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FLUIDS AT REST AND IN

MOTION

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covered b a! elastic s"i!# The surface thusa$$ears to be u!der so%e force or te!sio!

The te!sio! force acti!& $arallel to thesurface of the liquid is "!ow! as surfacete!sio!

This arises due to the stro!& i!ter%olecular

forces holdi!& the liquid %olecules at thesurface to&ether

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The co'e(cie!t of surface te!sio! T is de)!ed as the

force i! Newto! acti!& o! a %etre le!&th draw! o! thesurface# %athe%aticall*

T + F,L

The surface te!sio! T* is de)!ed as the ratio of the

ta!&e!tial force F* i! the surface to the le!&th d alo!&which the force acts# Mathe%aticall*

T + F,d

Surface te!sio! is a force $er u!it le!&th so its u!it is

N,%

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A--LI.ATIONS OF T/E EFFE.TS OF SURFA.E TENSION

Soa$s a!d deter&e!ts lower the surface te!sio! of water# This is

desirable for clea!i!& $ur$oses because the hi&h surface te!sio! of$ure water $reve!ts it fro% easil e!teri!& betwee! the )bre of%aterials# 0ith a lowered surface te!sio!* the water ca! wash awathe dirt $articles# Also* hi&h te%$eratures decrease the surfacete!sio! of water thus %a"i!& it %ore e1ective to use hot water forclea!i!& $ur$oses

The %aterial used to %a"e u%brellas* rai!coats a!d other water'$roof ob2ects te!d to tra$ a thi! )l% of water betwee! its )bres#Due to the surface te!sio!* the tra$$ed water %olecules for% a!elastic s"i! a!d $reve!t further see$a&e of water throu&h the )bres#Ofte!* the %aterial is %ade %ore water $roof b coati!& it with oil'

based substa!ces#

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AD/ESION AND .O/ESION The force of attractio! betwee!

%olecules of the sa%e substa!ce iscalled cohesio!

The force of attractio! betwee!%olecules of di1ere!t substa!ces iscalled adhesio!

Adhesio! of water to &lass isstro!&er tha! the cohesio! of water#/e!ce whe! water is s$illed o! aclea! &lass surface* it wets it# I!co!trast* the cohesio! of %ercur is&reater tha! its adhesio! to &lass#

Thus* whe! %ercur is s$illed o!&lass* it for%s s%all s$herical

dro$lets or lar&e 3atte!ed dro$s a!ddoes !ot wet &lass# For the sa%ereaso!* whe! these liquids are$laced i! &lass vessels* the water isco!cave to air while %ercur isco!cave to the liquid

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.A-ILLARIT4

.a$illarit is res$o!sible forthe rise of liquids i! a!arrrow &lass tube whe!

$laced i! a co!tai!er# .a$illarit is de)!ed as the

te!de!c of liquids to rise orfall i! !arrow ca$illar tubes

So%e co%%o! e5a%$les

i!clude6I# 0ater risi!& u$ the ste% of

a $la!t

II# I!" held o! the !ib of a $e!

III# 7lood s$readi!& throu&h

the )!e ca$illar cha!!elsof the bod

I8# Liquid ca!dle wa5 risi!& u$the wic" of a ca!dle

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.O'EFFI.IENT OF SURFA.E TENSION AND ITS DETERMINATION

The co'e(cie!t of surface te!sio!is the force o! a %etre le!&th ofli!e draw! o! the surface

If water rises i! a ca$illar tube ofradius r to a hei&ht h* the wei&ht ofthe water i! equilibriu% as a resultof surface te!sio! is %&

This will bala!ce the surfacete!sio! force 9:rT

9:rT + %&

7ut ; + %ass,volu%e + de!sit

% + ;v

v + volu%e of cli!der + :r9h

%& + ;&v + :r9h;&

9:rT + :r9h;&

T + rh;&,9

The co'e(cie!t of surface te!sio! isthus calculated if de!sit* hei&hta!d radius are "!ow!

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.ONTA.T AN

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8IS.OSIT4

The !a%e &ive! to thei!ter!al frictio! that e5ists

betwee! laers of a liquid or&as i! %otio!

The o$$osi!& force is "!ow!as dra&

I! liquids* the viscosit is

due to the cohesive forcesbetwee! liquid %olecules

I! &ases* it is due to thecollisio! betwee! %olecules

8iscosit i!creases withi!creasi!& te%$erature for&ases a!d decreases withi!creasi!& te%$erature forliquids

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TERMINAL 8ELO.IT4

0he! a sto!e falls throu&ha colu%! of 3uid* it is

sub2ected to three forces=wei&ht* dra& a!d u$thrust

The wei&ht a!d u$thrustdo !ot cha!&e duri!& thedesce!t but the dra& force

i!creases with i!creasi!&velocit* resulti!& i! as%aller resulta!t force

0he! the dra& force a!dthe u$thrust bala!ce the

wei&ht of the sto!e* thereis !o resulta!t force*he!ce !o acceleratio! a!dthe sto!e travels atco!sta!t ter%i!al velocit

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Mathe%aticall*

FR+ 0'D'U

0here FR+ resulta!t force + %a

0 is the wei&ht of the sto!e

D is the dra& force due toviscosit

U is the u$thrust

The reaso! the ter%i!al s$eedis reached is because theviscous force 8 is $ro$ortio!alto the ter%i!al velocit

8 + "v

0he! ter%i!al velocit is

reached* a + >Thus 0'D'U + >

D+ 0'U

D + %&'U

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E5ercise

A s$herical sto!e of %ass ?>>& is

released fro% the to$ of a tall buildi!Several seco!ds after the sto!e isdro$$ed* it achieves a ter%i!al s$eedof 9@%,s# a!other sto!e of equal

di%e!sio!s but twice the %ass isdro$$ed fro% the tall buildi!.alculate the ter%i!al velocit reached

b the sto!e# Assu%e the dra& forcedue to viscosit of air is $ro$ortio!al tothe velocit

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SOLUTIONIst sto!e

0ei&ht of sto!e + %& + >#?B#C + >#BCN

At ter%i!al velocit* the forces acti!& o! the sto!eare bala!ce

0 + D

D + "v

+ D,v + >#BC,9@ + >#>B9 Ns,%

9!d sto!e

0ei&ht of sto!e + %& + 9>#?GB#CG + ?#BH9NAt ter%i!al velocit 0 + D + ?#BHN

D + "v

v + D," + ?#BH,>#>B9 + @>%,s

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A--LI.ATIONS OF 8IS.OSIT4

Liquids with hi&h viscosit are usedas lubrica!ts i! the i!dustr

A $arachute uses the dra& forcee5erted b the air o! a free falli!&$erso! to slow dow! his desce!t a!dcushio! his fall

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