Download Fluids (Hydrostatics)

Physics Part 1
MECHANICS
Physics 1700
FLUIDS
W. Pezzaglia
Updated: 2013Jul23
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Fluids (Hydrostatics)
A. Pressure & Pascal’s Laws
B. Archimedes Principle
C. Surface Tension
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A. Pressure & Pascal’s Laws
Pascal’s Laws (1647)
1.
Pressure defined
2.
Hydraulics: Law of Transmitted Pressure
3.
Law of Depth
Blaise Pascal
1623-1662
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1. Pressure
(a) Definition: Force per area
(b) Units:
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SI: Pascal=Newton/m2
cgs: barye=Dyne/cm2
Imperial: psi=pound/inch2
Other: Torr=mm of Hg
Other: inches of Hg
Bar: millibar=100 Pascals
2. Pascal’s Law of Pressure
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Transmitted Pressure: if the weight of a fluid is neglected the
pressure throughout an enclosed volume will be the same
the static pressure in a fluid acts equally in all directions
the static pressure acts at right angles to any surface in contact
with the fluid
Major application is Hydraulics
Demo Breaking Bottle: http://www.youtube.com/watch?v=epOwdGIDzlY
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3. Law of Depth
• Pressure increases with
(vertical) depth in a fluid
of density :
P  P0  gh
P0 is atmospheric
pressure at top of fluid,
g is acceleration of
gravity
Water is shooting at
faster at bigger
depths due to more
pressure
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3b. Pascal’s Vases
Pressure is same at points
A, B, C, D as the are at
equal height
Pressure is
same at bottom
of these vases
3c. Pascal’s Barrel
• Pascal's barrel was a hydrostatics
experiment performed by Blaise
Pascal in 1646. In the experiment,
Pascal inserted a 10 m long (32.8
ft) vertical tube into a barrel filled
with water. When water was poured
into the vertical tube, Pascal found
that the increase in pressure
caused the barrel to burst.
• (Wikipedia)
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B. Archimedes Principle
287-212 BC
Discuss “the
story of the
crown”
1. Buoyancy Force
• Objects weigh less in water
• Hence, there is an upward
“Buoyant Force” on the
object inside the fluid.
• If the Buoyant force is big
enough, an object will “float”
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2. Archimedes's Principle (212 BC)
• “Any object, wholly or partially immersed in a fluid, is
buoyed up by a force equal to the weight of the fluid
displaced by the object.”
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3. The Crown
• Can show ratio of (dry) weight
“W” to Buoyant force “B” is
equal to the specific gravity of
the object.
• Compare “fake” crown with
equal weight of real gold.
• Since “fake” crown has less
density than real gold, its
buoyant force is greater so they
have different weights
underwater
 W

w B
4. Floating
• Archimedes: “Any floating object
displaces its own weight of fluid.“
• If density of object is less than water,
the buoyancy will exceed the weight
and the object will rise to the surface.
• At the surface, the object will float
such that the % of volume underwater
equals its specific gravity.
• For example, specific gravity of ice is
0.917 so the ice cube in ordinary water
will be 92% underwater and only 8%
above. However, an iceberg relative to
salty seawater (s.g. 1.025) will have:
0.917/1.025=0.895 or 89.5% underwater
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C. Surface Tension
1. Molecular Forces
2. Capillary Action
3. Surface Tension
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1. Molecular Forces
(a) Cohesion: tendency of
similar or identical
particles/surfaces to cling
to one another
(b) Adhesion: the tendency of
dissimilar particles or
surfaces to cling to one
another
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2. Capillary Action
(a) Capillary Rise when
adhesion>cohesion
[water in glass tube]
(b) Capillary Depression when
adhesion<cohesion
[mercury in glass tube]
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2c. Capillary Action
Capillary rise is greater in smaller
diameter tube
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3. Surface Tension
(a) Cohesion makes
surface of water behave
like elastic membrane
(b) Objects with
adhesion<cohesion
can float on surface
3c. Surface Tension
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x
https://upload.wikimedia.org/wikipedia/commons/f/f8/Cutting_a_water_drop
let_using_a_superhydrophobic_knife_on_superhydrophobic_surfaces.ogv
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Notes/Demos
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PHET: Pascal's law of depth
http://phet.colorado.edu/en/simulation/under-pressure
PHET Density
http://phet.colorado.edu/en/simulation/density
PHET Buoyancy
http://phet.colorado.edu/en/simulation/buoyancy
PHET Buoyancy and Balloons
http://phet.colorado.edu/en/simulation/balloons-andbuoyancy
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