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Archimedes Principle
An object immersed in a liquid
has an upward buoyant force
equal to the weight of the liquiddisplaced by the object.
An object will float if the
upward buoyant force is greaterthan the objects weight.
Archimedes
287 211 BC
(courtesy F. Remer)
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Archimedes Principle Square bubble
of gas in a tank
of water
(courtesy F. Remer)
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Archimedes Principle Water pressure
in tank increases
with depth
p = pressure
h = depth
ph
(courtesy F. Remer)
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Archimedes Principle Horizontal Pressure
Differences Balance
(courtesy F. Remer)
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Archimedes Principle Force on bottom of
bubble
Fbottom
pbottom !Fbottom
A
ApF bottombottom !
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Archimedes Principle Force on top of
bubble
Fbottom
Ftop
A
Fp
top
top !
ApF toptop !
(courtesy F. Remer)
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Archimedes Principle
Buoyancy Force
Fbottom
Ftop
FB ! (pbottom ptop ) A
FB
FB
! Fbottom
Ftop
FB ! (pA
(courtesy F. Remer)
FB ! Apbottom Aptop
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Archimedes Principle
Pressure Difference
Between Top & Bottom
Negative by convention pbottom
ptop
h
(p
h! Vg
(p ! Vgh
(courtesy F. Remer)
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Archimedes Principle
Combine Equations
pbottom
ptop
h
(p ! Vgh
B
B ! (pA
FB ! VghA
FB ! VgV
V ! hA
(courtesy F. Remer)
Note: Density () = density of liquid
Volume = displaced volume of liquid = volume of object
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Archimedes Principle
The net force on the object is thus thedifference between the objects weight and
the buoyancy force of the displaced fluid.
If the buoyancy of an object exceeds itsweight, it tends to rise. An object whose
weight exceeds its buoyancy tends to sink.
Fnet ! mg VVgWeight of
object
Buoyant
Force of displaced
fluid
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Archimedes Principle
Cartoon here??Archimedes
287 211 BC
At the moment of Archimedes famous discovery.
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Example
What is the buoyancy in seawater of a piece ofwood that weighs 10,000 N & measures 3m x
1m x 2m?
The weight of wood = 10,000 N The volume of wood = 3m x 2m x 1m= 6 m3
The corresponding weight of an equal volume of
seawater: 6 m
3
x 10300N/m
3
= 61,800Nweight of water displaced = upward force = 61,800Nweight of wood = downward force = 10,000N
Net Force = 51,800N up
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Example 2 A fully suited diver weighs 200 pounds. This diver
displaces a volume of 3.0 cubic feet of seawater.Will the diver float or sink?
weight of equal volume of seawater:
3.0 ft3
x 64 lb/ft3
. = 192 lb.Weight of diver = down force = 200 lbs
Displaced weight of sea water = up force = 192 lb
net force = 8 lbsdown
The diver will sink. This diver weighs 8 pounds in
the water and is over-weighted. Removal of eight
pounds will allow the diver to hover.
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Buoyancy
Similar to parcel of air
in atmosphere
At Equilibrium
Density of Parcel Same
as Density of
Environment
pVeV
pe V!V
(courtesy F. Remer)
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Archimedes Principle
Translation:
objects more dense than water will sink -
negatively buoyant ;
objects less dense than water will float -
positively buoyant;
objects of the same density will remain at the
same level and neither sink nor float -
neutrally buoyant.
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Buoyancy Density Difference
Results in Net
Buoyancy Force
pVeVpe V"V
B
(courtesy F. Remer)
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Buoyancy Density Difference
Results in Net
Buoyancy Force
pVeVpe VV
B
(courtesy F. Remer)
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Buoyancy Net Buoyancy Force
pVeV
BgV)(B pe VV!
(courtesy F. Remer)
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Archimedes Principle Water is in hydrostatic
equilibrium
= density
g = acceleration ofgravity
B
(p
(h! Vg
(p
(h
gV
(courtesy F. Remer)
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Buoyancy How is air displaced?
Two methods
1.) Forced Ascent
2.) Auto-Convective Ascent
(courtesy F. Remer)
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Forced Ascent Some mechanism forces air aloft
CoolAirCoolAir
Cold airCold airWarm airWarm air
(courtesy F. Remer)
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Auto-Convective Ascent Air becomes buoyant
by contact with warm
ground
HotHotCoolCool CoolCool(courtesy F. Remer)
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Buoyancy As Parcel Rises Parcel Temperature
Changes and it expands.
Unsaturated?
(courtesy F. Remer)
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Stability As Parcel of Air Rises The Parcel Temperature
Changes and expands.
Saturated? Gaseous water condenses to rain
(courtesy F. Remer)
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