Download - Fluids at Rest and in Motion
-
7/23/2019 Fluids at Rest and in Motion
1/15
FLUIDS AT REST AND IN
MOTION
-
7/23/2019 Fluids at Rest and in Motion
2/15
covered b a! elastic s"i!# The surface thusa$$ears to be u!der so%e force or te!sio!
The te!sio! force acti!& $arallel to thesurface of the liquid is "!ow! as surfacete!sio!
This arises due to the stro!& i!ter%olecular
forces holdi!& the liquid %olecules at thesurface toðer
-
7/23/2019 Fluids at Rest and in Motion
3/15
The co'e(cie!t of surface te!sio! T is de)!ed as the
force i! Newto! acti!& o! a %etre le!&th draw! o! thesurface# %athe%aticall*
T + F,L
The surface te!sio! T* is de)!ed as the ratio of the
ta!&e!tial force F* i! the surface to the le!&th d alo!&which the force acts# Mathe%aticall*
T + F,d
Surface te!sio! is a force $er u!it le!&th so its u!it is
N,%
-
7/23/2019 Fluids at Rest and in Motion
4/15
A--LI.ATIONS OF T/E EFFE.TS OF SURFA.E TENSION
Soa$s a!d deter&e!ts lower the surface te!sio! of water# This is
desirable for clea!i!& $ur$oses because the hi&h surface te!sio! of$ure water $reve!ts it fro% easil e!teri!& betwee! the )bre of%aterials# 0ith a lowered surface te!sio!* the water ca! wash awathe dirt $articles# Also* hi&h te%$eratures decrease the surfacete!sio! of water thus %a"i!& it %ore e1ective to use hot water forclea!i!& $ur$oses
The %aterial used to %a"e u%brellas* rai!coats a!d other water'$roof ob2ects te!d to tra$ a thi! )l% of water betwee! its )bres#Due to the surface te!sio!* the tra$$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 $roof b coati!& it with oil'
based substa!ces#
-
7/23/2019 Fluids at Rest and in Motion
5/15
AD/ESION AND .O/ESION The force of attractio! betwee!
%olecules of the sa%e substa!ce iscalled cohesio!
The force of attractio! betwee!%olecules of di1ere!t substa!ces iscalled adhesio!
Adhesio! of water to &lass isstro!&er tha! the cohesio! of water#/e!ce whe! water is s$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$laced i! &lass vessels* the water isco!cave to air while %ercur isco!cave to the liquid
-
7/23/2019 Fluids at Rest and in Motion
6/15
.A-ILLARIT4
.a$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
-
7/23/2019 Fluids at Rest and in Motion
7/15
.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!
-
7/23/2019 Fluids at Rest and in Motion
8/15
.ONTA.T AN
-
7/23/2019 Fluids at Rest and in Motion
9/15
8IS.OSIT4
The !a%e &ive! to thei!ter!al frictio! that e5ists
betwee! laers of a liquid or&as i! %otio!
The o$$osi!& force is "!ow!as dra&
I! liquids* the viscosit is
due to the cohesive forcesbetwee! liquid %olecules
I! &ases* it is due to thecollisio! betwee! %olecules
8iscosit i!creases withi!creasi!& te%$erature for&ases a!d decreases withi!creasi!& te%$erature forliquids
-
7/23/2019 Fluids at Rest and in Motion
10/15
TERMINAL 8ELO.IT4
0he! a sto!e falls throu&ha colu%! of 3uid* it is
sub2ected to three forces=wei&ht* dra& a!d u$thrust
The wei&ht a!d u$thrustdo !ot cha!&e duri!& thedesce!t but the dra& force
i!creases with i!creasi!&velocit* resulti!& i! as%aller resulta!t force
0he! the dra& force a!dthe u$thrust bala!ce the
wei&ht of the sto!e* thereis !o resulta!t force*he!ce !o acceleratio! a!dthe sto!e travels atco!sta!t ter%i!al velocit
-
7/23/2019 Fluids at Rest and in Motion
11/15
Mathe%aticall*
FR+ 0'D'U
0here FR+ resulta!t force + %a
0 is the wei&ht of the sto!e
D is the dra& force due toviscosit
U is the u$thrust
The reaso! the ter%i!al s$eedis reached is because theviscous force 8 is $ro$ortio!alto the ter%i!al velocit
8 + "v
0he! ter%i!al velocit is
reached* a + >Thus 0'D'U + >
D+ 0'U
D + %&'U
-
7/23/2019 Fluids at Rest and in Motion
12/15
E5ercise
A s$herical sto!e of %ass ?>>& is
released fro% the to$ of a tall buildi!Several seco!ds after the sto!e isdro$$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
-
7/23/2019 Fluids at Rest and in Motion
13/15
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
-
7/23/2019 Fluids at Rest and in Motion
14/15
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
-
7/23/2019 Fluids at Rest and in Motion
15/15