Transcript video slide
Chapter 14
Fluid Mechanics
PowerPoint® Lectures for
University Physics, Twelfth Edition
– Hugh D. Young and Roger A. Freedman
Lectures by James Pazun
Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley
Goals for Chapter 14
• Pressure, depth, and Pascal’s Law
• Buoyancy and Archimedes Principle
• Surface tension
• Bernoulli’s equation
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Densities of common substances—Table 14.1
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The pressure in a fluid
• Pressure in a fluid is force
per unit area. The Pascal is
the given SI unit for
pressure.
• Estimate the force act on a
paper due to air pressure of
1 atm?
• Estimate the thickness of
atmosphere. Compare your
result with data.
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Pressure, depth, and Pascal’s Law
• Pressure is everywhere equal in a uniform fluid of equal depth.
• What happen if the pressure is not everywhere equal?
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Buoyancy and Archimedes Principle
• The buoyant force is equal to the weight of the displaced fluid.
• Why?
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Surface tension
• How is it that water striders
can walk on water (although
they are more dense than the
water)?
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energy
Surface energy
area
force
length
W F x F
A x
72dynes/ cm 7210 N / m
3
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Capillarity
Vertical Force
F 2r cosc
Capillary pressure
F 2r cos c 2 cos c
p
2
A
r
r
Capillary rise
2 cos c
h
rg
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Q: How high could the water been
transport in a plant through capillary rise?
Typical diameter is about 20 micrometer
The calculated height is about 74 cm
What happen to plant higher than 74 cm?
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Pressure in spherical bubble
A 4r
2
dA
8r dA 8rdr
dr
Energy required for area increasing
E A 8rdr
Work done by pressure
W p V
p 4r dr
2
1 1
2
p
r
r1 r2
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Fluid flow I
• The flow lines at left are laminar.
• The flow at the right is turbulent.
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Fluid flow II
• The incompressibility of
fluids allows calculations to
be made even as pipes change.
• The continuity equation
A1v1 A2v2
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A stream of water emerging from a faucet, the initial
cross-section area is known to be 1 cm2. When the level
of water stream drop 5 cm, the stream cross-section is
found to reduce to 0.4 cm2. What is the flow rate from the
tap?
A. 20
B. 35
C. 50
D. 60
E. 70
cm3/s
A1v1 A2v2
2 ghA22
v1
2
2
( A1 A2 )
v v 2gh
2
2
2
1
2 10 0.05 0.4 2 10 8
0.19m / s
8
2
8
(10 0.4 10 )
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Introduction
• Submerging bath toys and
watching them pop back up
to the surface is an
experience with Archimedes
Principle.
• Fish move through water
with little effort and their
motion is smooth. Consider
the shark at right … it must
keep moving for its gills to
operate properly.
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Bernoulli’s equation
• Bernoulli’s equation allows
the user to consider all
variables that might be
changing in an ideal fluid.
dW p1 A1ds1 p2 A2 ds2 ( p1 p2 )dV
1
dK dV (v22 v12 )
2
dU dVg( y2 y1 )
dW dU dK
1
( p1 p2 ) gh (v22 v12 )
2
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The Venturi meter (Bernoulli’s Equation IV)
• Consider Example 14.9.
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Lift on an airplane wing
• The first time I saw lift
from a flowing fluid, a man
was holding a Ping-Pong
ball in a funnel while
blowing out. A wonderful
demonstration to go with
the lift is by blowing across
the top of a sheet of paper.
• Refer to Conceptual
Example 14.10.
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A curve ball (Bernoulli’s equation applied to sports)
• Bernoulli’s equation allows us to explain why a curve ball
would curve, and why a slider turns downward.
• Consider Figure 14.31.
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A 5 meter height, 2 meter radius water tank is filled up
with water. If at the bottom of the tank is been drilled
with a 1 cm diameter small hole, please estimate the
speed of water exiting the tank.
A. 1 m/s
B. 3 m/s
D. 10 m/s
E. 14 m/s
C. 7 m/s
1
1 2
2
2
( p1 p2 ) gh (v2 v1 ) gh v2
2
2
v2 2gh v 2gh 2 10 5 10m / s
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Danger of Tailing
By closely following another car, one can reduce the air
drag for saving energy. However, the disrupted air flow
will eliminate the negative lift effect on the rear car. This
is danger in the case of car racing. If the tailing car does
not notify this effect, it might slip out during a turn.
H.W. Estimate the negative lifting force on a car with a
speed of 100 Km/hr.
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