Lecture 2
Fluids in Motion
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Physics 103 Spring 2012
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Summary
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Last Lecture: FLUIDS at REST
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Ideal Fluids in Motion
A fluid element P traces out a streamline as it moves. The
velocity vector of the element is tangent to the streamline at
every point.
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The Equation of Continuity for
incompressible liquid
Fluid flows from left to right at a steady rate
through a tube segment of length L. The
fluid's speed is v1 at the left side and v2 at the
right
i ht side.
id The
Th tube's
t b ' cross-sectional
ti l area is
i
A1 at the left side and A2 at the right side.
From time t in (a) to time t + ∆t in (b), the
amount of fluid shown in p
purple
p enters at the
left side and the equal amount of fluid shown
in green emerges at the right side.
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A tube of flow is defined by the streamlines
that form the boundary.
boundary The volume flow rate
must be the same for all cross sections of the
tube of flow.
flow
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QZ6: The figure shows a pipe and gives the
volume flow rate (in cm3/s) and the
direction of flow for all but one section.
What are the volume flow rate and the
direction of flow for that section?
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Sample Problem
Figure shows how the stream of water emerging from a faucet “necks
down” as it falls. The indicated cross-sectional areas are A0 = 1.2 cm2
and
d A = 0.35
0 3 cm2. The
h two levels
l l are separatedd by
b a vertical
i l distance
di
h=
45 mm. What is the volume flow rate from the tap?
As water falls from a tap,
tap its speed
increases. Because the flow rate must be
the same at all cross sections, the stream
mustt ““neck
k down.”
d
”
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Sample Problem
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Bernoulli's Equation
Fluid
Fl
id flows
fl
att a steady
t d rate
t through
th
ha
length L of a tube, from the input end at
the left to the output end at the right.
From time t in (a) to time t + ∆t in (b),
(b)
the amount of fluid shown in purple
enters the input end and the equal amount
shown in green emerges from the output
end.
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Bernoulli's Equation for y = Const
Bernoulli's Equation for v = Const
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Bernoulli's Equation
Water flows
W
fl
smoothly
hl through
h
h the
h pipe
i shown
h
in
i the
h figure,
fi
descending
d
di
in the process. Rank the four numbered sections of pipe according to (a)
the volume flow rate RV through
g them,, (b)
( ) the flow speed
p
v through
g
them, and (c) the water pressure p within them, greatest first.
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Bernoulli's Equation
Water flows
W
fl
smoothly
hl through
h
h the
h pipe
i shown
h
in
i the
h figure,
fi
descending
d
di
in the process. Rank the four numbered sections of pipe according to (a)
the volume flow rate RV through
g them,, (b)
( ) the flow speed
p
v through
g
them, and (c) the water pressure p within them, greatest first.
a) all tie;
b) 1, then 2 and 3 tie, 4 (wider means slower);
c) (c) 4, 3, 2, 1 (wider and lower mean more pressure)
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Bernoulli's Equation
Sample Problem. Water pours through a hole
in a water tank, at a distance h below the
water surface
surface. The pressure at the water
surface and at the hole is atmospheric
pressure p0.
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Bernoulli's Equation
Sample Problem. Water pours through a hole
in a water tank, at a distance h below the
water surface
surface. The pressure at the water
surface and at the hole is atmospheric
pressure p0.
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Fountains
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How does it fly ?
anti-torque
q tail rotor
Main rotor
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Igor Sikorsky
FORWARD
TAKEOFF
AND HOVER
Main rotor
BACKWARD
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Why a sport car sits low ?
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Summary
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