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Physi cs 124, Spr i ng 2011
Lecture 2 Summary
1/29/2010
Lecture 3
Fluids
2/4/2010
Outline
Static Equilibrium if
∑
F
external
=
0, and
∑
external
=
0
Weight acts at CM
=
CofG
Stress
∝
strain
smalldeformations
L
L
=
F
AY
V
V
=−
P
B
x
h
=−
F
AS
x
cm
=
∫
dx x
r
m
y
cm
=
∫
dy y
r
m
•
Pascal
•
Archimedes
•
Continuity
•
Bernoulli
•
Toricelli
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Physi cs 124, Spr i ng 2011
Basics
P
atm
=
1.013x10
5
Pa
=
1.013x10
5
N
/
m
2
=
1 atm
=
...
•
Fluid: liquid or gas
•
Gases are highly compressible; liquids are not
–
Approximate: density / volume constant
•
Putting an object in a fluid leads to:
–
Pressure force, a force per unit area perpendicular to a face
–
A viscous (drag / frictional) force, parallel to a face
•
Generally ignored in what follows
P
=
F
⊥
A
Gauge pressure: Pressure relative to atmosphere
Be aware: absolute pressure vs. Gauge pressure
3
Physi cs 124, Spr i ng 2011
Pascal's Principle
•
A pressure applied to a liquid is transmitted undiminished to
every point of the liquid and to the walls of the container
Force
L
on Area
L
F
R
on A
R
Ignore effects of gravity for now.
a: to left as larger pressure there
For hydraulic lift in garage, car goes .
..
b: to right as larger pressure there
c: to left as larger force there
d: to right as larger force there
e: both sides are equally good
A
L
≪
A
R
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Physi cs 124, Spr i ng 2011
Pascal's Principle
•
A pressure applied to a liquid is transmitted undiminished to
every point of the liquid and to the walls of the container
For hydraulic lift in garage, car goes .
..
Force
1
on Area
1
F
2
on A
2
Ignore effects of gravity for now.
Pascal: P
=
F
1
A
1
=
F
2
A
2
If A
2
≫
A
1
, then F
2
≫
F
1
A small force on left can
support a big car on right.
5
Physi cs 124, Spr i ng 2011
Variation of Pressure with Depth
•
Fluid in a gravitational field has weight.
•
Each element of fluid supports the fluid above it.
•
Pressure increases with depth.
Consider a volume of fluid made out of smaller volumes; one is shown.
P
top
∑
F
vertical
=
0
P
top
A
mg
−
P
bottom
A
=
0
Use m
=
Ah, and divide out A to obtain:
P
bottom
h
P
bottom
=
P
top
gh
Height h, area of top and bottom A, density
, and pressure P
top
P
bottom
at top
bottom
or: P
gh
=
constant
Ignoring gravity: not a good idea
Pressure only depends on depth
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Physi cs 124, Spr i ng 2011
Example: water pressure
P
top
P
bottom
h
e: none of the above
d: narrow slanted
a: wide vertical
c:bulging vertical
b: curly vertical
In which tube will the water go highest?
And the demo answer is.
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This note was uploaded on 03/24/2011 for the course PHYSICS 123 taught by Professor Madey during the Fall '08 term at Rutgers.
 Fall '08
 Madey
 Physics, Static Equilibrium

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