Buoyancy des

8/3/2019 Buoyancy des

1/25

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)


2/25

Archimedes Principle Square bubble

of gas in a tank

of water

(courtesy F. Remer)


3/25

Archimedes Principle Water pressure

in tank increases

with depth

p = pressure

h = depth

ph

(courtesy F. Remer)


4/25

Archimedes Principle Horizontal Pressure

Differences Balance

(courtesy F. Remer)


5/25

Archimedes Principle Force on bottom of

bubble

Fbottom

pbottom !Fbottom

A

ApF bottombottom !


6/25

Archimedes Principle Force on top of

bubble

Fbottom

Ftop

A

Fp

top

top !

ApF toptop !

(courtesy F. Remer)


7/25


Buoyancy Force

Fbottom

Ftop

FB ! (pbottom ptop ) A

FB

FB

! Fbottom

Ftop

FB ! (pA

(courtesy F. Remer)

FB ! Apbottom Aptop


8/25


Pressure Difference

Between Top & Bottom

Negative by convention pbottom

ptop

h

(p

h! Vg

(p ! Vgh

(courtesy F. Remer)


9/25


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


10/25


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


11/25


Cartoon here??Archimedes

287 211 BC

At the moment of Archimedes famous discovery.


12/25

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


13/25

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.


14/25

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)


15/25


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.


16/25

Buoyancy Density Difference

Results in Net

Buoyancy Force

pVeVpe V"V

B

(courtesy F. Remer)


17/25

Buoyancy Density Difference

Results in Net

Buoyancy Force

pVeVpe VV

B

(courtesy F. Remer)


18/25

Buoyancy Net Buoyancy Force

pVeV

BgV)(B pe VV!

(courtesy F. Remer)


19/25

Archimedes Principle Water is in hydrostatic

equilibrium

= density

g = acceleration ofgravity

B

(p

(h! Vg

(p

(h

gV

(courtesy F. Remer)


20/25

Buoyancy How is air displaced?

Two methods

1.) Forced Ascent

2.) Auto-Convective Ascent

(courtesy F. Remer)


21/25

Forced Ascent Some mechanism forces air aloft

CoolAirCoolAir

Cold airCold airWarm airWarm air

(courtesy F. Remer)


22/25

Auto-Convective Ascent Air becomes buoyant

by contact with warm

ground

HotHotCoolCool CoolCool(courtesy F. Remer)


23/25

Buoyancy As Parcel Rises Parcel Temperature

Changes and it expands.

Unsaturated?

(courtesy F. Remer)


24/25

Stability As Parcel of Air Rises The Parcel Temperature

Changes and expands.

Saturated? Gaseous water condenses to rain

(courtesy F. Remer)


25/25

Buoyancy des

Documents

Transcript of Buoyancy des