chapter 8: fluid mechanics. learning goal to define a fluid. to distinguish a gas from a liquid
TRANSCRIPT
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Chapter 8:Fluid Mechanics
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Learning Goal
• To define a fluid.• To distinguish a gas from a liquid
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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.)
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What state of matter is glass?
Solid
Liquid
Gas
0% 0%0%
1. Solid
2. Liquid
3. Gas
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What state of matter is honey?
Solid
Liquid
Gas
0% 0%0%
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
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PROPERTIES OF STATIC FLUIDS
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Learning Goal
• To use density to describe a fluid.• To apply buoyant force to explain why some
objects float or sink in a fluid.
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Static Fluid Properties
• Density () = mass / volume• Viscosity = internal resistance to flow
Note: Atmospheric pressure and temperature influence a fluid’s density and viscosity
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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.
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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).
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Which is more dense, a pound of feathers or a pound of
bricks?
A pound of bric
ks
A pound of feath
ers
They are th
e same
0% 0%0%
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.
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A. (Refer to worksheet)
Sin
k
Flo
at
0%0%
1. Sink
2. Float
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B. (Refer to worksheet)
Sin
k
Flo
at
0%0%
1. Sink
2. Float
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C. (Refer to worksheet)
Sin
k
Flo
at
0%0%
1. Sink
2. Float
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D. (Refer to worksheet)
Sin
k
Flo
at
0%0%
1. Sink
2. Float
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E. (Refer to worksheet)
Sin
k
Flo
at
0%0%
1. Sink
2. Float
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F. (Refer to worksheet)
Sin
k
Flo
at
0%0%
1. Sink
2. Float
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G. (Refer to worksheet)
Sin
k
Flo
at
0%0%
1. Sink
2. Float
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H. (Refer to worksheet)
Sin
k
Flo
at
0%0%
1. Sink
2. Float
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I. (Refer to worksheet)
Sin
k
Flo
at
0%0%
1. Sink
2. Float
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J. (Refer to worksheet)
Sin
k
Flo
at
0%0%
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)
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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
objectgB FF ,
Only if floating
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Archimedes’ Principle
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 gmFF fluidfluidgB ,
Weig
ht of
the hot air ballo
on
Bu
oya
nt
forc
e of
di
spla
ced
air
The hot air balloon rises because of the large volume of
air that it displaces
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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
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The Red line
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Volume Displaced
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!
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If an object is sinking to the bottom of a glass of water, the buoyant force
must be?
Equal
to th
e N...
Less
than Fg
More
than Fg
Equal
to Fg
0% 0%0%0%
1. Equal to the Net Force
2. Less than Fg
3. More than Fg
4. Equal to Fg
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What must be true for the buoyant force to be greater than gravitational force?
Object
is floa..
.
Object
is floa..
.
Object
is sin
k...
0% 0%0%
1. Object is floating continuously upward
2. Object is floating at the top of the fluid
3. Object is sinking
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If a rock is completely submerged in a fluid, what must be true?
The volume of ..
.
The weigh
t of ..
.
Both 1 and 2
None of t
he ab...
0% 0%0%0%
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
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The apparent weight of an object in a fluid, FB – Fg , could also be called
what?
Net F
orce
Tensional F
orc...
Buoyant F
orce
Actual W
eight
0% 0%0%0%
1. Net Force
2. Tensional Force
3. Buoyant Force
4. Actual Weight
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If a raft is floating and is partially submerged in a fluid, what must be
true?
The volume of ..
.
The weigh
t of ..
.
Both 1 and 2
None of t
he ab...
0% 0%0%0%
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
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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?
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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.
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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)
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Pressure as a function of depth
damwater
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Which hole will have the water shoot out the furthest?
Top hole
Middle Hole
Bottom Hole
All will
be eq...
0% 0%0%0%
1. Top hole
2. Middle Hole
3. Bottom Hole
4. All will be equal
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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
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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?
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Pascal’s Principle
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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
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In order to use a lesser force to accomplish a difficult task, you should apply the force on the
hydraulic cylinder with
Smalle
r radius
Larg
er rad
ius
Doesn
’t matter
0% 0%0%
1. Smaller radius
2. Larger radius
3. Doesn’t matter
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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?
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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)
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15-6
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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.)
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Fluids in Motion
• Steady, Laminar Flow (Ideal Fluid): -Every fluid particle passing trough the same
point in the stream has the same velocity.
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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)
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How are cross-sectional area and velocity of fluids
proportional?
Inverse
ly
Dire
ctly
No re
lationshi...
0% 0%0%
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
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What will happen to the yellow foam ball?
It will
stay i..
.
It will
shoot ..
.
It will
explod...
0% 0%0%
1. It will stay in the funnel
2. It will shoot out
3. It will explode into yellow chunks
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What will happen to the pop cans when air is blown
between them?
They will
come...
They will
move...
It will
remain...
Pop will
fly o...
0% 0%0%0%
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.
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How are pressure and velocity of fluids proportional?
Inverse
ly
Dire
ctly
No re
lationshi...
0% 0%0%
1. Inversely
2. Directly
3. No relationship
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Bernoulli’s EquationP1 + ρgh1 + ½ ρv1
2 = 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
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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
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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
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Bernoulli’s principle
• Pressure in a fluid varies inversely with the velocity