Transcript Fluids Notes - Mayfield City Schools

Chapter 8:
Fluid Mechanics
Learning Goal
• To define a fluid.
• To distinguish a gas from a liquid
States of Matter
• Solids – definite volume, definite shape
• Liquids – definite volume, indefinite shape
• Gases – indefinite volume, indefinite shape
• (Also plasma and Bose-Einstein condensates
but we don’t need to worry about those.)
What state of matter is glass?
1. Solid
2. Liquid
3. Gas
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What state of matter is honey?
1. Solid
2. Liquid
3. Gas
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The Nature of Fluids
Fluids:
• Liquids and Gases comprise the
category of what we call fluids.
• Fluids exhibit certain characteristics
that solids do not – they flow when
subjected to shear stress
PROPERTIES OF STATIC FLUIDS
Learning Goal
• To use density to describe a fluid.
• To apply buoyant force to explain why some
objects float or sink in a fluid.
Static Fluid Properties
• Density () = mass / volume
• Viscosity = internal resistance to flow
Note: Atmospheric pressure and
temperature influence a fluid’s density
and viscosity
Density
The density of an object is
represented by:
Density = mass / volume
While this formula is familiar to us,
we will use it in subsequent
derivations.
Specific Gravity
• In order to have a constant comparison, we
use specific gravity instead of density
sometimes.
• Since water has a density of 1 g/mL or 1 x
103 kg/m3, we eliminate the units and call the
number specific gravity.
• Ex. For iron which has a density of 7.86 g/mL,
the specific gravity is 7.86 (or 7.86 as dense
as water).
Which is more dense, a pound
of feathers or a pound of
bricks?
1. A pound of bricks
2. A pound of feathers
3. They are the same
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Common Density
Misconceptions
• Let’s expel some common misconceptions
about density.
• Refer to your worksheet for the following
Turning Point questions about whether the
object will float or sink.
A. (Refer to worksheet)
1. Sink
2. Float
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B. (Refer to worksheet)
1. Sink
2. Float
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C. (Refer to worksheet)
1. Sink
2. Float
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D. (Refer to worksheet)
1. Sink
2. Float
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E. (Refer to worksheet)
1. Sink
2. Float
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F. (Refer to worksheet)
1. Sink
2. Float
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G. (Refer to worksheet)
1. Sink
2. Float
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H. (Refer to worksheet)
1. Sink
2. Float
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I. (Refer to worksheet)
1. Sink
2. Float
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J. (Refer to worksheet)
1. Sink
2. Float
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Buoyancy
• The upward force present when an object
floats in a fluid, or feels lighter, is the buoyant
force on the object.
• The weight of an object immersed in a fluid is
the apparent weight of the object (versus the
actual weight).
• Apparent weight = FG - FB (when sinking)
Floating Objects
• If, and only if, an object is
floating on the surface:
– The buoyant force exerted by
the fluid that is displaced is
equal in magnitude to the
weight of the floating object
• This is because when an
object is floating, it is not
moving up or down
– therefore the net force is zero
and the buoyant force must
equal the weight
FB   Fg ,object
FB  Fg , fluid  m fluid g
Weight of the
hot air balloon
Any object
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
Buoyant force of
displaced air
Archimedes’ Principle
The hot air balloon rises
because of the large volume of
air that it displaces
Apparent Weight
• The apparent weight of an object is the net
weight between the force of gravity and the
buoyant force.
Apparent Weight= Fnet = FG – FB
The Red line
A boat has a mass of 8450kg. What is the
minimum volume of water it will need to displace in
order to float on the surface of pure water without
sinking?
This is something you will have to think about
with your cardboard boats!
Volume Displaced
If an object is sinking to the bottom of
a glass of water, the buoyant force
must be?
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1. Equal to the Net
Force
2. Less than Fg
3. More than Fg
4. Equal to Fg
What must be true for the buoyant force
to be greater than gravitational force?
k.
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sin
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1. Object is floating
continuously
upward
2. Object is floating
at the top of the
fluid
3. Object is sinking
If a rock is completely submerged in
a fluid, what must be true?
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b.
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Bo
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1. The volume of the
displaced fluid = the
volume of the rock
2. The weight of the rock =
weight of the fluid that
was displaced.
3. Both 1 and 2
4. None of the above
The apparent weight of an object in a
fluid, FB – Fg , could also be called
what?
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Net Force
Tensional Force
Buoyant Force
Actual Weight
Ne
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1.
2.
3.
4.
If a raft is floating and is partially
submerged in a fluid, what must be
true?
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Bo
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1. The volume of the
displaced fluid = the
volume of the raft
2. The weight of the raft =
weight of the fluid that
was displaced.
3. Both 1 and 2
4. None of the above
Archimedes Principle example
• A bargain hunter purchases a “gold” crown at
a garage sale. After she gets home, she
hangs the crown from a scale and finds its
weight to be 7.84 N. She then weighs the
crown while it is immersed in water, and the
scale reads 6.86N. Is the crown made of
pure gold?
Pressure in Fluids
• In solids, pressure is defined as the amount
of force per unit area.
P = F/A
• Pressure occurs within fluids due to the
constant motion of their molecules but it is
more difficult to determine the area.
Common Pressure Units
• For example, standard atmospheric
pressure is:
• 14.7 psi (pounds per square inch)
• 1.01 x 105 Pa (Pascal) = N/m2
• 760 mmHg (millimeters mercury)
• 1 atm (atmosphere)
Pressure as a function of depth
water
dam
Which hole will have the water
shoot out the furthest?
be
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Top hole
Middle Hole
Bottom Hole
All will be equal
To
p
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2.
3.
4.
Absolute and Gauge Pressure
• Absolute pressure = Atmospheric + Gauge
Pressure
Pressure
• Atmospheric pressure is the pressure due to
the gases in the atmosphere (always present)
• Gauge pressure is the pressure due to a fluid
(not counting atmospheric pressure)
• Absolute pressure is the total pressure
Ex. 3
• Calculate the absolute pressure at an ocean
depth of 1,000m. Assume that the density of
water is 1,025 kg/m3 and that
Po= 1.01 x 105Pa.
What is the gauge pressure as well?
Pascal’s Principle
Pascal’s Principle
• Because force is directly proportional to area,
one can vary the cross-sectional area to
provide more force.
• Eg. Hydraulic brakes, car jacks, clogging of
arteries
In order to use a lesser force to accomplish a
difficult task, you should apply the force on the
hydraulic cylinder with
1. Smaller radius
2. Larger radius
3. Doesn’t matter
Do
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Ex. 2
• A car weighing 12000 N sits on a hydraulic
press piston with an area of 0.90 m2.
Compressed air exerts a force on a second
piston, which has an area of 0.20m2. How
large must this force be to support the car?
Laminar versus Turbulent Flow
Laminar flow:
– Low velocity relative to fluid medium
– Streamline path
Turbulent flow:
– High velocity relative to fluid medium
– Irregular Flow (Eddy currents)
15-6
Ideal Fluids
•
•
•
•
Laminar flow
Nonviscous
Incompressible
Constant density and pressure
• All these characteristics must be true for
these equations to hold true. (Hence, the
name for the ideal gas laws.)
Fluids in Motion
• Steady, Laminar Flow (Ideal Fluid):
-Every fluid particle passing trough the same
point in the stream has the same velocity.
Flow Rate
• Flow rate stays constant (at constant
pressure in a closed system)
Flow Rate = Av = V/t
A1v1 = A2v2
A = cross-sectional area (m2)
v = speed (m/s)
V = volume (m3/s)
t = time (s)
How are cross-sectional area
and velocity of fluids
proportional?
1. Inversely
2. Directly
3. No relationship
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Continuity Equation
• Based on Law of Conservation of Mass –
what comes in has gotta come out
What will happen to the yellow
foam ball?
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1. It will stay in the
funnel
2. It will shoot out
3. It will explode into
yellow chunks
What will happen to the pop
cans when air is blown
between them?
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1. They will come together
and collide.
2. They will move apart from
each other
3. It will remain motionless.
4. Pop will fly out from the
openings.
How are pressure and velocity
of fluids proportional?
1. Inversely
2. Directly
3. No relationship
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Bernoulli’s Equation
P1 + ρgh1 + ½ ρv12 = P2 + ρgh2 + ½ ρv22
Helpful notes:
• P = Patm if either side is open.
• Set bottom height (h2 ) = 0
• If there is a large volume up top, (v1 ) = 0
Bernoulli’s Equation
P + ρgh + ½ ρv2 = constant
-Results from conservation of energy.
P = Pressure energy resulting from internal forces
within the fluid
ρgh = similar to gravitational potential energy
½ ρv2 = similar to kinetic energy
Bernoulli’s Principle
• Bernoulli’s Principle states that the flow
speed (Av) in a constriction must be greater
than the flow speed before or after it.
• Also, swiftly moving fluids exert less pressure
than do slowly moving fluids.
• Eg. Tornadoes and blown off roofs
Bernoulli’s principle
• Pressure in a fluid varies inversely
with the velocity