how to calculate buoyancy

8/18/2019 How to Calculate Buoyancy

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http://www.wikihow.com/Calculate-Buoyancy

How to Calculate Buoyancy

Two Methods:Using the Buoyancy Force EquationPerforming a Simple BuoyancyExperimentuestions and !nswers

Buoyancy is the force acting opposite the direction of gra"ity that affects all

o#$ects su#merged in a fluid% &hen an o#$ect is placed in a fluid' the o#$ect(s

weight pushes down on the fluid )liquid or gas* while an upward #uoyancy force

pushes upward on the o#$ect' acting against gra"ity% +n general terms' this

#uoyancy force can #e calculated with the equation Fb = Vs × D × g' where F # is

the #uoyancy force' ,s is the su#merged "olume' - is the density of the fluid the

o#$ect is su#merged in' and g is the force of gra"ity% To learn how to determine an

o#$ect(s #uoyancy' see Step . #elow to get started%

Method 1

Using the Buoyancy Force Equation

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.%

.

Find the olu!e o" the sub!erged #ortion o" the ob$ect% The force of

#uoyancy that acts on an o#$ect is directly proportional to the "olume of the

o#$ect that is su#merged% +n other words' the more of a solid o#$ect that is

su#merged' the greater the force of #uoyancy that acts on it% This means that

e"en o#$ects that sin/ in liquid ha"e a #uoyancy force pushing upwards onthem% To #egin to calculate the #uoyancy force acting on an o#$ect' your first

step should generally #e to determine the "olume of the o#$ect that is

su#merged in fluid% For the #uoyancy force equation' this "alue should #e in

meters0%

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o For o#$ects that are completely su#merged in fluid' the su#merged

"olume will #e equal to the "olume of the o#$ect itself% For o#$ects

that are floating on the surface of a fluid' only the "olume under the

surface of the fluid is considered%

o !s an example' let(s say that we want to find the #uoyancy force

acting on a ru##er #all floating in water% +f the #all is a perfect sphere

with a diameter of . meter )0%0 ft* and it(s floating exactly halfway

su#merged in the water' we can find the "olume of the su#merged

portion #y finding the "olume of the entire #all and di"iding it in half%

Since the "olume of a sphere is )120*3)radius*0 ' we /now our #all(s

"olume is )120*3)4%5*0 6 4%571 meters0% 4%57127 6 &%'(' !eters)

sub!erged%

7%

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Find the "orce o" graity -or another downward "orce.% &hether an o#$ect

sin/s or floats in the fluid it(s su#merged in' it(s always su#$ect to the force

of gra"ity% +n the real world' this constant downward force is equal to a#out

/%01 ewtons,+ilogra!% owe"er' in situations in which another force' li/e

centrifugal force' is acting on the fluid and the o#$ect su#merged in it' thismust also #e ta/en into account to determine the total ;downward; force for

the entire system%

o +n our example' if we(re dealing with an ordinary' stationary system'

we can assume that the only downward force acting on the fluid and

o#$ect is the standard force of gra"ity < /%01 ewtons,+ilogra!%



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o owe"er' what if our #all was floating in a #uc/et of water #eing

swung at great speed in a hori=ontal circle> +n this case' assuming the

#uc/et is #eing swung fast enough to ensure that #oth the water and

the #all don(t fall out' the ;downward; force in this situation would #e

deri"ed from the centrifugal force created #y swinging the #uc/et' not

from the earth(s gra"ity%

1%

1

Multi#ly olu!e × density × graity% &hen you ha"e "alues for the

"olume of your o#$ect )in meters0*' the density of your fluid )in

/ilograms2meter 0*' and the force of gra"ity )or the downward force of your



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system*' finding the #uoyancy force is easy% Simply multiply these three

quantities to find the force of #uoyancy in newtons%

o ?et(s sol"e our example pro#lem #y plugging our "alues into the

equation F # 6 ,s @ - @ g% F # 6 4%7A7 meters0 @ .'444 /ilograms2meter 0

@ %C. newtons2/ilogram 6 '*23& ewtons%

5%

5

Find whether your ob$ect "loats by co!#aring with its graity "orce%

Using the #uoyancy force equation' it(s easy to find the force that(s pushing

an o#$ect up out of the fluid it(s su#merged in% owe"er' with a little extra

wor/' it(s also possi#le to determine whether the o#$ect will float or sin/%

Simply find the #uoyancy force for the entire o#$ect )in other words' use its



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entire "olume as ,s*' then find the force of gra"ity pushing it down with the

equation 8 6 )mass of o#$ect*)%C. meters2second7*% +f the force of #uoyancy

is greater than the force of gra"ity' the o#$ect will float% 9n the other hand' if

the force of gra"ity is greater' it will sin/% +f they are equal' the o#$ect is said

to #e neutrally buoyant %

o For example' let(s say we want to /now if a 74 /ilogram cylindrical

wooden #arrel with a diameter of %D5 meters )7%5 ft* and a height of

.%75 meters )1%. ft* will float in water% This will ta/e se"eral steps:

&e can find its "olume with the cylindrical "olume formula , 6

3)radius*7)height*% , 6 3)%0D5*7).%75* 6 &%22 !eters)%

ext' assuming ordinary gra"ity and water with ordinary

density' we can sol"e for the force of #uoyancy on the #arrel%

4%55 meters0 @ .444 /ilograms2meter 0 @ %C. newtons2/ilogram

6 2*)/2%2 ewtons%

ow' we(ll need to find the force of gra"ity on the #arrel% 8 6

)74 /g*)%C. meters2second7* 6 1/(%' ewtons% This is much

less than the #uoyancy force' so the #arrel will float%


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A%

A

Use the sa!e a##roach when your "luid is a gas% &hen performing

#uoyancy pro#lems' don(t forget that the fluid that the o#$ect is su#merged in

doesn(t necessarily ha"e to #e a liquid% 8ases also count as fluids' and'

although they ha"e "ery low densities compared to other types of matter' can

still support the weight of certain o#$ects floating in them% ! simple helium #alloon is e"idence of this% Because the gas in the #alloon is less dense than

the fluid around it )ordinary air*' it floats

Method '

4er"or!ing a 5i!#le Buoyancy E6#eri!ent



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4lace a s!all bowl or cu# inside a bigger one% &ith a few household

items' it(s easy to see the principals of #uoyancy in action +n this simple

experiment' we(ll demonstrate that a su#merged o#$ect experiences

#uoyancy #ecause it displaces a "olume of fluid equal to the "olume of the

o#$ect su#merged% !s we do this' we(ll also demonstrate how to practicallyfind an o#$ect(s #uoyancy force with this experiment% To #egin' place a small

open container' li/e a #owl or a cup' inside a larger container' li/e large #owl

or a #uc/et%



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7%

7

Fill the inner container to the bri!% ext' fill the small inner container

with water% Gou want the water le"el to #e at the "ery top of the container

without spilling% Be careful here +f you spill any water' empty the larger

container #efore trying again%

o For the purposes of this experiment' it(s safe to assume that water has

a standard density of .444 /ilograms2meter 0% Unless you(re using

saltwater or a different liquid entirely' most types of water will ha"e a

density close enough to this reference "alue that any minor difference

won(t alter our results%



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o +f you ha"e an eyedropper handy' this can #e "ery helpful for

precisely le"eling off the water in the inner container%

0%

0

5ub!erge a s!all ob$ect% ext' find a small o#$ect that can fit inside the

inner container and won(t #e damaged #y water% Find this o#$ect(s mass in/ilograms )you may want to use a scale or #alance which can gi"e you

grams and con"ert up to /ilograms*% Then' without letting your fingers get

wet' slowly and steadily dip this into the water until it starts to float or you

can $ust #arely hold on to it' then let go% Gou should notice some of the water

in the inner container spill o"er the edge into the outer container%



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o For the purposes of our example' let(s say that we(re lowering a toy car

with a mass of 4%45 /ilograms into the inner container% &e don(t need

to /now the "olume of this car to calculate its #uoyancy' as we(ll see

in the next step%

1%

1

Collect and !easure the water that s#ills oer% &hen you su#merge ano#$ect in water' it displaces some of the water < if it didn(t' there wouldn(t

#e any space for it to enter the water% &hen it pushes this water out of the

way' the water pushes #ac/' resulting in #uoyancy% Ta/e the water that

spilled out of the inner container and pour it into a small glass measuring

cup%The "olume of water in the cup should #e equal to "olume of the

su#merged o#$ect%



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o +n other words' if your o#$ect floats' the "olume of the water that

spills o"er will #e equal to the "olume of the o#$ect su#merged under

the surface of the water% +f your o#$ect san/' the "olume of the water

that spills o"er will #e equal to the "olume of the entire o#$ect%

5%

5

Calculate the weight o" the s#illed water% Since you /now the density ofwater and you can measure the "olume of the water that spilled into the

measuring cup' you can find its mass% Simply con"ert its "olume to meters0

)an online con"ersion tool' such as this one' can #e helpful here* and

multiply it #y the density of water ).'444 /ilograms2meters0*%

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o +n our example' let( say that our toy car sun/ into the inner container

and displaced a#out two ta#lespoons )%44440 meters0*% To find the

mass of our water' we(d multiply this #y its density: .'444

/ilograms2meters0 @ %44440 meters0 6 &%&) +ilogra!s%

A%

A

Co!#are the dis#laced water7s !ass to the ob$ect7s% ow that you /nowthe mass of #oth the o#$ect you su#merged in water and the mass of the

water it displaced' compare them to see which is greater% +f the mass of the

o#$ect su#merged in the inner container is greater than that of the displaced

water' it should ha"e sun/% 9n the other hand' if the mass of the displaced

water is greater' the o#$ect should ha"e floated% This is the principle of



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#uoyancy in action < for an o#$ect to #e #uoyant )float*' it has to displace

an amount of water with a mass greater than that of the o#$ect itself%

o Thus' o#$ects with low masses #ut #ig "olumes are the most #uoyant

types of o#$ects% This property means hollow o#$ects are especially

#uoyant% Thin/ of a canoe < it floats well #ecause it(s hollow in the

inside' so it(s a#le to displace a lot of water without ha"ing a "ery high

mass% +f canoes were solid' they wouldn(t float "ery well at all%

o +n our example' the car has a higher mass )4%45 /ilograms* than the

water it displaced )4%40 /ilograms*% This lines up with what we

o#ser"ed: the car san/%

8eader 9uestions and :nswers

Unanswered uestions• ow do + determine the #uoyancy force of a rectangular pontoon floating in

water of D4 mm depth' that weighs 7%A /g' has a length of 0A4 mm'and a

#readth of 74A mm>

!nswer this question Flag for remo"al

Show more unanswered questions

!s/ a uestion

Su#mit

Video

;i#s

• Use a scale or #alance that can #e set to =ero after each reading to help get

accurate measurements%

;hings


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•

Small su#mersi#le o#$ect )li/e a ru##er #all*

•

Measuring cup

8elated wi+iHows

ow to

-emonstrate Hharles(s ?aw

ow toHalculate orsepower

ow to

Halculate &a"elength

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ow to

Halculate eat Hapacity

5ources and Citations

• http:22www%howstuffwor/s%com2#uoyancyIinfo%htm

• http:22www%howstuffwor/s%com2scienceI"sImyth2e"erydayImyths2.4IscientificIlawsItheoriesD%htm

• http:22www%howstuffwor/s%com2outdoorIacti"ities2waterI

sports2sail#oat7%htm

Show more%%% )5*

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