Download Chapter 9 Fluid Mechanics

Chapter 9
Topics:
9-1
9-2
9-3
9-4
Fluid Mechanics
Fluids & Buoyant Force
Fluid Pressure & Temperature
Fluids in Motion
Properties of Gases
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Fluids
 A fluid is a non-solid state of matter in which atoms or
molecules are free to move past each other; a liquid or a
gas
 Liquids have a definite volume, but an indefinite shape
 Gases have indefinite volume and shape
 Density is mass per unit volume
 D = m/V
or
ρ =m/V
(Where ρ is mass density)
 Density of gases is measured at certain temperature &
pressure – usually 0C & 1atm
 Temperature & pressure influence gas density
 Solids & liquids are virtually incompressible, so
their densities are pressure-independent
 Density of water is 1g/mL or 1.0 x 103kg/L or
1.0 x 103kg/m3
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Buoyancy & Archimedes’Principle
 The upward force a fluid exerts on objects
partially or completely submerged in it –
the buoyant force
 Buoyant force acts in direction opposite
gravity
 Thus objects submerged in water, have a weight
less than that when on solid ground; this is
called the object’s apparent weight
 The buoyant force = the weight of the fluid
displaced by the object in the fluid
 Any object placed into a fluid will displace some
of the fluid & take its place; it is the weight of
that displaced fluid that provides the upward
buoyant force on the object
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Mass, density, buoyancy
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Buoyancy
http://www.youtube.com/wat
ch?v=eQsmq3Hu9HA
http://www.youtube.com/wat
ch?v=vJ36urazDu4
Note apparent decrease in mass
of rock 
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Buoyant Force
 The magnitude of buoyant force = to amount of fluid
displaced by the object that is submerged or partially
submerged in a fluid
 FB = Fg = mfg
 FB = buoyant force
 Fg = force of displaced fluid
 mfg = mass of displaced fluid x accel due to gravity
 mfg is the weight of the displaced fluid
 The relative densities of substances will determine
what floats, what becomes submerged, & what sinks
 An floating object cannot be denser than the fluid in
which it floats
 For floating objects
 ρf/ρo = Vo/Vf
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Altering buoyancy
 Devices that alter buoyancy change
the object’s average density
 Examples include, life jackets, ballast
tanks, ship’s hollow hulls, swim bladders
Submarines use ballast
tanks to change their
depth 
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How organisms use buoyancy
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Swim bladders inflate to change the overall density of the fish
when air is gulped at the surface or gas secreted by a gas gland
and the gas goes into the swim bladder; the fish can adjust the
gas content to control its diving trim
Sharks do not have swim bladders; their liver is huge and lipidrich; they adjust the lipid content to adjust their diving trim
Cephalopods (squid, octopus) have no swim bladder; they alter
buoyancy and thus diving trim by adjusting body fluids to alter
body density; also these organisms can withstand depths which
would crush other organisms (they have no swim bladders that
would implode, they have not internal bones which would be
crushed)
Human brain has a density of 1040kg/m3; the cerebro-spinal fluid
bathing the brain and spinal cord has a density of 1007kg/m3.
This fluid supports the brain with a buoyant force within the cranial
cavity. This is why when various spinal tap or other clinical
procedures are performed, the brain experiences great stress after
the procedure. Patients must stay in prone positions with medical
care until the brain fluid volume is restored.
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Floating objects
 Buoyant force = object’s weight for
floating objects
 FB = Fg =mog
 The force of gravity (object’s weight)
is in equilibrium with the buoyant
force acting against the Fg
 Since the 2 forces are equal and
opposite, the object floats at the
surface of the fluid
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Submerged objects
 If the 2 forces are not in equilibrium
& the densities differ, the object will
become submerged
 The degree of submergence depends on
the FB (buoyant force upwards) and
apparent weight of object (downwards)
 Fg/FB = ρo/ρf
 This equation is used to solve
buoyancy problems
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Pressure & Temperature
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Pressure = force/area

P=F/A
unit is N/m2
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Atmospheres (atm)
Millimeter of mercury (mmHg)
Pounds per square inch (lb/in2)
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105 Pa or 105 N/m2
1 atm
101 mmHg
14.8 lb/in2
A N/m2 is also called a Pascal (Pa)
Pressure can also be measured in:
At sea level atmospheric pressure is:
For each 33 feet an object is submerged in the ocean, they
experience an additional 1 atm of pressure
http://www.madsci.org/posts/archives/1998-11/912136521.Ph.r.html
If you have that much pressure on you at this instant at sea level,
how is it that you feel no pressure difficulties?
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Fluids exert pressure
 Fluids exert force equally in all directions when inside
an object
 Pascal’s Principle
 P 1 = P2
 F1/A1 = F2/A2
 This relationship is useful to understand how
pressure, force, & area are related
 Consider how a barber chair works
 Little Louie steps on a small lever at the base of the
chair (applying a small force) which raises Big Bubba
in the chair.
 How does a small force applied by Louie’s foot raise
massive Bubba in the barber chair?
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Hydraulic devices utilize Pascal’s
Principle!
 Remember fluids exert pressure in all directions
equally
 So, how much force does Little Louie have to apply to
a 0.004m2 piston which applies the pressure
throughout the liquid to push the second piston which
lifts Big Bubba in the chair?
 FLL = ?N ALL = 0.004m2
 FBB = 780N ABB= 0.5m2
 F1/A1 = F2/A2
 x/0.004 = 780/0.5
 X = 780 x 0.004/0.5 = 6.24N
 Little Louie needs to apply a mere 6.24N to lift Big
Bubba’s 780N body in the barber chair!
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A natural hydraulic system
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Man-made hydraulic system
(to make jobs easier)
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Equations
for Pressure (P) that varies with depth
 As objects go deeper into the water, the
pressure increases with depth; the weight (Fg)
of column of H2O above the object exerts a
force on the object
 The H2O column has a volume = Ah, where A =
cross-section area of column; h = height of
column
 So mass of the H2O column is: m = ρV =ρAh
 These relationships can be arranged in the
following sets of equalities for equations to use
in solutions for pressure problems:
 P=F/A=mg/A=ρVg/A=ρAhg/A=ρhg
 This is called “guage pressure” b/c it
represents the force on the object by the
column of H2O only
 What is absolute pressure?
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 Absolute pressure takes into account the
air pressure above the column of H2O
above the obejct
 Fluid pressure is a function of depth
 P = Po + ρgh; where Po = atmos P
 Temperature is an important quality of
fluids; the kinetic theory helps explain
molecular movement of particles which
have a direct influence on pressure;
changes in temperature affect particle
movement
 Absolute zero describes the instance
where all molecular movement
theoretically ceases; 0 Kelvin.
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Some good video links for fluid
topics

Video about pressure on an egg:
http://www.youtube.com/watch?v=4uRnPTQxZtw

Video on Pascal’s Principle Part 1:
http://www.youtube.com/watch?v=dIjAFW02PBM&feature=
related
 Video on Pascal’s Principle Part 2:
http://www.youtube.com/watch?v=Skran9E_Cjk&feat
ure=related

Video on atomspheric pressure:
http://www.youtube.com/watch?v=0fy4TLMNb6s&feature=r
elated
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Atmospheric Pressure
& Temperature
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The pressure of the atmosphere exerts pressure on the
atmospheric layers below
At sea level, atmospheric pressure is about 14.8lb/in2 or 1 atm
slide 11)
(see
Humans: 2m2 body surface area; so atmospheric force on our
bodies ~200,000N (40,000lbs)
 Why do we not collapse or feel this force?
Temperature – a measure of the average kinetic energy of the
particles in a substance
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Measure of how hot or cold a substance is; measured using a
thermometer
The higher the energy content of the particles, the higher the
temperature of the substance
Consider the phase change diagrams of substances to help you
visualize this connection
Temperature scales:
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Fahrenheit: 32F water freezes; 212F water evaporates
Celsius: 0C water freezes; 100C water evaporates
Kelvin: 273K water freezes; 373K water evaporates (add 273 to Celsius
temp to get Kelvin temp; NO degree symbol used for Kelvin)
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Fluids in Motion
Bernoulli’s Equation

Ideal fluids
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Fluids in motion are real fluids, but we will consider the
fluids in our discussion as ideal fluids
Conservation laws apply to moving fluids; when considering
fluids moving through a pipe, then the mass of fluid
entering the pipe during a certain interval must equal the
mass of the fluid exiting the pipe during the same interval
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1)incompressible (density remains same)
2)non-viscous (internal friction is zero)
3)have steady flow (velocity, pressure, density at each point in
fluid remain same)
4)non-turbulent flow (no angular speed, ie eddy currents, in
moving fluid)
A1v1 = A2v2
So, as a fluid moves faster its pressure decreases
Look at diagrams on next slide
20
Note how as
fluid speed
changes, its
pressure
changes; in
what natural
instances would
you notice this?
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Bernoulli’s Principle provides insight
as to why airplanes fly…
B
A
Air hitting wing front (A) splits its stream; top stream
must arrive at wing end (B) at same time the bottom
stream does; thus air speeds differ from top to bottom;
thus pressure differs & providing sufficient lift for plane!
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Bernoulli’s Equation
 Compares the energy of a fluid between 2
points:
 P1 + ½ ρv12 + ρgh1 = P2 + ½ ρv22 + ρgh2
 If fluid movement thru a pipe is at
same height, then the gravitational
potential energy would not change;
the ρgh now is removed from the
equation
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Ideal Gas Law
 PV = NkBT
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P = pressure (unit = atm)
V = volume (unit = L)
N = # particles
kB = Boltzmann’s constant = 1.38X10-23 J/K
T = temperature (unit = K)
 Real gases act like ideal gases under
normal conditions; so we can apply the
ideal gas law to real gases
 Note: in chemistry this law is written:
 PV = nRT
 Where n is #moles; R is gas constant (8.31
J/molK)
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