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8/4/2019 Lecture 05 Buoyancy
1/13
Buoyancy The buoyant force is equal to the
displaces.
1/21/2010 BIOT 405 Fluid mechanics 1
8/4/2019 Lecture 05 Buoyancy
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Buo anc The buoyant force is essentially
the pressure at the top of the object,,
the pressure at the bottom, which.
Since the pressure at the bottom is
,submerged in a fluid necessarily feels
1/21/2010 BIOT 405 Fluid mechanics 2
.
8/4/2019 Lecture 05 Buoyancy
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Buoyancy
O course, o jects a so ee adownward force due to gravity
The difference between the
ravitational force and buo antforce on a submerged objectdetermines whether that object will
sink, or rise to the surface.
1/21/2010 BIOT 405 Fluid mechanics 3
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Buoyancy
I t e weig t is greater t an t ebuoyant force, the object sinks.
If the liquid is denser, the buoyant
force is reater and the ob ect floats. Steel sinks in water, but floats in
ercur . Buoyancy is the ability to float.
1/21/2010 BIOT 405 Fluid mechanics 4
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Archimedes' Principle:
An o ject is uoye up wit aforce equal to the weight of theiqui it isp aces. T is is nown as
Archimedes' Principle
1/21/2010 BIOT 405 Fluid mechanics 5
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Archimedes' Principle:
e can ca cu ate t e orce exerteby static fluids on floating &immerse o ies y integrating t e
vertical component of the pressureorce over t e entire sur ace o
the body.
1/21/2010 BIOT 405 Fluid mechanics 6
8/4/2019 Lecture 05 Buoyancy
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Buoyancy
Ptop
l
1/21/2010 BIOT 405 Fluid mechanics 7
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Archimedes' Principle:
T e vertica component pressureforce integrated around entiresur ace o a oat or su merge
body is called buoyant force.
1/21/2010 BIOT 405 Fluid mechanics 8
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Archimedes' Principle:
But
1/21/2010 BIOT 405 Fluid mechanics 9
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Archimedes' Principle:
>>
1/21/2010 BIOT 405 Fluid mechanics 10
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Archimedes' Principle:
i.e., t e weig t o t e oatingbody is exactly equal to the weighto t e isp ace . T us, or oating
bodies Archimedes principle.
1/21/2010 BIOT 405 Fluid mechanics 11
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Archimedes' Principle:
T us or oating o ies Arc ime esprinciple is often stated that
A floating body displaces a volume of
fluid whose wei ht is exactl e ual toits own weight or
Buo ant orce is e ual to the wei htof the fluid displaced.
1/21/2010 BIOT 405 Fluid mechanics 12
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In e uations:buoyant forceb ,
Fb = mfluiddisplacedg.
u , mfluiddisplaced= en.fluid vo .object
mfluiddis laced=fluidVob ect.Thus, we get:
=
->
u o ec . Note: This only works if the object is
1/21/2010 BIOT 405 Fluid mechanics 13