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BUOYANCY AND STABILITY

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BUOYANCYDEFINITION

Itis an upward force exerted by a fluid that

opposes the weight of an immersed object. In a

column of fluid pressure increases with depth as a

result of the weight of the o!erlying fluid.

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Buoyant Force

" The force remains evenwithout the origina !ui"#

" It must $aance theweight that wou" have$een there#

" This is the buoyantforce#

# %&uas the fuidweight

# Directe" u'war"

# Acts on the voume

Fb = mg

VgFbuoy =

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Sin(ing an" )ising

" An o$*ect in a !ui""is'aces a voume thatha" some mass#

" If the o$*ect is heavierthan the !ui" it sin(s#

" If the o$*ect is ighter itrises#

Fb = Vg

W= mg

Fb = Vg

W= mg

mmgVgamgVgFnet

/)( =

=

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Archime"es+ ,rinci'e

" An o$*ect sus'en"e" in a !ui" hasess a''arent weight "ue to$uoyancy#

Fb = Vg

W= mg

FT = mg -

Vg

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Ice$erg

" An ice$erg has an average"ensity of -./ ofseawater#

" 0hat fraction of theice$erg is un"erwater1

The $uoyant force is theweight of water "is'ace"$y the ice$erg2 Fb3

waterVsubg#

The weight is the totaweight of the ice2 Wi3

iceViceg#

Fin" the ratio of Vsub/Vice 0e (now the ratio ice4water

waterVsubg = iceViceg

Vsub/Vice3 ice4water3 5#-.

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Center of Buoyancy

" The force of $uoyancy acts at thecenter of mass of the missing !ui"#

" The "is'acing o$*ect has a center ofgravity at its center of mass#

" The two forces may not act at thesame 'oint#

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Ti''y Canoe

" If a forces on an o$*ectact at "i6erent 'ointsthere is a tor&ue#

" Buoyant force a$ove thecenter of mass is sta$e#

# The tor&ue moves it$ac( to the center

" Buoyant force $eow thecenter of mass isunsta$e#

# The tor&ue moves itaway from the center

ne7t

http://var/www/apps/conversion/tmp/scratch_7/p210_09c.ppthttp://var/www/apps/conversion/tmp/scratch_7/p210_09c.ppt

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STABILITY

" A !oating o$*ect is sta$e if it ten"sto restore itsef to an e&uii$rium'osition after a sma "is'acement#

For e7am'e8 !oating o$*ects wigeneray have vertica sta$iity8 as ifthe o$*ect is 'ushe" "own sighty8

this wi create a greater $uoyancyforce8 which8 un$aance" $y theweight force8 wi 'ush the o$*ect

$ac( u'

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Stability o Immersed and Floating

Bodies9Centers of $uoyancy an" gravity "o not coinci"e9 A sma rotation can resut in either a restoring or

overturning cou'e#

9 Sta$iity is im'ortant for !oating $o"ies

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Stability o an immersed body

Sta$iity of acom'etey

immerse" $o"y :center

of gravity $eowentroi"#

Sta$iity of a com'eteyimmerse" $o"y : centerof gravity a$ovecentroi"#

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Stability o a foating body

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%CONO;IC ,I,% DIA;%T%)

The "iameter of the 'i'e strongyin!uences the 'resent vaue of the'ant8 through $oth the annua cost of

eectric 'ower an" the instaation costof the 'i'ing system

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%conomic 'i'e seection metho"

" Intro"uction

" The economic 'i'e seection metho" is use to$aance >7e" cost of 'i'e with annua energy

cost for 'um'ing" 0ith arge 'i'e si?es8 the average !ow veocityfor a given "ischarge "ecreases8 causing acorres'on"ing "ecrease in friction oss

" This re"uces the hea" on the 'um' an" energycan $e save"

" @owever8 arger 'i'es are e7'ensive

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" To $aance these costs an" to >n" theminimum cost8 we wi annuaise the

>7e" costs8 com'are" with annuaenergy costs#

" 0e wi ta(e into account interestrates an" in!ation rates to ma(e thecom'arison

" This is $asicay an engineeringeconomics 'ro$em s'eciay a"a'te"to ma(e the seection of 'i'e si?es

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,rinci'e ste's

" Determine the e&uivaent annuacost for 'urchasing each avaia$e'i'e si?e

" Determine the annua energy cost of'um'ing

" Baance the annua cost for a"*acent

'i'e si?e

" Construct a gra'h of system !owrate v4s section !ow rate

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,i'e si?e vs cost