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
What state of matter is honey?
1.
Solid
2.
Liquid
3.
Gas
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
10
3
kg/m
3
, 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
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
B. (Refer to worksheet)
1.
Sink
2.
Float
C. (Refer to worksheet)
1.
Sink
2.
Float
D. (Refer to worksheet)
1.
Sink
2.
Float
E. (Refer to worksheet)
1.
Sink
2.
Float
F. (Refer to worksheet)
1.
Sink
2.
Float
G. (Refer to worksheet)
1.
Sink
2.
Float
H. (Refer to worksheet)
1.
Sink
2.
Float
I. (Refer to worksheet)
1.
Sink
2.
Float
J. (Refer to worksheet)
1.
Sink
2.
Float
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 = F
G

F
B
Buoyant Force
•
F
B
= F
g
(displaced fluid) = m
f
g
•
Magnitude of
= weight of
of buoyant force
fluid displaced
Apparent Weight
•
The
apparent weight
of an object is the net
weight between the force of gravity and the
buoyant force.
F
net
= F
B
–
F
g
The apparent weight of an object in a
fluid, F
B
–
F
g
, could also be called
what?
1.
Net Force
2.
Tensional Force
3.
Buoyant Force
4.
Actual Weight
If an object is sinking to the bottom of
a glass of water, the buoyant force
must be?
1.
Equal to the Net
Force
2.
Less than
Fg
3.
More than
Fg
4.
Equal to
Fg
If an object is sinking to the bottom of
a glass of water, the buoyant force
must be?
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?
1.
Object is floating
continuously
upward
2.
Object is floating
at the top of the
fluid
3.
Object is sinking
Floating Objects
•
By Newton’s third law, if an object is floating,
and there is a force downward due to
acceleration of gravity, there must be an
equal buoyant force upward to bring about
equilibrium
•
F
b
= F
w
= m
o
g
Archimedes’ Principle
•
Displaced volume
of a fluid is the increase in
volume of a fluid due to the insertion of an
object.
•
Archimedes’ Principle
states that any object
completely or partially submerged in a fluid
experiences an upward buoyant force equal
to the
weight of the fluid displaced
.
If a rock is completely submerged in
a fluid, what must be true?
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
If a raft is floating and is partially
submerged in a fluid, what must be
true?
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
•
Pressure occurs within fluids due to the
constant motion of their molecules.
Common Pressure Units
•
For example,
standard atmospheric
pressure
is:
•
14.7 psi (pounds per square inch)
•
1.01 x 10
5
Pa (Pascal) = N/m
2
•
760 mmHg (millimeters mercury)
•
1
atm
(atmosphere)
Pressure cont.
•
Pressure is a measure of force per
given area.
•
P = F / A
•
Karate Chop demo
Bed of Nails
Pascal’s Principle
Pascal’s Principle
•
Because force is inversely 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
Ex. 2
•
A car weighing 12000 N sits on a hydraulic
press piston with an area of 0.90 m
2
.
Compressed air exerts a force on a second
piston, which has an area of 0.20m
2
. How
large must this force be to support the car?
Pressure as a function of depth
Which hole will have the water
shoot out the furthest?
1.
Top hole
2.
Middle Hole
3.
Bottom Hole
4.
All will be equal
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/m
3
and that
P
o
= 1.01 x 10
5
Pa.
What is the gauge pressure as well?
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.)
Continuity Equation
•
Based on Law of Conservation of Mass
–
what comes in has
gotta
come out
Bernoulli’s Equation
•
Results from conservation of energy.
•
Taken into account are kinetic energy,
potential energy, and also
pressure
because
we are dealing with fluids
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
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