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Properties of Matter

Regular Properties of Matter Worksheets and Solutions

PR1B: Pressure 3

PR1T: Pressure 7

PR2B: Buoyancy 11

PR2T: Buoyancy 15

PR3B: Fluid Flow 1 19

PR3T: Fluid Flow 1 23

PR4B: Fluid Flow 2 27

PR4T: Fluid Flow 2 31

PR5B: Surface Tension 35

PR5T: Surface Tension 39

PR6B: Solids I S!ress" S!rain and #las!ici!y 43

PR6T: Solids I S!ress" S!rain and #las!ici!y 47

PR7: Solids II $rys!als and Bondin% 51

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&or's(o) Tu!orials for Biolo%ical and #n*iron+en!al P(ysics

PR1B: Pressure

A. Qualitative Questions:

1. T(e dia%ra+ s(ows a reser*oir wall,a. &(y is !(e wall !(ic'er a! !(e -o!!o+ !(an a! !(e !o).b. Two reser*oirs of !(e sa+e de)!( are !o -e /oined !ofor+ a sin%le +uc( lar%er reser*oir, Is i! necessary !oreinforce !(e da+ wall.

2. 0ou are a-ou! !o se! ou! on a scu-a di*in% !ri)" and are (a*in% a +edical c(ec', T(e doc!or +easuresyour -lood )ressure !o -e a (eal!(y12 ++ %, T(e 12 ++ % is !(e +a i+u+ )ressure a! !(e )ea' of eac( )ulse" called !(e sys!ole" and !(e ++ % is !(e lowes! )ressure -e!ween )ulses" called !(e dias!ole,a. i*en !(a! nor+al a!+os)(eric )ressure is around 76 ++ %" w(y does -lood s)ur! fro+ a dee) cu!.

0ou c(ec' !(e wea!(er re)or!" and i! s %oin% !o -e a fine wee'end" wi!( a (i%( )ressure fron! of 1 2 'Pa -rin%in% war+ wea!(er, 0ou )ac' u) and (ead off, 0ou c(ec' your !yre )ressure w(en you fill u) wi!( )e!rol" and infla!e !(e+ !o 25 )si 817,2 'Pa ,b. &(ic( of !(e )ressures %i*en a-o*e are a-solu!e and w(ic( are %au%e )ressures.0ou arri*e a! !(e di*in% class and are issued wi!( ins!ruc!ions and e ui)+en!,c. &(y does !(e di*in% ins!ruc!or !ell you no! !o (old your -rea!( w(en surfacin%.d. &(y are you issued wi!( lead -el!s and infla!a-le )ac'e!s.

. Activit! Questions:1. Suction cups and Magdeburg plates

ow can you +a'e !(e suc!ion cu) s!ic' !o a surface.

# )lain w(a! (a))ens w(en i! s!ic's and w(en i! fails !o s!ic',&(en are !(e ;a%de-ur% )la!es (ard !o )ull a)ar!.&(en are !(e ;a%de-ur% )la!es easy !o )ull a)ar!. # )lain w(y,

2. "!drostatic parado#&a!er is )oured !o !(e sa+e le*el in eac( of !(e *essels s(own -elow" all (a*in% !(e sa+e -ase area, If !(e

)ressure is !(e sa+e a! !(e -o!!o+ of eac( *essel" !(e force e )erienced -y !(e -ase of eac( *essel is !(esa+e, &(y do !(e *essels (a*e differen! wei%(!s w(en )u! on a scale. T(is a))aren!ly con!radic!ory resul!is co++only 'nown as !(e (ydros!a!ic )arado , ou! of !(e (oles, &(a! can you say a-ou! !(e direc!ion of !(e wa!er /us!as i! lea*es !(e (oles.Pus( a drin'in% s!raw in!o !(e wa!er and !(en )u! your fin%er o*er !(e !o), ?if! !(e s!raw ou! of !(ewa!er, &(a! (a))ens. &(y.

&. "ollo' tube and disc

ollow !u-e and dis': &(y does !(e dis' fall away in air -u! s!ay a!!ac(ed !o !(e !u-e w(en !(ere is air in!(e !u-e and wa!er ou!side !(e !u-e.

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(. )he lungs&(a! (a))ens !o !(e )ressure surroundin% !(e lun%s w(en you )ull !(e dia)(ra%+ down.&(a! (a))ens !o !(e lun%s 8-alloons . # )lain w(y !(ey -e(a*e as !(ey do,

*. Quantitative Questions:

1. In a si+)le %eolo%ical +odel" !(e )ressure a! so+e (ori@on!al le*el far -elow !(e ear!( s surface"re%ardless of w(a! is a-o*e" is !(e sa+e o*er a lar%e re%ion, T(e )ressure is e ual !o !(a! e er!ed -y !(eo*erlyin% +a!erialA +oun!ains" la'es" *alleys" e!c, T(is le*el a! w(ic( !(e )ressure is e ual is called !(elevel of compensation. T(is +odel re uires !(a! +oun!ains (a*e roo!s" so !(a! !(e )ressure a! so+e )oin!

-elow !(e+ will -e e ual !o !(a! -elow surroundin% )lains and *alleys,T(e densi!y of !(e roc's w(ic( +a'e u) con!inen!s" includin% !(e +oun!ains" is 2,9 %,c+ 3" !(e densi!y of !(e +an!le is 3,3 %+,c+ 3, T(e +ean de)!( of !(e con!inen!al )la!e is around 3 '+,a. ;oun! Coscius@'o" Dus!ralia s !alles! +oun!ain" is 222 + !all, ow dee) are Coscius@'o s roo!s.b. &(a! would (a))en if !(e )ressure was no! !(e sa+e a! all )oin!s a! !(e le*el of co+)ensa!ion.c. Eoes i! +a!!er w(a! (ei%(! you c(oose !(e co+)ensa!ion le*el !o -e. Eoes i! ac!ually (a*e a )(ysicalde)!(.

2. T(e firs! recorded +easure+en! of -lood )ressure was in 1733 -y !(e Re*, S!e)(en ales, e

connec!ed a 9 foo! *er!ical %lass !u-e !o an ar!ery of a (orse usin% !(e !rac(ea of a %oose as a fle i-leconnec!ion, T(e -lood rose in !(e !u-e !o a (ei%(! of fee! 82,4 +a. Eurin% a -lood !ransfusion !(e needle is inser!ed in!o a *ein w(ere !(e )ressure is 1 Pa, T(e densi!yof -lood is 1 6 '%,+ 3, &(a! is !(e +ini+u+ (ei%(! !(e !ransfusion -a% needs !o -e raised !o for asuccessful !ransfusion.b. &(a! would (a))en if !(e -a% was lower !(an !(is.c. If a %iraffe is 5+ !all" wi!( (is (ear! a!a))ro i+a!ely (alf !(a! (ei%(!" w(a! )ressure does!(e (ear! need !o )roduce !o 'ee) !(e -rain su))liedwi!( o y%en.d. ow does !(e -lood )ressure in (is (ead

c(an%e w(en (e di)s (is (ead !o drin'.e. &(y do %iraffes s)read !(eir fron! le%s !o drin' 8a)ar! fro+ +a'in% i! easier !o reac( !(e wa!er .&(a! would (a))en if !(ey didn !.

4

?e*el of co+)ensa!ion

y

+oun!ain

Ee)!( ofroo!

3 '+con!inen!

roo!+an!le

2,2'+

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Solu!ions !o PR1B: Pressure


1. Pressure and de)!(,a. Pressure increases wi!( de)!( as P= ρ gh , Pressure G 8force area so !(e wall needs !o wi!(s!and%rea!er force a! !(e -o!!o+" (ence i! is -uil! !o -e !(ic'er a! !(e -o!!o+,b. $(an%in% !(e surface area does no! c(an%e !(e )ressure -ecause i! does no! c(an%e !(e de)!(" (ence!(ere is no need !o fur!(er reinforce !(e wall,

2. D-solu!e and %au%e )ressures,a. Blood )ressure is a +easure of )ressure a-o*e a!+os)(eric" i! is a rela!i*e or gauge )ressure,b. D!+os)(eric )ressure is !(e only a-solu!e )ressure %i*en (ere" -o!( -lood )ressure and !yre )ressureare %au%e )ressures" i,e, )ressure a-o*e a!+os)(eric,c. 0ou are !old no! !o (old your -rea!( w(en surfacin% -ecause as yourise !(e e !ernal )ressure fro+ !(e wa!er decreases, T(e air in your lun%s e er!s a )ressure ou!wards on your lun%s" w(ile !(e wa!er ou!side you e er!s an inward )ressure, Ds you rise and !(e wa!er

)ressure decreases" !(e air in your lun%s e )ands, If !(ere is !oo +uc(air )us(in% ou!wards" and no! enou%( )ressure ou!side" !(ey couldru)!ured. T(e lead -el!s and infla!a-le )ac'e!s are !o ad/us! your -uoyancyAlead !o +a'e you +ore dense" allowin% you !o sin'" infla!a-le )ac'e!s!o +a'e you less dense" allowin% you !o floa!,

. Activit! Questions:

+. Suction cups and Magdeburg platesT(e ;a%de-ur% )la!es are (ard !o )ull a)ar! w(en !(ere is a *acuu+ -e!ween !(e+" -u! easy !o )ull a)ar!w(en !(ere is air, D fluid e er!s a force )er)endicular !o a surface i! co+es in con!ac! wi!(: F=PA , If !(ereis a difference in )ressure across a surface !(is resul!s in a ne! force w(ic( is direc!ed fro+ !(e re%ion of %rea!er !o lower )ressure, In !(e case of !(e ;a%de-ur% )la!es" w(en air is re+o*ed fro+ !(e re%ion

-e!ween !(e )la!es !(e )ressure -e!ween !(e )la!es is less !(an !(e a!+os)(eric )ressure ou!side !(e )la!es,T(is difference in )ressure resul!s in a ne! force inwards" (oldin% !(e )la!es !o%e!(er,T(e suc!ion cu) +us! (a*e !(e air s uee@ed ou! of i! and +a'e a co+)le!e seal wi!( !(e surface !o s!ic' !oi!, If !(e seal isn ! co+)le!e" air can en!er !(e cu)" re+o*in% !(e )ressure difference and allowin% !(e cu)!o fall off,

,. "!drostatic parado#T(e con!ainers (a*e differen! +asses 8-ecause !(ey con!ain differen! a+oun!s of wa!er " so !(ey +us!(a*e differen! wei%(!s, Dno!(er ar%u+en! %oes as follows: !(e )ressure is !(e sa+e a! !(e -o!!o+ of eac(con!ainer 8-ecause !(ey are filled !o !(e sa+e (ei%(! , Bu! !(ey all (a*e !(e sa+e -ase area" so !(e forcee )erienced -y !(e -ase of eac( con!ainer is !(e sa+e, T(erefore" !(ey s(ould all %i*e !(e sa+e readin%on !(e scale, T(is second ar%u+en! is wron% -ecause we (a*e only considered !(e force of !(e wa!er on!(e -ase of !(e con!ainers, &(en calcula!in% !(e force of !(e wa!er on !(e con!ainer" we +us! include !(eforces on !(e sides" w(ic( +ay (a*e a co+)onen! in !(e *er!ical direc!ion,

-. S%uirting

T(e wa!er will co+e ou! )er)endicular !o !(e con!ainer wall" as !(is is !(e direc!ion of !(e ne! force,In eac( of !(ese ac!i*i!ies !(e li uid is (eld in -y !(e low )ressure in !(e !u-e or -o!!le" w(en !(is )ressureis increased !o a!+os)(eric )ressure" -y o)enin% !(e lid or re+o*in% !(e fin%er" !(e wa!er will co+e ou!,

5

Eee) wa!er" P

water =P

lung S(allow wa!er" P

water

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. "ollo' tube and discT(e disc s!ays a!!ac(ed w(en !(ere is a )ressure difference e er!in% a force w(ic( (olds i! in )lace, &(en!(e )ressure difference decreases suc( !(a! !(e force falls -elow mg of !(e disc" !(e disc falls,

1/. )he lungs&(en you )ull !(e dia)(ra%+ on !(e -o!!o+ of !(e -o!!le !(e *olu+e of !(e -o!!le increases, T(is lowers

!(e )ressure in !(e -o!!le, Inside !(e -alloons i! is a))ro i+a!ely a!+os)(eric )ressure" w(ile ou!side isnow lower, T(e -alloons infla!e due !o !(e )ressure difference" !(eir *olu+e increases" lowerin% !(eir in!ernal )ressure and drawin% air in!o !(e+, T(is is (ow we -rea!(e increasin% !(e *olu+e of our c(es!ca*i!y !o lower !(e )ressure in our lun%s and draw air in


1. T(e densi!y of !(e roc's w(ic( +a'e u) !(e con!inen! 8includin% !(e +oun!ain is ρ c G 2,9 %,c+ 3" and!(e con!inen! is 3 '+ dee)" wi!( a 2,2 '+ (i%( +oun!ain on !o)" w(ic( (as a roo! of de)!( d , T(e densi!yof !(e +an!le is ρ + G 3,3 %+,c+ 3, T(e )ressure is !o -e e ual a! !(e co+)ensa!ion le*el" so c(oose !wo

)oin!s" one -elow !(e +oun!ain" one no!" la-elled p and q, D! eac( )oin! !(e )ressure is e ual !o ρ gh of !(e+a!erial a-o*e, See !(e fi%ure -elow,a. Se! !(e )ressures a! !(e !wo )oin!s e ual: P p G 8 y d , ρ + , g H 8d H 2,2 H 3 , ρ c, g G P q G y, ρ + , g H 3 , ρ c, g

y. ρ m.g d , ρ m.g Hd , ρ c, g H 32,2, ρ c, g G y. ρ + , g H 3 , ρ c, g sol*e for de)!(" d :d. ρ + d , ρ c G 2,2, ρ c,d G 2,2, ρ c 8 ρ + ρ cd G 2,2 × 2,9 83,3 2,9 G 16 '+,

b. If !(e )ressure were no! !(e sa+e a! all )oin!s alon% !(is le*el" !(ere would -e a +o*e+en! of !(e +an!lefro+ areas of (i%( )ressure !o areas of low )ressure and +oun!ains would rise and fall" and !(e con!inen!swould +o*e" w(ic( in fac! does slowly (a))en,c. I! doesn ! +a!!er w(a! de)!( you !a'e as !(e de)!( of co+)ensa!ion" as lon% as i! is -elow !(e de)!( of !(e roo!,

2. Blood )ressures,a. 0ou need a )ressure %rea!er !(an 1 Pa, T(e densi!y of -lood is 1 6 '%,+ 3,

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&or's(o) Tu!orials for Tec(nolo%ical and D))lied P(ysics

PR1T: Pressure


1. Eraw a dia%ra+ and e )lain (ow eac( of !(e followin% con!ri-u!e !o a!+os)(eric )ressure:a. !(e wei%(! of !(e air in !(e a!+os)(ereb. !(e +olecular -o+-ard+en! of !(e air +olecules in !(e a!+os)(erec. con*ec!ion curren!s in !(e a!+os)(ere 8circula!ion of air +asses resul!in% in wea!(er )a!!erns

2. 0ou are a-ou! !o se! ou! on a scu-a di*in% !ri)" and are (a*in% a +edical c(ec', T(e doc!or +easuresyour -lood )ressure !o -e a (eal!(y12 ++ %, T(e 12 ++ % is !(e +a i+u+ )ressure a! !(e )ea' of eac( )ulse" called !(e sys!ole" and !(e ++ % is !(e lowes! )ressure -e!ween )ulses" called !(e dias!ole,e. i*en !(a! nor+al a!+os)(eric )ressure is around 76 ++ %" w(y does -lood s)ur! fro+ a dee) cu!.0ou c(ec' !(e wea!(er re)or!" and i! s %oin% !o -e a fine wee'end" wi!( a (i%( )ressure fron! of 1 2 'Pa

-rin%in% war+ wea!(er, 0ou )ac' u) and (ead off, 0ou c(ec' your !yre )ressure w(en you fill u) wi!(

)e!rol" and infla!e !(e+ !o 25 )si 817,2 'Pa ,f. &(ic( of !(e )ressures %i*en a-o*e are a-solu!e and w(ic( are %au%e )ressures.0ou arri*e a! !(e di*in% class and are issued wi!( ins!ruc!ions and e ui)+en!,g. &(y does !(e di*in% ins!ruc!or !ell you no! !o (old your -rea!( w(en surfacin%.h. &(y are you issued wi!( lead -el!s and infla!a-le )ac'e!s.


1. Suction cups and Magdeburg platesow can you +a'e !(e suc!ion cu) s!ic' !o a surface.

# )lain w(a! (a))ens w(en i! s!ic's and w(en i! fails !o s!ic',

&(en are !(e ;a%de-ur% )la!es (ard !o )ull a)ar!.&(en are !(e ;a%de-ur% )la!es easy !o )ull a)ar!. # )lain w(y,

2. "!drostatic parado#&a!er is )oured !o !(e sa+e le*el in eac( of !(e *essels s(own -elow" all (a*in% !(e sa+e -ase area, If !(e

)ressure is !(e sa+e a! !(e -o!!o+ of eac( *essel" !(e force e )erienced -y !(e -ase of eac( *essel is !(esa+e, &(y do !(e *essels (a*e differen! wei%(!s w(en )u! on a scale. T(is a))aren!ly con!radic!ory resul!is co++only 'nown as !(e (ydros!a!ic )arado ,

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&. S%uirtinga fluid e er!s an ou!ward force on !(e walls of i!s con!ainer>,=-ser*e !(e way wa!er >s uir!s> ou! of !(e (oles, &(a! can you say a-ou! !(e direc!ion of !(e wa!er /us!as i! lea*es !(e (oles.Pus( a drin'in% s!raw in!o !(e wa!er and !(en )u! your fin%er o*er !(e !o), ?if! !(e s!raw ou! of !(e

wa!er, &(a! (a))ens. &(y. =-ser*e w(a! (a))ens w(en you undo !(e lid of !(e wa!erin% -o!!leJ,# )lain your o-ser*a!ions,

(. "ollo' tube and discollow !u-e and dis': &(y does !(e dis' fall away in air -u! s!ay a!!ac(ed !o !(e !u-e w(en !(ere is air in

!(e !u-e and wa!er ou!side !(e !u-e.

C. Quantitative Questions:

1. D (ydraulic lif! is used !o raise a den!is! s c(air w(ic( wei%(s 15 '%, T(e c(air res!s on a )is!on of area 15 c+ 2, D force is a))lied !o a s+all )is!on of area 75 c+ 2 !o raise !(e c(air,

a, ow +uc( force +us! -e a))lied !o !(e s+all )is!on !oraise !(e c(air. -, &(a! dis!ance +us! !(e s+all )is!on -e +o*ed !o raise!(e c(air -y 1 c+.

2. 0our di*in% ins!ruc!or (as -een as'ed !o in*es!i%a!e !(e in!e%ri!y of a da+ wall, T(e reser*oir isa-ou! !o -e enlar%ed !o co)e wi!( Sydney s %rowin% )o)ula!ion and !(e wa!er au!(ori!y +ay need !oreinforce !(e (oldin% wall, T(e da+ is 3 + dee) and (as a )i)e 6+ -elow !(e surface of !(e wa!er, T(edia+e!er of !(e )i)e is 2 c+ and i! is -loc'ed -y a )lu%,

a. &(y is !(e wall !(ic'er a! !(e -o!!o+ !(an a! !(e !o).b. If !wo reser*oirs of !(e sa+e de)!( are !o -e /oined !o for+ a sin%le +uc( lar%er reser*oir" is i!necessary !o reinforce !(e da+ wall.

c. &(a! is !(e fric!ion force -e!ween !(e )lu% and !(e )i)e wall.

3 +

6+

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Solu!ions !o PR1T: Pressure


1. Dir )ressure,a. T(e wei%(! of !(e air in !(e a!+os)(ere is a +a/or fac!or in de!er+inin% a!+os)(eric )ressure on ear!(on a %lo-al scale, I! is !(e cons!an! +o!ion of !(e air +olecules !(a! %i*es !(e a!+os)(ere !(e densi!y weare accus!o+ed !o and !(e *aria!ions in )ressure wi!( (ei%(!,b. ;icrosco)ically" !(e )ressure is due !o !(e

-o+-ard+en! of +olecules, ?e! us i+a%ine !(ee !re+e: If !(e air +olecules were no!cons!an!ly +o*in% !(ey would fall down"c(an%in% !(e densi!y and 'ee)in% !(e )ressurea! !(e surface of !(e ear!( !(e sa+e, owe*er !(e )ressure would c(an%e dras!ically wi!(

(ei%(!c. $on*ec!ion curren!s in !(e a!+os)(ere are )ar! of !(e wea!(er )a!!ern, &ar+ air risin%" cool air sin'in%and !(e +o!ion of air +asses (ori@on!ally are )ar! of low and (i%( )ressure sys!e+s in !(e a!+os)(ere,

2. D-solu!e and %au%e )ressures,a. Blood )ressure is a +easure of )ressure a-o*e a!+os)(eric" i! is a rela!i*e or gauge )ressure,b. D!+os)(eric )ressure is !(e only a-solu!e )ressure %i*en (ere" -o!( -lood )ressure and !yre )ressure are%au%e )ressures" i,e, )ressure a-o*e a!+os)(eric,c. 0ou are !old no! !o (old your -rea!( w(en surfacin% -ecause asyou %e! (i%(er" !(e e !ernal )ressure fro+ !(e wa!er decreases,T(e air in your lun%s e er!s a )ressure ou!wards on your lun%s"

w(ile !(e wa!er ou!side you e er!s an inward )ressure, Ds yourise and !(e wa!er )ressure decreases" !(e air in your lun%s is a-le!o e )and, If !(ere is !oo +uc( air in !(e+ )us(in% ou!wards" andno! enou%( )ressure ou!side !(e+" !(ey could ru)!ured. T(e lead -el!s and infla!a-le )ac' are !o ad/us! your -uoyancyAlead !o +a'e you +ore dense" allowin% you !o sin'" infla!a-le

)ac's !o +a'e you less dense" allowin% you !o floa!,


11. Suction cups and Magdeburg plates

T(e suc!ion cu) +us! (a*e !(e air s uee@ed ou! of i! and +a'e a co+)le!e seal wi!( !(e surface !o s!ic' !oi!, If !(e seal isn ! co+)le!e" air can en!er !(e cu)" re+o*in% !(e )ressure difference and allowin% !(e cu) !ofall off,T(e ;a%de-ur% )la!es are (ard !o )ull a)ar! w(en !(ere is a *acuu+ -e!ween !(e+" -u! easy !o )ull a)ar!w(en !(ere is air, D fluid e er!s a force )er)endicular !o a surface i! co+es in con!ac! wi!(: F=PA , If !(ereis a difference in )ressure across a surface !(is resul!s in a ne! force w(ic( is direc!ed fro+ !(e re%ion of %rea!er !o lower )ressure, In !(e case of !(e ;a%de-ur% )la!es" w(en air is re+o*ed fro+ !(e re%ion

-e!ween !(e )la!es !(e )ressure -e!ween !(e )la!es is less !(an !(e a!+os)(eric )ressure ou!side !(e )la!es,T(is difference in )ressure resul!s in a ne! force inwards" (oldin% !(e )la!es !o%e!(er,

9

mg mg

Eee) wa!er" P

water =P

lung S(allow wa!er" P

water

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12. "!drostatic parado#T(e con!ainers (a*e differen! +asses 8-ecause !(ey con!ain differen! a+oun!s of wa!er " so !(ey +us! (a*edifferen! wei%(!s,Dno!(er ar%u+en! %oes as follows: !(e )ressure is !(e sa+e a! !(e -o!!o+ of eac( con!ainer 8-ecause !(eyare filled !o !(e sa+e (ei%(! , Bu! !(ey all (a*e !(e sa+e -ase area" so !(e force e )erienced -y !(e -ase of

eac( con!ainer is !(e sa+e, T(erefore" !(ey s(ould all %i*e !(e sa+e readin% on !(e scale, T(is secondar%u+en! is wron% -ecause we (a*e only considered !(e force of !(e wa!er on !(e -ase of !(e con!ainers,&(en calcula!in% !(e force of !(e wa!er on !(e con!ainer" we +us! include !(e forces on !(e sides" w(ic(+ay (a*e a co+)onen! in !(e *er!ical direc!ion,

1$. Pascal0s vasesDn increase in !(e )ressure in one !u-e will -e !rans+i!!ed !o !(e o!(er !u-es" and !(e li uid le*el in !(ese!u-es will rise, T(is is )ossi-le -ecause !(e *ases are all connec!ed and (ence are really a sin%le *essel,

1&. S%uirtingT(e wa!er will co+e ou! )er)endicular !o !(e con!ainer wall" as !(is is !(e direc!ion of !(e ne! force,

In eac( of !(ese !(e li uid is (eld in -y !(e low )ressure in !(e !u-e or -o!!le" w(en !(is )ressure isincreased !o a!+os)(eric )ressure -y o)enin% !(e lid or re+o*in% !(e fin%er !(e wa!er will co+e ou!,

1(. "ollo' tube and discT(e disc s!ays a!!ac(ed w(en !(ere is a )ressure difference e er!in% a force w(ic( (olds i! in )lace, &(en!(e )ressure difference decreases suc( !(a! !(e force falls -elow mg of !(e disc" !(e disc falls,


$. D (ydraulic lif! is used !o raise a den!is! s c(air w(ic( wei%(s 15 '%, T(e c(air res!s on a )is!on of area 15 c+ 2, D force is a))lied !o a s+all )is!on of area 75 c+ 2 !o raise !(e c(air,

a. T(e force needed !o /us! o*erco+e !(e wei%(! of !(e c(air is 15 '% × g G 147 K, T(is is !(e forceneeded on !(e c(air, T(e )ressure will -e !(e sa+e a! all )oin!s in !(e fluid" so we need a force a))lied !o!(e s+all )is!on w(ic( will %i*e enou%( )ressure !o )roduce !(is force a! !(e lar%e )is!on, ence we need a

)ressure of P G F/A = 147 K 15 × 1 4 + 2 G 9 Pa,D! !(e s+all )is!on we +us! a))ly a force !o )roduce !(is )ressure" w(ic( will -e

F G PA G 9 Pa × 75 × 1 4 + 2 G 73,5 K,T(is is !(e +ini+u+ force w(ic( +us! -e a))lied !o +o*e !(e c(air,b. To raise !(e c(air -y 1 c+ a *olu+e of V G 1 c+ × 15 c+ 2 G 15 c+ 3 of !(e fluid +us! -edis)laced in!o !(e area -enea!( !(e c(air, T(is *olu+e +us! co+e fro+ !(e fluid -enea!( !(e s+all )is!on"(ence i! +us! +o*e downwards a (ei%(! of h G V / area G 15 c+ 3 75 c+ 2 G 2 c+ G 2+,

&. Pressure and de)!(,a. Pressure increases wi!( de)!( as P= ρ gh , Pressure G 8force area so !(e wall needs !o wi!(s!and %rea!er force a! !(e -o!!o+" (ence i! is -uil! !o -e !(ic'er a! !(e -o!!o+,b. $(an%in% !(e surface area does no! c(an%e !(e )ressure -ecause i! does no! c(an%e !(e de)!(" (ence!(ere is no need !o fur!(er reinforce !(e wall,c. T(e )lu% is no! +o*in% so i! is a s!a!ic fric!ional force (oldin% i! in )lace, T(e force will -e e ual !o !(e

)ressure × !(e area" F = P × A, and !(e )ressure is P G P a!+ H ρ gh. owe*er -o!( sides of !(e )lu% will(a*e !(e sa+e con!ri-u!ion fro+ a!+os)(eric )ressure" so we can i%nore !(is con!ri-u!ion as i! will cancelou! anyway,

F = ρ water gh8πr G 1 '%,+ 3 × 9, +,s 2 ×6 + ×π× 8 , 2 + 2 G 74 K,

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PR2B: uo!anc!


1. &(en you /oin a %y+ you +ay (a*e a s'in fold !es! done!o !ell you (ow +uc( of your -ody is fa!, D +ore accura!e"

-u! less )leasan!" +eans of +easurin% -ody co+)osi!ion is*ia su-+ersion in wa!er, T(e )erson is wei%(ed in air and!(en wei%(ed a%ain w(en co+)le!ely su-+er%ed in wa!er,8Eon ! !ry !(is a! (o+ea. # )lain (ow !(is )rocess can -e used !o +easure a*era%edensi!y,

T(e -ody densi!y %i*es an indica!ion of -ody co+)osi!ion" asfa! is +uc( less dense !(an ei!(er +uscle or -one,b. &(y is i! i+)or!an! !o -rea!(e ou! as +uc( as )ossi-le w(en doin% suc( a !es!.c. &(y do wo+en floa! -e!!er !(an +en.&(y is i! easier !o floa! in *ery sal!y wa!er" for e a+)le !(e Eead Sea" !(an in fres( wa!er,

2. T(e fi%ure s(ows four iden!ical o)en!o) con!ainers, =ne con!ainer (as /us!wa!er, D cor' floa!s in ano!(er con!ainer and a !oy duc' floa!s in !(e !(ird, T(efour!( con!ainer (as a s!eel +ar-le in i!,

Dll four con!ainers are filled !o !(e -ri+wi!( wa!er, &(ic( con!ainer wei%(s !(e+os!. &(ic( con!ainer wei%(s !(e leas!.# )lain your answer,


1. uo!ant force Dn o-/ec! is sus)ended fro+ a s)rin% -alance,&(a! is !(e readin% on !(e s)rin% -alance w(en !(e o-/ec! is in air.

Kow i++erse !(e o-/ec! in wa!er.ow will !(e readin% c(an%e.# )lain w(a! (a))ens and draw a dia%ra+ s(owin% !(e forces ac!in% on !(e o-/ec! !o (el) e )lain your answer,

2. uo!ant force D con!ainer of wa!er is )laced on a wei%(in% scale, Dn o-/ec!" sus)ended fro+ a s)rin% -alance" isi++ersed in !(e con!ainer of wa!er, &ill !(e readin% on !(e wei%(in% scale c(an%e. Eraw a dia%ra+s(owin% !(e forces ac!in% !o (el) e )lain your answer,

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$. "!dro etersT(ere are (ydro+e!ers and se*eral li uid sa+)les on !(e de+ons!ra!ion -enc(es, &al' o*er and !a'e afew +easure+en!s, $an you iden!ify !(e sa+)les fro+ !(e !a-le of densi!ies %i*en.Iden!ical (ydro+e!ers are )laced in !(ree differen! li uids, T(ey floa! a! differen! le*els, Is !(e -uoyan!force on !(e (ydro+e!ers !(e sa+e or differen!. &(y.

&(y is !(e scale on !(e (ydro+e!er +ar'ed !(e way i! is.

&. *artesian diver&(a! (a))ens !o !(e di*er as you )us( on !(e -o!!le. &(y.&(a! con!rols !(e +o!ion of !(e di*er.


1. D fis( +ain!ains i!s de)!( in wa!er -y ad/us!in% !(e air con!en! of )orous -one or swi+ -ladders !o+a'e i!s a*era%e densi!y !(e sa+e as !(a! of !(e wa!er, T(e swi+ -ladder 8also called !(e %as -ladder or air

-ladder is a fle i-le walled" %as filled sac, T(is or%an con!rols !(e fis(>s -uoyancy and is also used for

(earin% in so+e s)ecies,

Su))ose !(a! wi!( i!s swi+ -ladder colla)sed" a +ac'erel (as a densi!y of 1, %,c+ 3, By w(a! frac!ion of i!s ori%inal -ody *olu+e +us! !(e fis( infla!e !(e air sacs !o reduce i!s densi!y !o !(a! of !(e wa!er. Eensi!yof sea wa!er is 1, 2 %,c+ 3,

2. In Fe-ruary 1995" an ice-er% so -i% !(e en!ire Sydney re%ion fro+ !(e coas! !o !(e Blue ;oun!ainscould fi! on i!s surface -ro'e free of Dn!arc!ica, T(e ice-er% was a))ro i+a!ely rec!an%ular wi!( a len%!(of 7 '+" a wid!( of 37 '+ and 2 + !(ic',a. &(a! frac!ion of !(is ice-er% was underwa!er.b. Eo you ac!ually need !(e s(a)e and si@e of !(e ice-er% !o de!er+ine !(is frac!ion.

c. T(e unsin'a-leJ Ti!anic was sun' -y an ice-er%, &(y do ice-er%s )resen! suc( a )ro-le+ for s(i))in%.d. &ould ice-er%s -e a )ro-le+ if wa!er densi!y increased on free@in%" li'e +os! o!(er li uids.

TDB?# =F E#KSITI#S

Ice 917 '%,+ 3 8a! 1 a!+ and L$Sea wa!er 1 24 '%,+ 3 8a! 1 a!+ and 2 L$&a!er 99 '%,+ 3 8a! 1 a!+ and 2 L$

12

-rain

li*er s!o+ac( in!es!ines s'i bladder

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Solu!ions !o PR2B: uo!anc!A. Qualitative Questions:

1.

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T(e -uc'e! will wei%( +ore wi!( !(e o-/ec! in i! -ecause e*en !(ou%( !(e o-/ec! is no! res!in% on !(e -o!!o+"i! (as raised !(e le*el of wa!er" (ence increased !(e )ressure a! !(e -o!!o+ and increased !(e wei%(! of !(e

-uc'e!,

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$. "!dro etersT(e -uoyan! force is e ual !o !(e wei%(! of dis)laced li uid, T(e wei%(! of dis)laced li uid is e ual !o !(ewei%(! of !(e (ydro+e!er" (ence !(e -uoyan! force will -e !(e sa+e in eac( case as lon% as !(e (ydro+e!ersfloa! and do no! sin' !o !(e -o!!o+,D (ydro+e!er floa!s (i%(er in denser li uids, &(en !(e (ydro+e!er is floa!in% !(e -uoyan! force" w(ic( is e ual!o !(e wei%(! of wa!er dis)laced" +us! -e e ual !o !(e wei%(! of !(e (ydro+e!er, D denser li uid needs less

wa!er dis)laced !o %i*e !(e sa+e -uoyan! force" (ence !(e (ydro+e!er floa!s (i%(er !(e denser !(e fluid is,

&. *artesian 3iver&(en you )us( !(e -o!!le !(e )ressure you a))ly is !rans+i!!ede*enly and wi!(ou! loss !o all )ar!s of !(e fluid, &a!er isal+os! inco+)ressi-le" -u! air is *ery co+)ressi-le" (ence!(e air -u--le in !(e di*er is co+)ressed" c(an%in% (is a*era%edensi!y, 0ou s(ould -e a-le !o see !(e -u--le %e! s+aller, T(e+ore you s uee@e" !(e denser (e -eco+es" and !(e fas!er (e sin's,&(en you le! %o" (e deco+)resses and rises a%ain,

*. Quantitative Questions:1. Before !(e fis( infla!es i!s air sacs i! (as a densi!y of $i = m/V G 1, %,c+ 3,

Df!er infla!in% !(e sacs !o lower i!s densi!y i!s densi!y is $f = m/%V "$V&G 1, 2 %,c+ 3, &eare !ryin% !o find !(e fractional c(an%e in *olu+e" $V/V.T(e ac!ual +ass is no! i+)or!an!" and can -e re+o*ed fro+ !(e e ua!ions -y di*idin% $' -y $f, w(ic( %i*es:$i / $f G %V"$V V G 1, %,c+ 3 1, 2 %,c+ 3,&e can rewri!e !(is as 1 H %$V/V&G 1, 6"and (ence $V/V G , 6 G 6N,

2. Ice-er%s and !(e Ti!anic,

a. For a floa!in% -ody" suc( as an ice-er% in !(e sea" !(e wei%(! of dis)laced wa!er is e ual !o !(e wei%(! of !(eice-er%,( water displaced = ( ice)erg

mwater displaced * g = mice)erg * g now usin% m = $V+

$water * V water displaced * g = $ice)erg * Vice)erg * g T(e *olu+e of wa!er dis)laced +us! -e e ual !o !(e *olu+e of !(e ice-er% w(ic( is su-+er%ed,

V su)merged / Vice)erg = $ice)erg / $water V su)merged / Vice)erg G 917 '%,+ 3 1 24 '%,+ 3 G , 96 G 9,6NSo 9 N of !(e ice-er% is su-+er%ed,b. Ds can -e seen fro+ e a+inin% !(e calcula!ion" !(is )ro)or!ion does no! de)end on !(e s(a)e or si@e of !(eice-er%" only !(e densi!y of !(e ice and !(e wa!er,c. ;os! of !(e ice-er% is underwa!er" and i! +ay -e +uc( lon%er -enea!( !(an a-o*e" +a'in% i! difficul! !osee,d. If wa!er densi!y increased on free@in%" li'e +os! o!(er li uids" ice-er%s would sin' and no! -e a (a@ard,

owe*er !(is would lead !o o!(er )ro-le+s" li'e a ua!ic )lan!s and crea!ures -ein% fro@en and a %radual -uild u) of ice a! !(e -o!!o+ of la'es" ri*ers and seas,

#he (or shop #utorial Pro-ect P 0!+ Pressure 13

P

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PR2T: uo!anc!


1. S!a!e w(e!(er you a%ree or disa%ree wi!( eac( of !(e c(oices %i*en -elow and wri!e a -rief e )lana!ionof w(y you a%ree or disa%ree,D s(i) -uil! of s!eel can floa! on sea wa!er -ecause:a. Sea wa!er is denser !(an s!eel,b. T(e -uoyan! force on !(e s(i) is %rea!er !(an i!s wei%(!,c. T(e -uoyan! force on !(e s(i) is %rea!er !(an !(e wei%(! of sea wa!er dis)laced,d. Drc(i+edes> )rinci)le is no! a))lica-le !o a (ollow -ody li'e a s(i),e. T(e ra!io of !(e +ass of !(e s(i) !o i!s *olu+e is less !(an !(e densi!y of sea wa!er,

2. T(e fi%ure s(ows four iden!ical

o)en !o) con!ainers, =ne con!ainer (as /us! wa!er, D cor' floa!s in ano!(er con!ainer and a !oy duc' floa!s in !(e!(ird, T(e four!( con!ainer (as a s!eel+ar-le in i!, Dll four con!ainers arefilled !o !(e -ri+ wi!( wa!er,&(ic( con!ainer wei%(s !(e +os!.&(ic( con!ainer wei%(s !(e leas!.# )lain your answer,


1. uo!ant force Dn o-/ec! is sus)ended fro+ a s)rin% -alance, &ill !(e readin% on !(e s)rin% -alance -e differen! w(en !(eo-/ec! is in air !o w(en !(e o-/ec! is i++ersed in wa!er. Eraw a dia%ra+ s(owin% !(e forces ac!in% !o (el)e )lain your answer,

2. uo!ant force D con!ainer of wa!er is )laced on a wei%(in% scale, Dn o-/ec!" sus)ended fro+ a s)rin% -alance" isi++ersed in !(e con!ainer of wa!er, &ill !(e readin% on !(e wei%(in% scale c(an%e. Eraw a dia%ra+

s(owin% !(e forces ac!in% !o (el) e )lain your answer,

$. "!dro etersT(ere are (ydro+e!ers and se*eral li uid sa+)les on !(e ac!i*i!y -enc(es, &al' o*er and !a'e a few+easure+en!s, $an you iden!ify !(e sa+)les fro+ !(e !a-le of densi!ies %i*en.Iden!ical (ydro+e!ers are )laced in !(ree differen! li uids, T(ey floa! a! differen! le*els,Is !(e -uoyan! force on !(e (ydro+e!ers !(e sa+e or differen!. &(y.&(y is !(e scale on !(e (ydro+e!er +ar'ed !(e way i! is.

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&. *artesian diver&(a! (a))ens !o !(e di*er as you )us( on !(e -o!!le. &(y.&(a! con!rols !(e +o!ion of !(e di*er.


1. In Fe-ruary 1995" an ice-er% so -i% !(e en!ire Sydney re%ion fro+ !(e coas! !o !(e Blue ;oun!ainscould fi! on i!s surface -ro'e free of Dn!arc!ica, T(e ice-er% was a))ro i+a!ely rec!an%ular wi!( a len%!(of 7 '+" a wid!( of 37 '+ and 2 + !(ic',e. &(a! frac!ion of !(is ice-er% was underwa!er.f. Eo you ac!ually need !(e s(a)e and si@e of !(e ice-er% !o de!er+ine !(is frac!ion.g. T(e >unsin'a-le> Ti!anic was sun' -y an ice-er%, &(y do ice-er%s )resen! suc( a )ro-le+ for s(i))in%.h. &ould ice-er%s -e a )ro-le+ if wa!er densi!y increased on free@in%" li'e +os! o!(er li uids.

TDB?# =F E#KSITI#S

Ice 917 '%,+3

8a! 1 a!+ and L$Sea wa!er 1 24 '%,+ 3 8a! 1 a!+ and 2 L$&a!er 99 '%,+ 3 8a! 1 a!+ and 2 L$

2. In !(e 193 s a new way !o cross !(e D!lan!ic was -y air @e))elin, T(e @e))elins were li'e %i%an!ics!eera-le -li+)s" wi!( ri%id fra+es w(ic( con!ained %as -a%s" w(ic( were filled wi!( (ydro%en or (eliu+!o %i*e !(e s(i) -uoyancy, T(ey were a )eaceful and lu urious way !o !ra*el, ;os! of !(ese @e))elinswere -uil! in er+any" and one of !(e -i%%es! and +os! lu urious was !(e inden-ur%J, I! (ad ali-rary" dinin% roo+" a loun%e and (o! wa!er in all ca-ins, I! was !(e world>s firs! !ransa!lan!icco++ercial airliner and was 'e)! o*er(ead -y u) !o 2 " cu-ic +e!ers of (ydro%en in 16 cells,a. T(e densi!y of air a! 2 o$ is 1,2 '%,+ 3" !(e densi!y of (ydro%en is , 9 '%,+ 3, &(a! *olu+e of (ydro%en was re uired !o lif! !(e inden-ur% if i!s !o!al +ass" includin% )ayload" was 12" '%.=n ;ay 6 !(" 1937 !(e inden-ur% cras(ed in ?a'e(urs!" Kew ersey" a year af!er i!s firs! fli%(!, T(e(ydro%en of !(e airs(i) was i%ni!ed w(ile +aneu*erin% !o land and !(e inden-ur% was des!royed and35 )assen%ers and crew died,b. eliu+ is now used -y airs(i)s suc( as -li+)s and (o! air -alloons" (owe*er a! !(e !i+e of !(e

inden-ur% !(e (eliu+ %as" )roduced al+os! en!irely in !(e

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Solu!ions !o PR2T: uo!anc!


1. Eensi!y and -uoyancy" and (ow s(i)s floa!,a. Sea wa!er is not denser !(an s!eel,b. T(e -uoyan! force on !(e s(i) is not %rea!er !(an i!s wei%(!" if !(is was !(e case !(ere would -e a ne!force u)wards" and !(e s(i) would accelera!e u),c. T(e -uoyan! force on !(e s(i) is not %rea!er !(an !(e wei%(! of sea wa!er dis)laced" i! is e ual !o !(ewei%(! of sea wa!er dis)laced,d. Drc(i+edes )rinci)le is a))lica-le !o a (ollow -ody li'e a s(i)" -u! you +us! use !(e !o!al *olu+e of !(e -ody" includin% !(e ca*i!y,e. T(e ra!io of !(e +ass of !(e s(i) !o i!s *olu+e is less !(an !(e densi!y of sea wa!er" !(e densi!y of !(es(i) is less !(an !(a! of !(e wa!er" !(is is !rue if !(e s(i) is !o floa!, Ko!e a%ain !(a! !(is is !(e !o!al *olu+eof !(e s(i)" includin% airs)aces" no! /us! !(e *olu+e of !(e s!eel,

2. $on!ainers 2 and 3 -o!( con!ain o-/ec!sw(ic( are floa!in% and (ence dis)lace awei%(! of wa!er e ual !o !(e o-/ec!s wei%(!"so !(e !o!al wei%(! of con!ainers 2 and 3 is!(e sa+e as con!ainer 1 w(ic( (as only wa!er in i!, $on!ainer 4 (as a s!eel +ar-le" w(ic((as sun'" and dis)laced a *olu+e of wa!ere ual !o !(e +ar-le>s *olu+e,

owe*er !(e +ar-le is +ore dense !(an wa!er" and (ence wei%(s +ore !(an !(e *olu+e of wa!er i! (asdis)laced, So con!ainer 4 wei%(s +ore !(an !(e o!(er !(ree con!ainers,


1. uo!ant force T(e o-/ec! will wei%( less in wa!er !(an air -ecause wa!er is +oredense !(an air and (ence !(e -uoyan! force is %rea!er,In -o!( cases F ! " # G mg " and !(e scale +easures !(e !ension" #.

F ! is %rea!er in wa!er" (ence # is less,

2. uo!ant force The bucket will weigh more with the object in it because

even though the object is not resting on the bottom, it hasraised the level of water, hence increased the pressure at thebottom and increased the weight of the bucket.

$. "!dro etersT(e -uoyan! force is e ual !o !(e wei%(! of dis)laced li uid,T(e wei%(! of dis)laced li uid is e ual !o !(e wei%(! of !(e (ydro+e!er" (ence !(e -uoyan! force will -e!(e sa+e in eac( case as lon% as !(e (ydro+e!ers floa! and do no! sin' !o !(e -o!!o+, D (ydro+e!er floa!s (i%(er in denser li uids, &(en !(e (ydro+e!er is floa!in% !(e -uoyan! force" w(ic( is e ual !o !(e

wei%(! of wa!er dis)laced" +us! -e e ual !o !(e wei%(! of !(e (ydro+e!er, D denser li uid needs lessli uid dis)laced !o %i*e !(e sa+e -uoyan! force" (ence !(e (ydro+e!er floa!s (i%(er !(e denser !(e fluidis,

16

mg

#

F !

#

mg F !

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&. *artesian 3iver&(en you )us( !(e -o!!le !(e )ressure you a))ly is !rans+i!!ede*enly and wi!(ou! loss !o all )ar!s of !(e fluid, &a!er is al+os!inco+)ressi-le" -u! air is *ery co+)ressi-le" (ence !(e air -u--lein !(e di*er is co+)ressed" c(an%in% (is a*era%e densi!y, 0ou

s(ould -e a-le !o see !(e -u--le %e! s+aller, T(e +ore yous uee@e" !(e denser (e -eco+es" and !(e fas!er (e sin's, &(enyou le! %o" (e deco+)resses and rises a%ain,

*. Quantitative Questions: 1. Ice-er%s and !(e Ti!anic,a. For a floa!in% -ody" suc( as an ice-er% in !(e sea" !(e wei%(! of dis)laced wa!er is e ual !o !(e wei%(! of !(e ice-er%: ( water displaced = ( ice)erg or mwater displaced × g = m ice)erg × g,and now usin% m = ρ V+ ρ water × V water displaced × g = ρ ice)erg × V ice)erg × g T(e *olu+e of wa!er dis)laced +us! -e e ual !o !(e *olu+e of !(eice-er% w(ic( is su-+er%ed,V su)merged / V ice)erg = ρ ice)erg / ρ water G 917 '%,+ 3 1 24 '%,+ 3 G , 96 G 9,6N, So 9 N of !(e ice-er% is su-+er%ed,b. Ds can -e seen fro+ e a+inin% !(e calcula!ion" !(is )ro)or!ion does no! de)end on !(e s(a)e or si@e of !(e ice-er%" only !(e densi!y of !(e ice and !(e wa!er,c. ;os! of !(e ice-er% is underwa!er" and i! is +uc( -i%%er -enea!( !(an a-o*e" and also difficul! !o see,d. If wa!er densi!y increased on free@in%" li'e +os! o!(er li uids" ice-er%s would sin' and no! -e a (a@ard,

owe*er !(is would lead !o o!(er )ro-le+s" li'e a ua!ic )lan!s and crea!ures -ein% fro@en and a %radual -uild u) of ice a! !(e -o!!o+ of la'es" ri*ers and seas,e. If wa!er densi!y increased on free@in%" li'e +os! o!(er li uids" ice-er%s would sin' and no! -e a (a@ard,

owe*er !(is would lead !o o!(er )ro-le+s" li'e a ua!ic )lan!s and crea!ures -ein% fro@en,

2. Buoyancy and !(e inden-ur%,a. For !(e airs(i) !o floa! and +ain!ain i!s )osi!ion we re uire !(a! !(e wei%(!force 8mg +us! -e e ual !o or less !(an !(e -uoyan! force 8 F ! ,T(e !o!al wei%(! of !(e s(i)" 1 " is !(e wei%(! of !(e (ydro%en )lus !(ewei%(! of !(e s(i) wi!( )ayload" 8 (=mg , D%ain we use m= ρ V ,

1g = ρ 2 .V 2 .g " m ship .gas a-o*e" !(is +us! -e e ual !o !(e wei%(! of air dis)laced" w(ic( is mair g = ρ air V air .g ρ 2 .V 2 .g H m ship .g G ρ air V air .g

T(e *olu+e of air dis)laced will -e a))ro i+a!ely !(e *olu+e of !(e (ydro%en as !(e (ydro%en cells areenor+ous co+)ared !o !(e ca-in w(ic( si!s -elow !(e+" so we can se! V 2 =V air " and cancellin% !(e g s%i*es: ρ 2 .V H m ship = ρ air V and V G 1 8 ρ air 3 ρ 2 G 12" 81,2 , 9 G 1 " +3,b. Re)ea! !(e a-o*e calcula!ion usin% !(e *olu+e /us! found and !(e densi!y of (eliu+ ra!(er !(an(ydro%en" -u! now we sol*e for +ass: ρ 2e .V 2e .g H m ship .g = ρ air V air .g

m ship G % ρ air 3 ρ 2e , V 2e G 11"2 '%c. eliu+ is used in )reference !o (ydro%en -ecause i! is iner!, ydro%en is (i%(ly fla++a-le" as wasdra+a!ically de+ons!ra!ed -y !(e inden-ur%,d. T(e (eliu+ %radually lea's ou! -e!ween !(e +olecules of !(e -alloon s'in and %oes in!o !(e a!+os)(ere,

eliu+ is li%(!er !(an air and a! !y)ical a!+os)(eric !e+)era!ures (as enou%( 'ine!ic ener%y !o esca)e !(ea!+os)(ere and !(e %ra*i!a!ional a!!rac!ion of !(e ear!( 8+any of !(e a!o+s (a*e a *eloci!y %rea!er !(an!(e esca)e *eloci!y , I! lea*es !(e a!+os)(ere and %oes in!o ou!er s)ace,


mg

F !

P

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PR3B: 4luid 4lo'


1. &a!er flows !(rou%( !(e )i)e s(own -elow fro+ lef! !o ri%(!,

a. Ran' !(e *olu+e ra!e of flow a! !(e four )oin!s A" " * and 3 ,b. Ran' !(e *eloci!y of !(e fluid a! !(e )oin!s A" " * and 3 , # )lain your answer,c. Ran' !(e )ressure in !(e fluid a! )oin!s A" " * and 3 , # )lain your answer,

2. Bernoulli s e ua!ion follows fro+ Kew!on s laws and is essen!ially a s!a!e+en! of conser*a!ion of ener%y for fluid flow,a. &ri!e down Bernoulli s e ua!ion and" referrin% !o eac( !er+" e )lain (ow i! is a s!a!e+en! of conser*a!ion of ener%y,b.

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1. S+o'in% causes infla++a!ion of !(e -ronc(ioles" !(e s+all air )assa%es in !(e lun%s" w(ic( !ends !o

decrease !(e flow of air in!o !(e lun%s and (ence !(e o y%en su))ly !o !(e -lood, Dir is flowin% down anor+al sec!ion of a -ronc(iole wi!( a dia+e!er of 1, ++ a! a *eloci!y of ,5 +,s 1,

a. Par! of !(e -ronc(iole is narrowed due !o infla++a!ion" and (as a dia+e!er of only ,77 ++, &(a! is!(e *eloci!y of !(e air in !(is sec!ion of !(e -ronc(iole.

b. &(a! are !(e conse uences of !(is for %as e c(an%e in !(e lun%.

2. Re-ecca and Bren! are -rewin% !(eir own %in%er -eer and (a*e se! u) a lar%e *a! wi!( a narrow )i)e near !(e

-o!!o+ !o !a'e sa+)les so !(ey can !ell w(en i!s ready for -o!!lin%, T(e *a! (as a dia+e!er of 6 c+" is o)en a! !(e!o)" and (as a )ressure %au%e +oun!ed on !(e )i)e 1, +

-elow !(e !o) of !(e *a!, T(e *a! is full" and as Re-ecca!a'es a sa+)le !(e fluid le*el falls a! a ra!e of 1, c+,s 1

and flows ou! !(e -o!!o+ of !(e )i)e a! 5 c+,s 1, T(edensi!y of !(e %in%er -eer is 1, × 1 3 '%,+ 3,&(a! )ressure readin% 8a-solu!e does !(e %au%e s(ow.8 in!: use Bernoulli s e ua!ion,


1, +

6 c+

1++ ,7++

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Solu!ions !o PR3B: 4luid 4lo'


1. &a!er flows !(rou%( !(e )i)e fro+ lef! !o ri%(!,d. &a!er is inco+)ressi-le" and as!(ere is no wa!er ei!(er en!erin% or lea*in% -e!ween )oin!s D and E !(e*olu+e flow ra!e +us! -e sa+e a! all

)oin!s" /us! as curren! +us! -e !(esa+e a! all )oin!s alon% an ar+ of acircui!, T(is is called !(e )rinci)le of con!inui!y A×v G cons!an!,e. Ds !(e wa!er flows fro+ A !o !(e area increases" (ence !o +ain!ain con!inui!y v +us! decrease"!(erefore vA Q v , Ds !(e wa!er !(en flows down(ill !o )oin! * i! will %ain ener%y" (owe*er !(e area (as no!c(an%ed so we 'now" -ecause of con!inui!y" !(a! !(e *eloci!y (as no! c(an%ed" v G v* , &(en !(e wa!er flows fro+ * !o 3 !(e area increases a%ain" so !(e *eloci!y will decrease a%ain" v* Q v3 , T(e ran'in% is!(erefore vA Q v G v* Q v3 .f. &(en !(e wa!er flows fro+ A !o !(ere is no c(an%e in %ra*i!a!ional )o!en!ial ener%y" (owe*er !(e*eloci!y (as decreased w(ic( +eans !(a! !(e 'ine!ic ener%y of !(e wa!er (as decreased, By conser*a!ion of ener%y we 'now !(a! if 'ine!ic ener%y decreases" so+e o!(er for+ of ener%y +us! increase, If we loo' a!Bernoulli s e ua!ion" ρ gh" ρ v2 H P = cons!an!" 8w(ic( is a s!a!e+en! of conser*a!ion of ener%y densi!y "we can see !(a! !(e )ressure +us! (a*e increased" P 6 P A, &(en !(e wa!er flows down(ill fro+ !o * i!loses %ra*i!a!ional )o!en!ial ener%y" -u! !(e *eloci!y and (ence 'ine!ic ener%y does no! c(an%e, T(e

)ressure +us! a%ain increase in %oin% fro+ !o * " P * 6 P . Finally" as !(e wa!er flows fro+ * !o 3 !(e*eloci!y decreases a%ain and !(e )ressure +us! once +ore increase" P 3 6 P * . So !(e final )ressure ran'in%will -e P A 7 P 7 P * 7 P 3

a. Bernoulli s e ua!ion follows fro+ Kew!on s laws and is essen!ially a s!a!e+en! of conser*a!ion of ener%yfor fluid flow,a. Bernoulli s e ua!ion says !(a! for an inco+)ressi-le fluid of densi!y ρ: P H ρ gh H ρ v 2 G cons!an!"w(ere P is !(e )ressure in !(e fluid" h is !(e (ei%(! of !(e fluid and v is !(e *eloci!y, T(is is a s!a!e+en! of conser*a!ion of ener%y, Bu!" as fluids are usually considered !o -e con!inuous" ra!(er !(an si+)le o-/ec!s"!(e e ua!ion s!a!es !(e conser*a!ion of ener%y density , #ner%y densi!y is !(e ener%y )er uni! *olu+e, If weloo' a! !(e !er+s in !(e e ua!ion and +ul!i)ly -y a *olu+e we indeed end u) wi!( ener%ies, Pressure ×*olu+e %i*es wor' 8force )er uni! area !i+es a *olu+e %i*es a force × dis!ance " pgh is !(e %ra*i!a!ional

)o!en!ial ener%y )er uni! *olu+e and ρ v2

is !(e 'ine!ic ener%y )er uni! *olu+e,b. ;any ani+als w(ic( li*e in co++unal -urrows (a*e a +ound around one en!rance !o !(e -urrow, T(eair flows fas!er o*er !(e +ound" %i*in% a lower )ressure o*er !(is -urrow en!rance, T(e air inside !(e

-urrow will flow ou! of !(e -urrow due !o !(e )ressure difference" and !(is will draw air in a! o!(er en!rances" 'ee)in% !(e air fres( inside !(e -urrows and )re*en!in% !(e ani+als fro+ suffoca!in%,

2

* 3

A

low v"(i%( P

(i%( v"low P

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. Activit! Questions:Dll !(e ac!i*i!y ues!ions can -e e )lained in !er+s of Bernoulli s Princi)le, For a si+)le +odel in w(ic(air is +o*in% (ori@on!ally" P " ρ v2 G cons!an!, T(us if s)eed of flow increases !(en !(e )ressure +us!decrease, D )ressure difference )roduces a force F G ∆ P , A direc!ed fro+ !(e re%ion of (i%( )ressure !o !(ere%ion of low )ressure,

1. all in an air 5etT(e air /e! (as a *eloci!y )rofile wi!( !(e air in !(e +iddle (a*in% %rea!er *eloci!ies !(an !(e air near !(e ed%es, So if !(e -all is -alanced in !(e air

/e! as s(own" * 1 Q *2 and P 1 P 2, T(is )ressure difference resul!s in a>lif!> force u) w(ic( is e ual and o))osi!e !o !(e wei%(! of !(e -all,

2. *hi ne! effectT(e air rus(in% )as! !(e !o) of !(e c(i+ney (as lower )ressure !(an !(eair in !(e c(i+ney, T(ere is a ne! u)ward force on !(e air and foa+ -allsin !(e c(i+ney" and !(e air and !(e -alls rise, T(is effec! is also used -y

-urrowin% ani+als !o *en!ila!e !(eir -urrows

,

$. lo'ing and liftingDs air rus(es !(rou%( !(e narrow %a) i! s)eeds u) and !(e

)ressure dro)s, T(ere is a!+os)(eric )ressure under !(e )olys!yrene so !(e )ressure difference resul!s in a force u)"e ual and o))osi!e !o !(e wei%(! of !(e )olys!yrene,

&. )'o sheets of paper

T(ere is reduced )ressure -e!ween !(e s(ee!s of )a)er and !(ey+o*e inwards, =!(er e a+)les are )assin% *e(icles" lower endof a s(ower cur!ain curlin% !owards !(e wa!er,


1. S+o'in% causes infla++a!ion of !(e -ronc(ioles" !(e s+all air )assa%es in !(e lun%s" w(ic( !ends !odecrease !(e flow of air in!o !(e lun%s and (ence !(e o y%en su))ly !o !(e -lood, Dir is flowin% down anor+al sec!ion of a -ronc(iole wi!( a dia+e!er of 1 ++ a! a *eloci!y of ,5 +,s 1,a. Par! of !(e -ronc(iole is narrowed due !o infla++a!ion" and (as a dia+e!er of only ,7 ++, &e can usecon!inui!y !o find !(e flow ra!e in !(is re%ion: A1v1 G A2v2,

v2 G A1v1 A2 G πr 1 2

× v1 πr 2 2

G π8 × 1, × 13

+ 2

× ,5 +,s1

π8 × ,7 × 13

+ 2

G 1, +,s1,b. If !(e air +o*es )as! !(e surfaces +uc( fas!er !(en !(e o y%en s)ends less !i+e in con!ac! wi!( !(e %ase c(an%e surfaces and is less li'ely !o -e a-sor-ed" decreasin% !(e o y%en su))ly !o !(e -ody, Toco+)ensa!e for !(is !(e lun%s and (ear! (a*e !o wor' (arder !o %e! +ore o y%en and +o*e i! around +oreeffec!i*ely,

2. &e can use Bernoulli s e ua!ion !o sol*e !(is" !a'in% !(e !o) of !(e !an' as one )oin! D in !(e flow" and!(e %au%e as )oin! B, &e can call !(e (ei%(! a! B hB = " !(en !(e (ei%(! a! D is hD G 1, +, &e (a*e:

P D H ρ gh D H ρ vD 2 G P B H ρ gh B H ρ vB 2" and !(e )ressure a! B is now: P B G P D H ρ gh D H ρ 8vD 2 vB 2

G 1 'Pa H 1 × 1 3 '%,+ 3 × 9, +,s 2 × 1, + H 1 × 1 3 '%,+ 388 , 1 +,s 1 2 ,5 +,s 1 2G 1 'Pa H 9, 'Pa ,25 'Pa G 11 'Pa,

&or's(o) Tu!orials for Tec(nolo%ical and D))lied P(ysics#he (or shop #utorial Pro-ect P 0!+ Pressure 21

air flow

P atm

P < P atm

s+o'e

air flow

P atm

P < P atm

P atm

P atm

P < P atm

v

v2 , P

2

v1 , P 1

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PR3T: 4luid 4lo'


1. Four arran%e+en!s of )i)es are s(own -elow" in eac( of !(e+ wa!er flows fro+ lef! !o ri%(!, T(e crosssec!ional area a! )oin! is A" and a! 0 !(e cross sec!ional area is A or A as s(own,a. For eac( arran%e+en!" draw s!rea+lines and co++en! on !(e *eloci!y and )ressure a! )oin!s and 0,

b.

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1. D !an' is filled wi!( wa!er !o a (ei%(! 2 , D (ole is )unc(ed in one of !(e walls a! a de)!( h -elow !(ewa!er surface 8see fi%ure -elow ,a. S(ow !(a! !(e *eloci!y * wi!( w(ic( !(e wa!er lea*es

!(e (ole is %i*en -y * G √82 ghb. S(ow !(a! !(e dis!ance fro+ !(e -ase of !(e !an' !o!(e )oin! w(ere !(e s!rea+ of wa!er (i!s !(e %round is%i*en -y G 2 √8h8 23hc. $ould a (ole -e )unc(ed a! ano!(er de)!( !o

)roduce a second s!rea+ w(ic( would (a*e !(e sa+eran%e. If so" a! w(a! de)!(.d. D! w(a! de)!( s(ould !(e (ole -e )laced !o +a'e !(ee+er%in% s!rea+ s!ri'e !(e %round a! !(e +a i+u+dis!ance fro+ !(e -ase of !(e !an'.e. T(e )ic!ure is fro+ a !e ! -oo', $an you iden!ify aflaw in i!.

2. D /e! aero)lane is cli+-in% a! an an%le of 25 o !o !(e (ori@on!al a! a cons!an! s)eed, T(e )lane (as 2win%s" eac( wi!( a surface area of 1 , + 2, Dir flows o*er !(e u))er win% surfaces a! 4 , +,s 1 and under !(e lower win% surfaces a! 4 , +,s 1,a. #s!i+a!e !(e )ressure difference -e!ween !(e u))er and lower win% surfaces, Is !(e )ressure %rea!er a-o*e or -elow !(e win%. &(y.b. Eraw a free -ody dia%ra+ s(owin% and na+in% all !(e forces ac!in% on !(e )lane" includin% air resis!ance" -u! ne%lec!in% -uoyancy,c. #s!i+a!e !(e +ass of !(e )lane,

Ea!a: densi!y of air is 1,2 '%,+ 3,


v

4

h

2

25 o

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Solu!ions !o PR3T: 4luid 4lo'


1. Four arran%e+en!s of )i)es are s(own -elow" in eac( of !(e+ wa!er flows fro+ lef! !o ri%(!,a. See dia%ra+, &(ere !(e s!rea+lines are close !o%e!(er !(e *eloci!y is (i%(" and !(e )ressure is low" andw(ere !(ey are far a)ar! !(e *eloci!y is low and !(e )ressure is (i%(,

b. &(en wind flows -e!ween !all -uildin%s i!s *eloci!y increases -ecause !(e cross sec!ional area of !(eflow decreases, If you drew !(e s!rea+lines !(ey would loo' li'e !(e u))er lef! flow,c. T(e %rea!ly increased *eloci!y of !(e airflow resul!s in a lower )ressure, If !(e difference in )ressure

-e!ween !(e inside and ou!side of !(e -uildin% is %rea! enou%(" !(e windows will )o) ou!,

2. Dero)lane )ilo!s )refer !o !a'e off in!o !(e wind !o

+a i+i@e !(e *eloci!y of !(e air )assin% o*er and under !(ewin%" !o %e! +ore lif!, T(e (i%(er *eloci!y air a-o*e !(e win%is a! lower )ressure !(an !(e air -elow" %i*in% a )ressuredifference ∆ P = ρ 8va-o*e 2 v -elow 2 , T(is )ressure )ro*ides!(e u)wards force" called a lif!" on !(e win%,

. Activit! Questions:Dll !(e ac!i*i!y ues!ions can -e e )lained in !er+s of Bernoulli s Princi)le, For a si+)le +odel in w(ic(air is +o*in% (ori@on!ally" P " ρ v2 G cons!an!, T(us if s)eed of flow increases !(en !(e )ressure +us!decrease, D )ressure difference )roduces a force F G ∆ P A direc!ed fro+ !(e re%ion of (i%( )ressure !o!(e re%ion of low )ressure,

(. all in an air 5etT(e air /e! (as a *eloci!y )rofile wi!( !(e air in !(e +iddle (a*in% %rea!er *eloci!ies !(an !(e air near !(e ed%es, So if !(e -all is -alanced in !(e air

/e! as s(own" * 1 Q *2 and P 1 P 2, T(is )ressure difference resul!s in a>lif!> force u) w(ic( is e ual and o))osi!e !o !(e wei%(! of !(e -all,

+. *hi ne! effectT(e air rus(in% )as! !(e !o) of !(e c(i+ney (as lower )ressure !(an !(eair in !(e c(i+ney, T(ere is a ne! u)ward force on !(e air and foa+ -allsin !(e c(i+ney" and !(e air and !(e -alls rise, T(is effec! is also used -y

-urrowin% ani+als !o *en!ila!e !(eir -urrows

,

24

low v" ( i%( P

(i%( v" low P

lif!

low v" (i%( P (i%( v" low P To!al cross sec!ional area re+ains !(e sa+e" so v and P do

no! c(an%e,

To!al cross sec!ionalarea re+ains !(esa+e" so v and P dono! c(an%e,

8

9

9

8

8

9

(i%( v" low P low v" (i%( P

98

air flow

P atm

P < P atm

s+o'e

v2 , P

2

v1 , P

1

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,. lo'ing and liftingDs air rus(es !(rou%( !(e narrow %a) i! s)eeds u) and !(e

)ressure dro)s, T(ere is a!+os)(eric )ressure under !(e )olys!yrene so !(e )ressure difference resul!s in a force u)"e ual and o))osi!e !o !(e wei%(! of !(e )olys!yrene,

-. )'o sheets of paperT(ere is reduced )ressure -e!ween !(e s(ee!s of )a)er and !(ey+o*e inwards, =!(er e a+)les are )assin% *e(icles" lower endof a s(ower cur!ain curlin% !owards !(e wa!er,


1. &a!er flowin% ou! of a !an',a. T(e wa!er flows ou! of !(e (ole wi!( a (ori@on!al *eloci!y of V = 2 γη and @ero *er!ical *eloci!y, I! free

falls 8i%norin% air resis!ance ie falls wi!( accelera!ion of 9, +,s2

, &e can !rea! !(is as )ro/ec!ile +o!ion,$onsider !(e *er!ical +o!ion:

S = ς ο τ +

12

ατ 2 , Σ = ( Η − η ), w(ere V o = 0 , α = γ so !(a! (H − η ) =12

γτ 2 ,τ = 2( Η − η ) / γ

Su-s!i!u!e !i+e in!o e ua!ion for (ori@on!al +o!ion:

x = ς ξ τ so 4= ς ξ 2( Η − η ) / γ and su-s!i!u!in% for V x = ς w(ere V = 2 γη

x = 2 ( Η − η )η b. Fro+ !(e sy++e!ry of !(is e ua!ion a second (ole can -e a! a de)!( of H − η ,c. To find !(e *eloci!y wi!( w(ic( wa!er is co+in% ou! of !(e (ole we use Bernoulli>s e ua!ionP

1 +12

ρς 12 + ργψ 1 = Π 2 +

12

ρς 22 + ργψ 2

KowP

1 = Π

2 = Π

αιρ D! !(e !o) surface of !(e wa!erV

1= 0, ψ

1 = η

w(ile !(e wa!er flowin% ou! of !(e (ole(as V 2 = ς , ψ 2 = 0 ,T(us !(e wa!er flows ou! wi!( V = 2 γη ,d. To %e! !(e +a i+u+ ran%e" 4" we need !o +a i+ise !(e func!ion 8 2 − η )η ,Se! f 8h = (Η − η )η and f > 8h = Η − 2η !(en !(e +a i+u+ ran%e occurs w(en 8 23 2h G "h G 2/ 2,e. Fallin% wa!er" as descri-ed (ere" does no! s)read ou!" i! %e!s narrower as s)eed increases -ecause !(e

)ressure is lower, If we consider !(e e ua!ion of con!inui!y" increasin% !(e *eloci!y of !(e flow as i! fallsalso +eans a decrease in !(e cross sec!ional area of !(e flow, 8 i%( )ressure flows +ay s)read ou! due !o!ur-ulence,

2. Bernouilli s e ua!ion and aero)lanes,a. Bernouilli s e ua!ion says P H ρ gh H ρ v 2 G cons!an!" in !(is case !(e (ei%(!" h will -e al+os! !(esa+e w(ile *eloci!y will -e differen!: P 1 H ρ v1 2 G P 2 H ρ v2 2

&(ic( we can rearran%e !o %e! P 1

P 2

G ρ ,8v1

2

v2

2

G , 1,2 84 ,2

4 ,2

G 422 Pa,

T(e )ressure is %rea!er -enea!( !(e win%" as !(e air is +o*in% +ore slowly (ere, Dlso" if i! was !(e o!(er

way around !(e )lane would -e )us(ed downwards -y !(e air ins!ead of lif!ed,b. T(rus!" T" is in !(e direc!ion of +o!ion, Era%" E" 8air resis!ance is in !(e o))osi!e direc!ion !o !(e +o!ion,&ei%(! force" &" 8+% is down,?if!" ?" is )er)endicular !o !(e direc!ion of +o!ion,c. T(e ne! force is @ero, &e ne%lec! !(e -uoyancy of !(e

)lane 8w(ic( is no! *ery +uc( ,


air flow

P atm

P < P atm

P atm

P atm

P < P atm

v

)

W

3

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?if! force is ? G 2 PA G 44 K, Resol*in% forces in !(e direc!ion of lif!" we see !(a! ? G mg cos θ " so !(e+ass of !(e )lane is m G ? /g cos θ = 44 9, ,cos15o G 92 '%,

26

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PR4B: 4luid 4lo'


1. T(e -e(a*iour of fluids de)ends on !(eir *iscosi!y and densi!y" and !(ese )ro)er!ies also influence !(eway ani+als and +ac(ines can +o*e !(rou%( fluids,a. ow would rowin% -e differen! if wa!er (ad @ero *iscosi!y and w(a! would -irds -e li'e if air (ad @ero*iscosi!y.b. ow would s'ydi*in% and (o! air -alloonin% -e differen! if air (ad @ero *iscosi!y. &(a! if i! (ad +uc(%rea!er *iscosi!y.c. ow would s'ydi*in% and (o! air -alloonin% -e differen! if air (ad @ero densi!y. &(a! if i! (ad +uc(%rea!er densi!y.d. S)iders +o*e -y )u+)in% fluid in!o and ou! of !(eir le%s, &(y are s)iders slower +o*in% in win!er.

2. Blood carries o y%en !o our or%ans" i! !rans)or!s nu!rien!s and w(i!e -lood cells w(ic( (el) !o fi%(!

infec!ion and re+o*es was!e )roduc!s suc( as car-on dio ide fro+ our !issues, I! is i+)or!an! !(a! !(e flowof -lood is consis!en! and !(a! !(e su))ly is no! reduced or cu! off as !issues w(ic( are de)ri*ed of -loodare uic'ly da+a%ed,a. &(y s(ould !ur-ulence +ean !(a! !(e *olu+e ra!e of flow is less !(an in s!rea+lined flow.

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$. Rheological Materials# a+ine !(e *arious +a!erials on !(e !a-le, Dre !(ey fluids. &(a! defines a fluid.;easure !(e flow ra!es of !(e *arious fluids,&(ic( ones are Kew!onian. ow can you !ell.&(a! is (a))enin% !o !(e ones w(ic( are non Kew!onian. ow is !(e *iscosi!y of !(ese fluids c(an%in%

wi!( flow ra!e.


1. Dn ele)(an! wi!( a !run' 2, + lon% is s uir!in% wa!er 8 η G 1, 5×1 3 Pa,s a! a !ouris!, T(e !run' con!ains !wo nos!rils 8!u-es w(ic( are !(e len%!( of !(e !run' and (a*e an in!ernal dia+e!er of 2, c+,T(e flow ra!e is 5, li!res )er second !o!al fro+ !(e !wo nos!rils,a. Eraw a dia%ra+ of !(is si!ua!ion,b. &(a! is !(e a*era%e *eloci!y of !(e wa!er in !(e !run'.c. &(y is !(e !er+ average velocity ra!(er !(an velocity used in )ar! a.

d. &i!( w(a! )ressure is !(e ele)(an! -lowin% !o s uir! !(e wa!er.e. ow (ard would !(e ele)(an! (a*e !o -low if (e were !o s uir! cus!ard 8 ηG 2,5 Pa,sf. $alcula!e !(e Reynold s nu+-er" 6 G vρr η" !o find w(e!(er !(e wa!er and cus!ard flows are la+inar or !ur-ulen!, ρwa!er G 1 '%,+ 3" ρcus!ard G 9 '%,+ 3,g. Eoes one need !o assu+e la+inar flow for answerin% b .

2. T(e +ain ar!ery w(ic( !a'es o y%ena!ed -lood fro+ !(e lef! *en!ricle of !(e (ear! !o !(e -ody is !(eaor!a, I! (as a +ean radius of around 1 c+" -efore -ranc(in% in!o s+aller ar!eries w(ic( su))ly -lood !o!(e *arious or%ans, T(e *iscosi!y of nor+al -lood is around 2,1 × 1 3 Pa,s a! -ody !e+)era!ure,a. If !(e flow ra!e alon% !(e aor!a is 25 l,+in 1" w(a! is !(e )ressure dro) )er cen!i+e!re alon% !(e aor!a.b. &(a! would -e !(e )ressure dro) if !(e flow ra!e was +ain!ained" -u! !(e +ean radius of !(e ar!ery wasreduced !o ,9 c+.c. S+o'in%" a )oor die! and lac' of e ercise con!ri-u!e !o (ardenin% of !(e ar!eries" +a'in% !(e+ less a-le!o fle !o allow %rea!er -lood flow, D die! (i%( in fa! and c(oles!erol can also lead !o !(e for+a!ion of fa!!yde)osi!s in !(e ar!eries, &(y are !(ese con!ri-u!in% fac!ors !o (ear! disease.

2

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Solu!ions !o PR4B: 4luid 4lo'


1. Oiscosi!y and densi!y,a. Rowin% would no! -e )ossi-le" /us! as wal'in% would no! -e )ossi-le if !(ere were no fric!ion, 0ouwould (a*e a *ery li+i!ed reac!ion force" and no! %e! *ery far, ?i'e rowin%" flyin% would -e i+)ossi-le -yfla))in%, Birds could %lide 8or use /e! )ro)ulsion ,b. If air (ad @ero *iscosi!y you d ne*er reac( !er+inal *eloci!y, S'ydi*in% would -e *ery e ci!in% un!il youreac(ed !(e %round -ecause )arac(u!es wouldn ! wor' ei!(er, o! air -alloonin% would -e +uc( !(e sa+ea! @ero *iscosi!y" as -alloons +o*e rela!i*ely slowly, owe*er s!eerin% would -e difficul!, D! *ery (i%(*iscosi!y you d reac( !er+inal *eloci!y *ery uic'ly 8and +ay-e e*en -urn u) li'e a +e!eori!e andascendin% in a (o! air -alloon would -e +uc( slower,c. S'ydi*in% would no! c(an%e +uc( if air (ad lower densi!y" e ce)! !(a! -rea!(in% would -e difficul!, o!air -alloonin% would -e difficul! -ecause -uoyancy would -e +uc( reduced, If air was denser -uoyancywould increase and -alloons would ascend fas!er and -e a-le !o carry +ore wei%(!, If i! was dense enou%(you wouldn ! -e a-le !o s'ydi*e" you d /us! (an% in !(e air,d. S)iders +o*e +ore slowly in win!er -ecause !(e *iscosi!y of !(e fluid in !(eir le%s increases w(en i! %e!scolder, ;os! fluids" includin% -lood" -eco+e +ore *iscous w(en !(ey are cooled,

2. Blood flow,a. Tur-ulence +eans !(a! !(e *olu+e ra!e of flow for a %i*en )ressure is less !(an in s!rea+lined flow

-ecause +uc( of !(e )ressure difference 8force )er uni! area is -ein% used !o )us( !(e fluid in direc!ionso!(er !(an s!rai%(! alon% !(e !u-e,b. &(en !(ere is an o-s!ruc!ed ar!ery !(e effec!i*e radius of !(e !u-e is lower, For *iscous fluids flow ra!e%oes li'e r 4" so e*en a s+all c(an%e in radius (as a -i% effec! on flow ra!e, =-s!ruc!ions also !end !o cause!ur-ulence" fur!(er decreasin% !(e flow ra!e, To 'ee) !(e sa+e flow ra!e" !(e (ear! (as !o wor' (arder !o

)ro*ide a %rea!er dri*in% )ressure,c. For !(e flow ra!e !o increase fro+ 5 D !o5 B w(en !(ere is an o-s!ruc!ed ar!ery !(e(ear! (as !o increase i! s )ressure fro+ P 3 !o

P 4" w(en !(e ar!ery is nor+al i! only (as !oincrease fro+ P 1 !o P 2,Increasin% *iscosi!y also re uires !(e (ear!!o wor' (arder as i! !a'es +ore force !o

)us( !(e -lood around, Se*eral cyclis!s (a*edied fro+ !a'in% )erfor+ance en(ancin%dru%s w(ic( increase !(eir nu+-er of red

-lood cells,

B. Activity Questions:

&. "ot hone!T(e densi!y of !(e (oney c(an%es *ery li!!le w(en i! is (ea!ed, owe*er !(e *iscosi!y c(an%es a lo!" !(e(oney %oes fro+ flowin% *ery slowly !o *ery uic'ly as i!s *iscosi!y decreases,

(. Measuring flo' rateFor real fluids w(ic( (a*e a non @ero *iscosi!y" flow ra!e increases wi!( r 4" so lar%er dia+e!er needles %i*e+uc( %rea!er flow ra!e, Flow ra!e decreases wi!( increasin% len%!(,


Flowra!e"U

5 A

5 !

P 0 P P 7 Pressure

!ur-ulen!

la+inar

P 8

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$. Rheological MaterialsD fluid is a su-s!ance w(ic( will flow !o !a'e !(e s(a)e of i!s con!ainer, So+e fluids" so+e!i+es calledsu)er cooled fluids" flow e !re+ely slowly so i! is *ery (ard !o !ell !(a! !(ey are flowin% a! all, lass is ane a+)le of a su)er cooled fluid,

Kew!onian fluids (a*e cons!an! *iscosi!y wi!( c(an%in% a))lied s!ress, &a!er and wa!er %lycerine +i esare Kew!onian fluids, Pseudo )las!ics (a*e a coefficien! of *iscosi!y" η" w(ic( falls wi!( a))lied s(ear s!ress, D solu!ion of s!arc( will flow uic'ly" and !(en !(e flow ra!e will slow down, T(e force due !o !(efluid a-o*e dro)s as !(e fluid le*el dro)s, Ds !(e force dro)s" η rises" so !(e flow ra!e decreases, Eila!an!fluids do !(e o))osi!e" !(ey (a*e a *iscosi!y w(ic( increases wi!( increasin% s!ress, D corn flour wa!er +iis a %ood e a+)le of a dila!an! fluid, =!(er e a+)les include )rin!in% in's and we! sand, T(e flow ra!e of adila!an! fluid increases wi!( !i+e as !(e s(ear forces dro), Too!()as!e does no! flow un!il a lar%e enou%(s!ress is a))lied" !(en i!s *iscosi!y dro)s suddenly, ence i! will si! on a -rus( wi!(ou! s)readin% ou! anddro))in% off" -u! can s!ill -e s uee@ed ou! of !(e !u-e easily,


1. Dn ele)(an! wi!( a !run' 2, + lon% is s uir!in% wa!er 8 ηG 1, 5×1 3 Pa,s a! a !ouris!, T(e flow ra!eis 5, li!res )er second !o!al" fro+ !(e !wo nos!rils eac( wi!( an in!ernal dia+e!er of 2, c+,a. b. Flow ra!e G 5 li!re,s 1 G 5 × 1 3+ 3,s 1, T(e cross sec!ional

area is 2 ×π×r 2 82 nos!rils G 2×π× , 12G6,3×1 4+ 2,* a*eG flow ra!e area G 5 × 1 3+ 3,s 1 6,3×1 4+ 2 G +,s 1,c. T(e fluid is *iscous so !(e *eloci!y is %rea!es! a! !(e cen!re of !(e !run' and less !owards !(e ed%es" (ence we use a*era%e*eloci!y,

d. ∆P G 5 , ,η l πr 4 G vaveη l/r = × , +,s 1,× 1, 5×1 3 Pa,s × 2, + 8 , 1+ 2 M 1'Pa,e. Kow η G 2,5 Pa,s : ∆P G vaveη l/r = × , +,s 1,× 2,5 Pa,s × 2, + 8 , 1+ 2 G 3,2×1 6 Pa M 3;Paf. 6 G vρr η, For wa!er: 6 Gvρr ηG , +,s 1×1 '%,+ 3× , 1+ 1, 5×1 3Pa,sG , T(is is *ery

!ur-ulen!For cus!ard: 6 Gvρr ηG +,s 1×9 '%,+ 3× , 1+ 2,5 Pa,s G 3 , T(is is no! !ur-ulen!,g. Ko" you don ! need !o assu+e la+inar flow" a*era%e *eloci!y is s!ill flow area,

2. T(e aor!a (as a +ean radius of M1 c+" !(e *iscosi!y of -lood is M 2,1 × 1 3 Pa,s a! -ody !e+)era!ure,a. T(e flow ra!e alon% !(e aor!a is 25 l,+in 1 G , 25 + 3,+in 1 G 4,2 × 1 4 + 3,s1 &e can use Poisueille slaw" flow ra!e , 5, = l

P r η∆π

8

4 "!o find !(e )ressure dro)" ∆ P alon% a len%!( l in a !u-e of radius r , &e wan!

∆ P l so we rearran%e !o %e!:

∆ P l G 4r 5

π

η

= 43B134

+1,8

Pa,s11,2s+12,4

π

×××× −−

= 22 Pa,+1

G 2,2 Pa,c+1

,b. If !(e +ean radius of !(e ar!ery was reduced !o ,9 c+" !(en !(e )ressure dro) would -e

∆ P l G 4r 5

π

η = 43B134

+9,8Pa,s11,2s+12,4

π×××× −− = 34 Pa,+ 1 G 3,4 Pa,c+ 1,

T(is is a 5 N increase in )ressure difference for only a 1 N decrease in radiusc. Ds seen in )ar! b" a s+all decrease in !(e a*era%e radius of !(e aor!a +eans a +assi*e increase in

)ressure difference is needed !o +ain!ain flow ra!e, i*en !(a! !(e len%!( of !(e ar!eries is a))ro i+a!elycons!an!" so !(a! !(e len%!( l does no! c(an%e" !(e !o!al )ressure difference !o +o*e !(e -lood fro+ !(e(ear! !o !(e or%ans +us! dras!ically increase if an ade ua!e flow ra!e is !o -e +ain!ained, T(is +eans !(a!!(e (ear! +us! wor' +uc( (arder !o +ain!ain !(is flow ra!e" and will no! -e a-le !o easily su))ly anincreased ra!e w(en re uired" for e a+)le durin% s!ress or ac!i*i!y, I! is li'ely !(a! !(e flow ra!e will -ereduced" and !(e o y%en su))ly !o or%ans" includin% !(e (ear! i!self" will -e reduced,

3

2 c+v

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PR4T: 4luid 4lo'


$. T(e -e(a*iour of fluids de)ends on !(eir *iscosi!y and densi!y" and !(ese )ro)er!ies also influence !(eway ani+als and +ac(ines can +o*e !(rou%( fluids,a. &(y are differen! %rade +o!or oils used in war+ and cold coun!ries.b. ow would rowin% -e differen! if wa!er (ad @ero *iscosi!y and w(a! would -irds -e li'e if air (ad @ero*iscosi!y.c. ow would s'ydi*in% and (o! air -alloonin% -e differen! if air (ad @ero *iscosi!y. &(a! if i! (ad +uc(%rea!er *iscosi!y.d. ow would s'ydi*in% and (o! air -alloonin% -e differen! if air (ad @ero densi!y. &(a! if i! (ad +uc(%rea!er densi!y.

2. In !(e )ic!ure -elow" a non ideal 8*iscous li uid flows s!eadily !(rou%( a !u-e w(ic( is cons!ric!ed a!

!(e +iddle, T(ree *er!ical s!and)i)es" )ro!rudin% fro+ !(e !u-e" (a*e li uid a! !(e (ei%(!s indica!ed,a. In w(ic( direc!ion is !(e li uid flowin%.b. In w(ic( sec!ion" if ei!(er" is !(e fluid +o*in% fas!er" !(e lef! or !(e ri%(!.c. &(y is !(e li uid colu+n in !(e ri%(! s!and)i)e (i%(er !(an !(e one in !(e +iddle.d. &(y is !(e li uid a! !(e lef! lower !(an a! !(e ri%(!" e*en !(ou%( !(e (ori@on!al !u-e (as !(e sa+edi+ensions a! !(ese !wo )oin!s.


+. "ot hone!oney is a %ood e a+)le of a *iscous fluid,

# )lain w(a! (a))ens !o !(e densi!y and *iscosi!y w(en !(e (oney is (ea!ed, Eoes one c(an%e +ore !(an!(e o!(er.

,. Measuring flo' rateow does !(e dia+e!er of !(e needle affec! !(e flow ra!e.

&(a! a-ou! !(e len%!( of !(e needle.

-. Rheological Materials# a+ine !(e *arious +a!erials on !(e !a-le, Dre !(ey fluids. &(a! defines a fluid.;easure !(e flow ra!es of !(e *arious fluids,&(ic( ones are Kew!onian. ow can you !ell.&(a! is (a))enin% !o !(e ones w(ic( are non Kew!onian. ow is !(e *iscosi!y of !(ese fluids c(an%in%wi!( flow ra!e.


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1. Two s!ro'e en%ines" suc( as !(ose used !o )ower +any lawn +owers and +o!or-i'es" run on a +i !ureof fuel and oil, Bren! is )ullin% a)ar! (is lawn +ower !o ser*ice i!" and is !ryin% !o re+o*e a )is!on, T(e

)is!on (as a dia+e!er of 1 c+ and a len%!( of , c+, I! si!s snu%ly in!o !(e cylinder wi!( a %a) of ,1

++ and a fil+ of fuel and oil fillin% !(is %a), T(e fuel oil +i (as a *iscosi!y of η G , 1 Pa,s,a. &(a! force does Bren! need !o a))ly !o )ull !(e )is!on !(rou%( !(e cylinder a! 1, +,s 1.b. &(a! will (a))en w(en !(e )is!on s!ar!s !o co+e ou! of !(e cylinder.Re-ecca su%%es!s !(a! as wa!er is +uc( less*iscous !(an oil (e s(ould consider usin% afuel wa!er +i ins!ead of !(e !radi!ionalfuel oil +i , Ko! only would !(is +a'e !(een%ine easier !o )ull a)ar!" -u! i! would run

-e!!er as i! would -e fi%(!in% less fric!ion !o+o*e !(e )is!ons,c. &(a! force would -e necessary if !(e

s)ace was filled wi!( a fuel wa!er +i wi!(ηG 1, 5×1 3 Pa,s.d. &(y +i%(! oil -e )refera-le !o wa!er as alu-rican!.

2. D fuel in/ec!or can in/ec! 3 +l of fuel )er +inu!e in!o an en%ine cylinder, T(e in/ec!or is cylindrical"

wi!( a len%!( of 5, ++ and dia+e!er 1, ++, T(e fuel (as a *iscosi!y of ηG 1,2×1 3 Pa,s,a. Eraw a dia%ra+ of !(is si!ua!ion,b. &(a! is !(e a*era%e *eloci!y of !(e fuel in !(e in/ec!or.c. &(y is !(e !er+ average velocity ra!(er !(an velocity used in )ar! b .d. &(a! is !(e )ressure dro) necessary !o ac(ie*e !(is flow ra!e.

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Solu!ions !o PR4T: 4luid 4lo'


1. Oiscosi!y and densi!y,a. Eifferen! %rade +o!or oils are used in war+ and cold coun!ries -ecause !(e *iscosi!y of oil" and +any o!(er fluids"c(an%es wi!( !e+)era!ure, T(e %rade of a +o!or oil is a +easure of i!s *iscosi!y, In cold cli+a!es an oil wi!( lower *iscosi!y is used" as *iscosi!y increases w(en oil cools, In (o! cli+a!es a +ore *iscous oil is used,b. Rowin% would no! -e )ossi-le" /us! as wal'in% would no! -e )ossi-le if !(ere were no fric!ion, 0ou would (a*e a*ery li+i!ed reac!ion force" and no! %e! *ery far, ?i'e rowin%" flyin% would -e i+)ossi-le -y fla))in%, Birds could%lide 8or use /e! )ro)ulsion ,c. If air (ad @ero *iscosi!y you d ne*er reac( !er+inal *eloci!y, S'ydi*in% would -e *ery e ci!in% un!il you reac(ed!(e %round -ecause )arac(u!es wouldn ! wor' ei!(er, o! air -alloonin% would -e +uc( !(e sa+e a! @ero *iscosi!y" as

-alloons +o*e rela!i*ely slowly, owe*er s!eerin% would -e difficul!, D! *ery (i%( *iscosi!y you d reac( !er+inal*eloci!y *ery uic'ly 8and +ay-e e*en -urn u) li'e a +e!eori!e and ascendin% in a (o! air -alloon would -e +uc(slower,d. S'ydi*in% would no! c(an%e +uc( if air (ad lower densi!y" e ce)! !(a! -rea!(in% would -e difficul!, o! air

-alloonin% would -e difficul! -ecause -uoyancy would -e +uc( reduced, If air was denser -uoyancy would increaseand -alloons would ascend fas!er and -e a-le !o carry +ore wei%(!, If i! was dense enou%( you wouldn ! -e a-le !os'ydi*e" you d /us! (an% in !(e air,

2. Flow of a *iscous fluid,a. T(e li uid is flowin% fro+ ri%(! !o lef!,b. T(e areas of !(e lef! and ri%(! sec!ions are !(e sa+e" so -ycon!inui!y !(e *eloci!y in !(ese !wo sec!ions +us! -e !(e sa+e,c. Ds !(e li uid +o*es in!o !(e narrow sec!ion i! s)eeds u) 8area × *eloci!y G cons!an! , If area decreases *eloci!yincreases, Since !(e li uid in !(e narrower sec!ion (ad (i%(er *eloci!y" i! (as lower )ressure !(an !(e li uid in !(e

wider sec!ion ence !(e le*el in !(e +iddle is lower !(an !(e le*els on !(e ri%(! or lef!,d. If !(e li uid were an ideal fluid" !(e )ressure would -e !(e sa+e a! !(e lef! and ri%(! )oin! -ecause !(e !u-e (as !(esa+e si@e, T(e loss in )ressure" as seen -y co+)arin% !(e lef! and ri%(! le*els" is due !o in!ernal fric!ion in !(e li uid"w(ic( +os!ly occurs w(en i! rus(es !(rou%( !(e narrow sec!ion, T(is is a non ideal fluid and so Bernoulli s e ua!iondoes no! a))ly, So+e ener%y 8)ressure is los! as (ea!,

B. Activity Questions:

1. "ot hone!T(e densi!y of !(e (oney c(an%es *ery li!!le w(en i! is (ea!ed, owe*er !(e *iscosi!y c(an%es a lo!" !(e (oney %oesfro+ flowin% *ery slowly !o *ery uic'ly as i!s *iscosi!y decreases,

2. Measuring flo' rateFor real fluids w(ic( (a*e a non @ero *iscosi!y" flow ra!e increases wi!( r 4" so lar%er dia+e!er needles %i*e +uc(%rea!er flow ra!e, Flow ra!e decreases wi!( increasin% len%!(,

$. Rheological MaterialsD fluid is a su-s!ance w(ic( will flow !o !a'e !(e s(a)e of i!s con!ainer, So+e fluids" so+e!i+es called su)er cooledfluids" flow e !re+ely slowly so i! is *ery (ard !o !ell !(a! !(ey are flowin% a! all, lass is an e a+)le of a su)er cooled fluid, Kew!onian fluids (a*e cons!an! *iscosi!y wi!( c(an%in% a))lied s!ress, &a!er and wa!er %lycerine +i esare Kew!onian fluids, Pseudo )las!ics (a*e a coefficien! of *iscosi!y" η" w(ic( falls wi!( a))lied s(ear s!ress, Dsolu!ion of s!arc( will flow uic'ly" and !(en !(e flow ra!e will slow down, T(e force due !o !(e fluid a-o*e dro)s as!(e fluid le*el dro)s, Ds !(e force dro)s" η rises" so !(e flow ra!e decreases, Eila!an! fluids do !(e o))osi!e" !(ey (a*e

a *iscosi!y w(ic( increases wi!( increasin% s!ress, D corn flour wa!er +i is a %ood e a+)le of a dila!an! fluid, =!(er e a+)les include )rin!in% in's and we! sand, T(e flow ra!e of a dila!an! fluid increases wi!( !i+e as !(e s(ear forcesdro), Too!()as!e does no! flow un!il a lar%e enou%( s!ress is a))lied" !(en i!s *iscosi!y dro)s suddenly, ence i! willsi! on a -rus( wi!(ou! s)readin% ou! and dro))in% off" -u! can s!ill -e s uee@ed ou! of !(e !u-e easily,


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1. Pullin% a )is!on ou!,a. To find !(e force we can use !(e defini!ion of *iscosi!y, If !wo )la!es are se)ara!ed -y a layer of fluid"!(en a force F is needed !o +o*e one )la!e rela!i*e !o !(e o!(er a! a *eloci!y v" and !(is force is %i*en -y

F G y Avη w(ere η is !(e *iscosi!y of !(e fluid" A is !(e area of !(e )la!es and y is !(e !(ic'ness of !(e fluid

se)ara!in% !(e+, In !(is case we (a*e a )is!on" w(ic( is se)ara!ed fro+ !(e cylinder -y a !(in fluid filled%a), T(e !(ic'ness of !(e %a) is *ery +uc( s+aller !(an !(e dia+e!er of !(e )is!on" so we can consider !(esurfaces of !(e cylinder and !(e )is!on as !wo )la!es, T(e area of !(e )la!es is A G 2πr ×l w(ere l is !(elen%!( of !(e )is!on and r is !(e radius of !(e )is!on"

A G 2π×5 × 1 2 + × × 1 2 + G , 25 + 2,&e can now find !(e force:

F G y Avη G

+11,+,s,1+25,Pa,s1,

3

12

−

−

××× G 2,5 K,

b. Ds Bren! )ulls !(e )is!on ou! !(e area" A" decreases" so !(e force needed !o +ain!ain !(a! *eloci!ydecreases also,

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PR5B: Surface )ension


1. $(ro+a!o%ra)(y is used -y c(e+is!s" )(ysicis!s and -iolo%is!s !o se)ara!e co+)onen!s of a %as or li uid, For e a+)le" !(is is (ow EKD fin%er)rin!in% is done !o de!er+ine )aren!a%e or in forensic +edicine!o de!er+ine w(o was !(e cri+inal,D si+)le under%radua!e -ioc(e+is!ry )rac!ical uses c(ro+a!o%ra)(y !o do si+)le EKD fin%er )rin!in%,T(e EKD is e !rac!ed fro+ !(e cells and )u! in!o a solu!ion, T(e EKD in solu!ion is !(en -ro'en in!ofra%+en!s usin% an en@y+e, Ero)le!s of !(e solu!ion con!ainin% !(e EKD fra%+en!s are )u! on!o a )iece of

)a)er w(ic( is sus)ended in a -ea'er wi!( !(e end /us! di))in% in!o a sol*en! as s(own,

a. # )lain (ow !(e fra%+en!s of !(e EKD are se)ara!ed -y !(e +o*e+en! of !(e sol*en!,

b. &(y is )a)er used for !(is ra!(er !(an )las!ic.

2. ?a)lace s law s!a!es !(a! a! e uili-riu+ r 8 P i3P o G 2γ ,a. &(a! does eac( of !(ese sy+-ols +ean.T(e dia%ra+ s(ows !(e al*eoli" !(e s+alles!

-ranc(es of a -ronc(iole and !(e si!e of %ase c(an%e in !(e lun%s, T(e )ressure inside !(elun%s is fairly cons!an! and close !oa!+os)(eric )ressure, T(e al*eoli are linedwi!( a surfac!an!" al!(ou%( +any )re+a!ure

-a-ies (a*e an inade ua!e layer of surfac!an!w(ic( +a'es -rea!(in% *ery difficul! for !(e+,T(e surfac!an! is +ade u) of lon% +olecules called li)o)ro!eins, T(e li)o)ro!eins lie al+os! side -y sideclose !o%e!(er un!il you in(ale" e )andin% !(e al*eoli and )ulin% !(e+ a)ar!" and increasin% !(e wall!ension, &(en you e (ale !(e li)o)ro!eins slide -ac' !o%e!(er and !(e wall !ension decreases,b. Eraw a si+)le dia%ra+ s(owin% !(e lun%s and c(es! ca*i!y 8)leural ca*i!y , ?a-el P i and P o on your dia%ra+ and on !(e dia%ra+ s(own a-o*e,&(en you in(ale !(e al*eoli e )ands" and !(e )leural )ressure decreases,c. By w(a! +ec(anis+ do you c(an%e P o as you -rea!(e.d. &(a! +us! (a))en !o !(e surface !ension" γ " !o allow in(ala!ion !o !a'e )lace.&(en you e (ale" r decreases and P o increases,e. &(a! +us! (a))en !o !(e surface !ension now.


sol*en!

EKD+i !ure

)a)er

r

Pleura c(es!

ca*i!y

-ronc(iole al*eoli

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1. *apillarit!# )lain w(y wa!er rises !o differen! (ei%(!s in differen! dia+e!er ca)illary !u-es,Is !(is (ow wa!er rises !o !(e lea*es in )lan!s.

&a!er rises u) -e!ween !wo %lass )la!es -u! no! -e!ween )ers)e )la!es, # )lain w(y,

2. Surface tension ; floatingIs i! )ossi-le for a needle !(a! is ini!ially we! !o floa! on wa!er.Dn e !ra lar%e needle will no! floa! on wa!er w(ile a s+all one will, # )lain w(y,;a!c(s!ic's are +ade of wood" and floa!,&ould you e )ec! an e !ra lar%e +a!c(s!ic' !o floa! on wa!er /us! as well as a s+all one.# )lain w(y or w(y no!,

$. Surface tension ; detergentsFill a cu) wi!( wa!er and s)rin'le so+e )e))er on !o),

Ddd a dro) of li uid soa), # )lain w(a! (a))ens,

&. Surface tension < paintbrushT(e -ris!les of a )ain!-rus( loo' differen! w(en !(ey are su-+er%ed in wa!er !o w(en !(ey are ou! of !(ewa!er -u! s!ill we!, ow are !(ey differen! and w(y.

(. Soap fil sT(e wire loo) (as a )iece of !(read across i!,Ei) !(e loo) in!o !(e soa) solu!ion so !(a! you %e! a soa) fil+ across !(e en!ire loo),

Kow )unc!ure !(e fil+ on one side of !(e !(read,&(a! (a))ens !o !(e !(read and !(e re+ainin% fil+. # )lain your o-ser*a!ions,

# )eri+en! wi!( for+in% -u--les in !(e differen! fra+es,&(a! do you no!ice a-ou! !(e surfaces of !(e -u--les.

*. Quantitative Questions: 1. &a!er is !rans)or!ed u) !rees -y !(e yle+" w(ic( are dead (ollow !u-es, T(e yle+ are ri%id !u-es"wi!( a !y)ical dia+e!er of around 2 µ+" w(ic( also %i*e a )lan! s!ruc!ural su))or!, T(e inside of !(e

yle+ are effec!i*ely we!!ed -y wa!er so !(a! !(e con!ac! an%le is @ero, T(e surface !ension of wa!er is, 73 K,+ 1 and i! (as a densi!y of 1 '%,+ 3,

a. &(a! is !(e +a i+u+ (ei%(! !(a! ca)illary )ressure can raise wa!er !(rou%( !(e yle+ of a !ree.b. ow does !(is co+)are !o !(e !y)ical (ei%(!s of !rees.

c. &(a! o!(er fac!ors or +ec(anis+s +ay -e necessary !o raise wa!er fro+ !(e %round !o !(e lea*es of a!ree.

2. D! !(e end of e (ala!ion !(e radius of an al*eoli is , 5 ++, T(e %au%e )ressure inside !(e al*eoli is 4 Pa" ou!side in !(e )leural ca*i!y !(e )ressure is 534Pa,a. &(a! is !(e wall !ension in !(e al*eoli.b. ow does !(is co+)are !o a wall !ension of , 5 K,+ 1 wi!(ou! surfac!an!.

36

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Solu!ions !o PR5B: Surface )ension


2. EKD fin%er)rin!in% usin% c(ro+a!o%ra)(y,c. T(e +o*in% wa!er carries !(e fra%+en!s of EKD alon% wi!( i!, T(ere is an u)ward force due !o !(ewa!er and a downward force" mg, due !o %ra*i!y, T(e force due !o !(e wa!er decreases wi!( increasin%(ei%(!" w(ile !(e %ra*i!a!ional force re+ains 8a))ro i+a!ely cons!an! , ence li%(!er fra%+en!s of EKDare carried fur!(er u) !(e )a)er,d. Pa)er is used ra!(er !(an )las!ic -ecause )a)er is fi-rous, T(e s+all %a)s -e!ween !(e fi-res ac! asca)illary !u-es" causin% !(e wa!er !o rise, =!(er )orous +edia suc( as a s)ecial %el coa!ed )las!ic can also

-e used" -u! nor+al )las!ics are no! )orous and wa!er will no! rise on !(e+,

2. ?a)lace s law s!a!es !(a! a! e uili-riu+ r 8 P i3P o G 2γ ,a. r is !(e radius of !(e -u--le or dro)" P i is !(e in!ernal )ressure" P o is !(e e !ernal )ressure and γ is!(e surface !ension" w(ic( is !(e force )er uni! len%!( e er!ed -y a surface,b. see dia%ra+s,

c. 0ou c(an%e P o -y e )andin% your c(es!, T(is increases !(e *olu+e so !(e )ressure in !(e )leuralca*i!y +us! decrease, &(en you rela i! a%ain !(e *olu+e decreases" increasin% !(e )ressure inside,d. If r increases and a! !(e sa+e !i+e P o decreases w(ile P i re+ains a))ro i+a!ely cons!an!" !(en !(elef! (and side (as increased, To +ain!ain e uili-riu+ γ +us! also increase" o!(erwise !(e al*eoli wouldincrease in si@e and ru)!ure,e. T(is is !(e o))osi!e !o d" r decreases as does !(e )ressure difference" so γ +us! also decrease, If i!didn !" !(e lun%s would colla)se,T(e surfac!an! is +ade u) of lon% +olecules called li)o)ro!eins, T(e li)o)ro!eins lie al+os! side -y sideclose !o%e!(er un!il you in(ale" e )andin% !(e al*eoli and )ulin% !(e+ a)ar!" and increasin% !(e wall!ension, &(en you e (ale !(e li)o)ro!eins slide -ac' !o%e!(er and !(e wall !ension decreases,


1. *apillarit!

&a!er +olecules are a!!rac!ed !o %lass +ore !(an !o eac( o!(er, &(en !(e %lass !u-es are di))ed inwa!er !(e ad(esion -e!ween !(e %lass and wa!er causes a !(in fil+ of wa!er !o -e drawn u) o*er !(e%lass 8a , Surface !ension causes !(is fil+ !o con!rac! 8- , T(e fil+ on !(e inner surface con!inues !ocon!rac!" raisin% wa!er wi!( i! un!il !(e wei%(! of !(e wa!er is -alanced -y !(e ad(esi*e force 8c ,$a)illary rise (el)s" -u! i! does no! allow %rea! enou%( wa!er rise for )lan!s" !(ey rely on )ressuredifference -e!ween !(e !o) of !(e wa!er colu+n 8!(e lea*es and !(e -o!!o+ 8!(e roo!s ,&a!er does no! ad(ere !o )ers)e " (ence i! will no! rise -e!ween )ers)e )la!es" -u! i! will rise -e!ween%lass )la!es,


lun%s" P i

c(es! ca*i!y" P o

Pleurac(es!ca*i!y

r

P i

P o

ca -

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2. Surface tension ; floating&(en a needle floa!s on wa!er !(e surface of wa!er ac!s li'e a s!re!c(ed s'in 8!ra+)oline and !(e needlesi!s on i!, T(e s'in lowers if !(e needle is (ea*ier, If !(e needle is !oo (ea*y and !(e s'in canno! su))or!!(e wei%(! of !(e needle" !(e s'in ru)!ures, T(e s'in can also ru)!ure if i! is )ric'ed, So if !(e needle isli%(! enou%( !o -e su))or!ed -y !(e s'in -u! !(e s'in is )ric'ed in !(e )rocess of +a'in% i! floa! !(e needlesin's, T(e needle s(ould %o on )arallel !o !(e wa!er surface so !(a! !(e )ressure" P G F A" is +ini+ised -y

+a i+isin% !(e area A, If !(e needle is ini!ially we! !(e wa!er on !(e needle /oins !(e wa!er in !(e con!ainer and is e ui*alen! !o a )ric'ed s'in" so a we! needle will no! floa!, T(e wei%(! of an e !ra lar%e needlecanno! -e su))or!ed -y !(e surface !ension,&ood floa!s in wa!er due !o -uoyancy -ecause i! is less dense !(an wa!er" so an e !ra lar%e +a!c(s!ic' willfloa!, D needle can only floa! on wa!er due !o surface !ension,

$. Surface tension ; detergentsT(e +o!ion of !(e )e))er is due !o !(e lowered surface !ension wi!( !(e de!er%en! fil+, T(e de!er%en! fil+is li'e a s!re!c(ed +e+-rane w(ic( is wea' in !(e +iddle, &(en a (ole for+s i! e )ands and !(e )e))er is+o*ed away fro+ !(e cen!re wi!( !(e re!rac!in% fil+,

&. Surface tension < paintbrush&(en !(e )ain! -rus( is )ulled ou! of !(e wa!er !(e surface !ension of !(e wa!er on !(e -ris!les )ulls !(e+!o%e!(er, &(en i! is in !(e wa!er !(ere is no force due !o surface !ension )ullin% !(e -ris!les !o%e!(er" and!(e -uoyan! force and s+all curren!s in !(e wa!er fluff ou! !(e -ris!les,

(. Soap fil s&(en !(e fil+ inside !(e loo) of !(read is )unc!ured" !(e loo) !a'es u) a circular s(a)e, T(is is !(e s(a)ewi!( !(e +a i+u+ inside surface area !(e !(read can for+, T(e surface area is !(e !o!al area +inus !(a! in!(e !(read" so !(is %i*es !(e +ini+u+ !o!al surface area, Surface !ension is a +easure of ener%y )er uni!area !o crea!e a surface" !(e -i%%er !(e surface !(e +ore ener%y re uired, &(en %i*en a c(ance" a surface8li'e any!(in% else" includin% )eo)le will %o !o i!s lowes! ener%y s!a!e" w(ic( is !(e +ini+u+ )ossi-le

surface area, ence freeJ -u--les are s)(erical" %i*in% !(e +ini+u+ surface area for !(e *olu+e of air,

*. Quantitative Questions: 2. yle+ in !rees,a. &e wan! !o find !(e +a i+u+ (ei%(! !(a! ca)illary )ressure can raise wa!er !(rou%( !(e yle+ of a !ree,T(e force due !o !(e surface !ension is F G γ 9 G γ 2πr for a circular !u-e suc( as !(e yle+, T(e *er!icalco+)onen! of !(is force is F * G γ 2πr cos φ G γ 2πr if !(e con!ac! an%le is s+all,T(e o!(er force ac!in% on !(e wa!er is %ra*i!y" ( G mg = ρ Vg = ρ πr 2hg , &(en !(e wa!er reac(es i!s+a i+u+ (ei%(! !(e !wo forces are in e uili-riu+" and ( G = ρ πr 2hg G γ 2πr.

rearran%in% for !(e (ei%(! h %i*es: h G +12+,s,9'%,+1 K,+73,22

623

1

−−−

−

×××

×

= ρ γ ρ γ

G ,74 +,b. ;os! !rees are +uc( !aller !(an ,74 +" +any are well o*er !en !i+es !(is (ei%(!, So ca)illary rise canno! accoun! for !(e rise of wa!er !o !(e !o)s of !rees" so+e o!(er +ec(anis+ is necessary,c. Trees (a*e )ores in !(eir lea*es !(rou%( w(ic( wa!er e*a)ora!es" crea!in% a lower )ressure a! !(e !o) of !(e yle+, T(is )ressure difference also (el)s !o draw wa!er u) !(e yle+,

$. D! !(e end of e (ala!ion !(e radius of an al*eoli is , 5 ++, T(e %au%e )ressure inside !(e al*eoli is 4 Pa" ou!side in !(e )leural ca*i!y i! is 534Pa,a. &e can use ?a)lace s law : r 8 P i3P o G 2γ " !o find !(e wall !ension" γ ,γ G : r 8 P i3P o G × , 5 × 1 3 + 8 4 Pa 534 Pa G 3,4× 1 3 K,+ 1 G , 3 K,+ 1,

b. D wall !ension of , 5 K,+1

wi!(ou! surfac!an! is +ore !(an 1 !i+es %rea!er !(an !(e wall !ension wi!(surfac!an!, I! would -e *ery (ard !o e )and an al*eoli wi!( suc( a lar%e !ension" +a'in% -rea!(in% *ery*ery difficul!,

&or's(o) Tu!orials for Tec(nolo%ical and D))lied P(ysics3

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PR5T: Surface )ension


1. T(e under%round wa!er !a-le is *ery i+)or!an! in +any )laces w(ere -ores are used !o su))ly wa!er"for e a+)le in +any re%ional areas w(ere !(ere is no !own wa!er and unrelia-le rainfall, T(e de)!( of

-ores *aries fro+ )lace !o )lace, #*en o*er ui!e s(or! dis!ances !(e de)!( of !(e wa!er !a-le can *arysu-s!an!ially due !o soil !y)e" and a dee)er -ore is +ore e )ensi*e !o di%" and re uires a lar%er )u+)w(ic( uses +ore ener%y !o run, &(y is !(e wa!er !a-le (i%(er in fine %rained soils !(an in coarse %rainedsoils.

2. ;os! car was( -o!!les reco++end wa in% 8wi!( a wa of !(e sa+e -rand as !(e de!er%en! of courseaf!er you (a*e was(ed your car and dried i! !(orou%(ly,

ow does wa in% a car (el) !o 'ee) i! clean. Eraw a dia%ra+ s(owin% !(e con!ac! an%les of wa!erdro)le!s wi!( and wi!(ou! wa !o (el) e )lain your answer,


1. Surface tension ; floatingIs i! )ossi-le for a needle !(a! is ini!ially we! !o floa! on wa!er. Dn e !ra lar%e needle will no! floa! onwa!er w(ile a s+all one will, # )lain w(y !(is is !(e case,;a!c(s!ic's are +ade of wood, &ould you e )ec! an e !ra lar%e +a!c(s!ic' !o floa! on wa!er /us! as wellas a s+all one. # )lain w(y or w(y no!,

2. Surface tension ; detergentsFill a cu) wi!( wa!er and s)rin'le so+e )e))er on !o),Ddd a dro) of li uid soa), # )lain w(a! (a))ens,

$. Surface tension < paintbrush.T(e -ris!les of a )ain!-rus( loo' differen! w(en !(ey are su-+er%ed in wa!er !o w(en !(ey are ou! of !(ewa!er -u! s!ill we!, &(y.

&. *apillarit!# )lain w(y wa!er rises !o differen! (ei%(!s in differen! dia+e!er ca)illary !u-es,&a!er rises u) -e!ween !wo %lass )la!es -u! no! -e!ween )ers)e )la!es, # )lain w(y !(is is !(e case,

old !(e )la!es !o%e!(er a! one end and use a )a)er cli) or lu+) of -lu !ac' !o (old !(e+ sli%(!ly a)ar! a!!(e o!(er side, &(a! (a))ens w(en you )u! !(e -o!!o+ of !(e )la!es in!o !(e wa!er. Eescri-e and e )lainw(a! you o-ser*e,


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