Chapter 10: Fluids

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Chapter 10 Fluids
Fluids substances which flow Liquids take the
shape of their container but have a definite
volume Gases take the shape and volume of their
container Pressure in a fluid force per area p
F/A Force normal force, pressure exerts a
force perpendicular to the surface. Units for
pressure 1 N/m2 1 Pa 1 Bar 105 Pa
atmospheric pressure (14.7 psi) atmospheric
pressure varies from .970 bar to 1.040 bar
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Example A flat roof of a house is 10.0 m by 8.0
m, and has a mass of 7500kg. Just before a
severe storm the windows of the house are shut so
tightly that the air pressure inside remained at
1.013 bars even when the out side pressure fell
to 980 mb. Compare the net force on the house
due to the difference in pressure to the weight
of the roof.
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Most pressure gages detect pressure differences
between the measured pressure and a reference
pressure. absolute pressure the actual pressure
exerted by the fluid. gauge pressure the
difference between the pressure being measured
and atmospheric pressure. p pgauge patm
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Some important aspects of pressure in a fluid The
forces a fluid at rest exerts on the walls of its
container (and visa versa) always perpendicular
to the walls. An external pressure exerted on a
fluid is transmitted uniformly throughout the
volume of the fluid. The pressure on a small
surface in a fluid is the same regardless of the
orientation if the surface.
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An application of pressure in a fluid the
hydraulic press
F2 p A2
F1 p A1
p
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Pressure and Depth A fluid supports itself
against its weight with pressure. The fluid also
must support itself against external pressure p
F/A pexternal w w mg rVg V Ah p
pexternal rgh
h
A
p
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Example Find the pressure on a scuba diver when
she is 15.0 m below the surface. How many
atmospheres of pressure is this?
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Buoyant force pressure balances gravity for a
fluid to support itself.
Fnet w rVg
Fnet rfluidVg
Buoyant force weight of fluid
displaced Fbuoyant Vrg
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Example An iron anchor weighs 200 N in air. How
much force is necessary to lift it if it is
submerged in water? The densities of iron and
water are 7800 Kg/m3 and 1000 Kg/m3 respectively.
Question Since a floating object needs only
displace enough water to offset its weight, the
displaced volume is less than the total volume of
the floating object. Consider a man with a rock
in a rowboat . If the man takes the rock and
throws it overboard into the pond, will the water
level of the pond go up, go down or stay the same?
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Fluid Flow with approximations incompressible
fluid no viscosity (friction) laminar flow
(a.k.a. streamline flow) in contrast with
turbulent flow Rate of flow volume per time
V vtA
A
A
vt
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If no fluid is added/lost, flow rate must be the
same throughout
Rin v1A1
Rout v2A2
Rin Rout v1A1 v2A2
Example 10.8 Water flows at 2.5 m/s through a
garden hose whose inside radius is 6.0 mm. (a)
What should the nozzle radius be for water to
leave it at 10.0 ms? (b) What is the rate of
flow of water through the hose? (c) How many
cubic meters of water will flow in an hour?
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Bernoullis Equation flow with changing heights
and pressure Work-Energy Theorem incompressible
fluid
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Water flows through the pipe as shown at a rate
of .015 m3/s. If water enters the lower end of
the pipe at 3.0 m/s, what is the pressure
difference between the two ends?
A2 20 cm2
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Applications of Bernoullis Equation Liquid at
rest p2 - p1 r g(h1 - h2 ) No pressure
difference, one part at rest Torricellis
theorem typically atmospheric pressure for both
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A boat strikes an underwater rock and opens a
pencil-sized crack 7mm wide and 150mm long in its
hull 65 cm below the waterline. The crew takes
5.00 minutes to locate the crack and plug it up.
How much water entered the boat during those 5
minutes?