Example 1: Heating Duct – Eqtn of Continuity
What area must a heating duct have if air moving 3.0 m/s along it can
replenish the air every 15 minutes in a room of volume 300 m3? Assume
the air’s density remains constant.
Example 2: Blood Flow – Eqtn of Continuity
In humans, blood flows from the
heart into the aorta, from which it
passes into the major arteries. These
branch into arterioles, which in turn
branch into capillaries. The blood
returns to the heart via the veins.
The radius of the aorta is about 1.2
cm, and the blood passing through
it has a speed of about 40 cm/s. A
typical capillary has a radius of
about 4 x 10-4 cm, and blood flows
through it at a speed of about 5x10-4
m/s. Estimate the number of
capillaries that are in the body.
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Example 2: Blood Flow – Eqtn of Continuity (continued)
Example 3: Bernoulli’s Equation
Water circulates throughout a house in a hot-water heating system. If the
water is pumped at a speed of 0.50 m/s through a 4.0 cm diameter pipe in
the basement under a pressure of 3 atm, what will be the flow speed and
pressure in a 2.6 cm diameter pipe on the second floor 5.0 m above?
Assume the pipes do not divide into branches.
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Example 3: Bernoulli’s Equation
Example 3: Bernoulli’s Equation
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Torricelli’s Theorem
Predicts the speed a fluid will shoot come out of a pipe
Assumes the height of the water doesn’t change appreciably ie. V2=0
The pressure at the top and bottom of the container is the same (1 atm)
Moving Fluids – Bernoulli’s Principle
Bernoulli’s Principle
Where fluid flow is fast, pressure is low
Where fluid flow is slow, pressure is high
Activities:
Dime in cup
Ping Pong Ball and coffee stir
“two sheets to the wind”
Ball in stream of water
Bernoulli, Mexican and movies??
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Fluids in Motion
Physics of Flight
Physics of baseball
Physics of Chimneys
Physics of Sailboats
Fluids in Motion
B
A
C
Where is the pressure the greatest, at point
A, B or C?
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