1. /.1 I 1.1 The force. F. of the wind blowing against a building is given by F = CDPV'A/2. where Vis the wind speed. P the density of the air. A the cross-sectional area of the building. and CDis a constant tenned the drag coefficient. Detennine the dimensions of the drag coefficient. Qr Thus) F i: ML T-' e,;, (VlL-3 V.= L 7-1 I/L2. C/) -J; (!YIL T 2)/UML"l)(L T -,)2- (L")] =: M 0 LO TO HenceJ CD is dimensionless. I-I

2. /.2. I (6 ) L2 YeJify the dimensions, in both the FLTand MLTsystems, of the following quantities which appear in Table 1.1: (a) vol ume, (b) acceleration, (e) mass, (d) moment of inertia (area), and (e) work. Volume L3 t-ITn! r' of- c.hl/n1 yt/o,/';'y L T -, -=- L T -.2. T () 1ir1.a.sS M or- w;tn F"':" M L 7-2 rm;l5S= !=L-'TZ (vi) mOI7lt!I'Jt- 11- ,nu!:,p.. (Art'.c.) :: sel1d l7111mt'"f "f art!. (L2. ) (L 2) . L If !=L WtN"k: /-1.. 3. 1.3 I 1.3 Determme the dimensions, in both the FLT system ancd'j a reA. rn meni-llm volume (P)(LT-') PL-' r-I L2- . (I1f.T-1(LT-').=.. I1T-3 rnps " Ve/oci.f V&)/Unt (FT2L-t)(L 7-1) L3 /-3 4. 1.4- I (a.) (b) (c) VI- Verify.lhe dimensions. in both the FLT system and the MLT system. of the following quantities whicA-.appear in Table 1.1: (a) fre quency. (b) stress. (e) strain. (d) torque, and (e) work. .51-rss Since. rce -- Ol"t!'tt F-'- M L rl.- ) .5.J-r5s ;" F :;- L2. ML r-2 L"- C)"'1.n1t!' I", /e/lji"h ...: It'l1fll1 FL-2 - 1'1L -I T-2 L . L FL = (e) work = ..force. dis/t,nu!. - FL I-lf 5. /.5 I (aJ (h) (C) 1.5 Ifu is a velocity, x a length, and t a time, what are the dimensions (in the MLTsystem) of (a) aulat, (b) a'ulaxat, and (c) I (aulat) dx? PtA.. L T-1 L T-Z- - - dt:- T zu. L T-1 . T-2- - h(}t {L){T} fJu. dx . (iT-I) fL)- - dt; T /- 5 L 2 T-.2 6. /. 6 I 1.6 If p is .8 pressure, Va velocity, and p a fluid density what are the dimensions (in the MLT system) of (a) pip (b) pVp, and (c) p/pV2? ' (a. ) 1- 6 7. 1.7 I (a.J (h) (C: ) 1.7 If V is a velocity, e a length, and v a fluid properly (the kine matic viscosity) having dimensions of L2T-', which of the fol lowing combinations are dimensionless: (a) vev, (b) velv, (c) vtv, (d) Vlev? VJ.-z/ - (L T-,)(L)fL2.r - L T-l fn"f tltmeniot1less) vj (L7-')(L) . LOTfj (dimnsicm less)- - -V (L '2. r-I) V 2 7/ - (L T-'2.(L2. r-'j L"T-3 (nof dimfns/on/(ss) (d) V . (LT-1) , -2.. (no! dlfnension/e:'j)L ).7/ (L )(e r') - /-7 8. 1.8 T 1.8 If V is a velocity, detennine the dimensions of Z, a, and G, which appear in the dimensionally homogeneous equation V = Z(a - I) + G v == r (o(-I) -t- G [LT-J == [r][0nJlfyt -/:0 ;V/--m 3, /-/6 o 17. (a) (b) - -- . o o 1.1q For Table 1.4 verify the conversion re- lationships for: (a) acceleration, (b) density, (e) pressure, and (d) volume flowrate. Use the basic conversion relationships: 1 m = 3.2808 ft; 1 N = 0.22481 lb; and 1 kg = 0.068521 slug. 3.2;/ 1-1: 5" Thf.;ls; me.c/h'pllj trn/s' b:f 3.;28/ 1:0 e'nileyi -to -!-t/.s '-. _ I 40 ;< 10-3 S//.{5S. 1 .f-t3 Thl.4s) mul+ipllj --'1 a. il1 de'pend,d t!)f 3 - IY>1, os S d/rnMsion/ess -the. uni t /-1 'I c ') /.25 partlrne-t ey :Jfjs-fem. IS 20. 1.2-3 .23 A ta . nk contains 500 kg of a liquid whose specific gravity is . DetennlOe the volume of the liquid in the tank. m::: V := SG r/hO V Thus, V:= m/(SG PI/1.0 ) = SOO K9j((2)(qqq )) = 0.2';0 m3 J.2Jf , I I.Z'f- Clouds can weigh thousands of pounds due to their liquid water content. Often this content is measured in grams J + . , per cubic meter (glm3). Assume that a cumulus cloud occupies - ++t a volume of one cubic kilometer. and its liquid water content e is 0.2 glm3 (a) What is the volume of this cloud in cubic + - miles? (b) How much does the water in the cloud weigh in t pounds? , , . i .'.' I r = 3]1; ul 1+ + ti r- I + I + + ,.-Yot,LLL .' (;01,1114(:-5'.i8'1 ).J , . I (s.Z3b IIJJ 'ft) +--1----,--1- + .. 1:-p. 2 13 /-20 21. o o " ':,,v r------------------------------------------, I.;Z .5 I 1.25 A tank of oil has a mass of ZS- slugs, (a) Determine its weight in pounds and in new tons at the earth's surface, (b) What would be its ,'mass (in slugs) and its weight (in pounds) if 10- .. cated on the moon's surface where the gravita tional attraction is approximately one-sixth that at the earth's surface? ( It) w.e i:Jh f ;: tf as.s x. d - (25 5/uqS) (32,.2 )= _80S Ib - (ZSS/U9S)(It;,Sf ) (l.g/ ;,.)=- 3S"8o.lI/ (b) t???4S,$ = .25' :;/'.((lS (tyr.ASS clots j'J/)t depfnd II JY'vikfiIJHQ/ a H-rad-it)f1 ) w.eijlJi = (25"' S/U'j5 ) (32.:) :::: /3Lf 11, /.6-'-1------------------------------------1.2,6 A certain object weighs 300 N at the earth's surface. Detennine the mass of the object (in kilograms) and its weight (in newtons) when located on a planet with an acceleration of gravity equal to 4.0 ft/s2. l?'yta,55 - -- fo fi/s2 ) - (30,r;, Jj. ) (If, 0 r;;) (0. 301ft ;; ) N /- 2.1 22. 1,2.7 I 1.27 The density of a certain type of jet fuel is 775 kg/m'. Determine its specific gravity and specific weight. 0,775" - (775 !::1.) (q; / )= 7. fa() Y3/?n 3 S /111 23. 1,1-1 I 1.28 A hydrometer is used to measure the specific gravity of liq uids. (See Video V2.8.) For a certain liquid a hydrometer read ing indicates a specific gravity of 1.15. What is the liquid's den sity and specific weight? Express your answer in SI units. 5G - , - t- t t- /-2.3 I r 24. 1,1). j, Z 9 J 1.'2..q An open, rigid-walled, cylindrical tank contains 4 ft3 of water at 40 of. Over a 24-hour period of time the water temperature varies from 40 of to 90 of. Make use of the data in Appendix B to determine how much the volume of water will change. For a tank diameter of 2 ft, would the corresponding change in water depth be very noticeable? Explain. InllsS of. WtJ.-/;ey =- -Xf tJheve -If Is jne lIo/l1me and;; 171e derlsrf3-'1< 'Th",s) fll'llllr$ 0.0214- != O. D 1'15- fe.. ,.-r... /.2 Z /Il"2 1-30 Je,- 0.D2.14 """3I'm :: I. 2. '2 -h /l!'13 - 1. t'J 5 010 31. ,,",,, v 1.3 q A closed tank having a volume of 2 ft3 is filled with 0.30 lb of a gas. A pressure gage attached to the tank reads 12 psi when the gas temperalUre is 80 OF. There is some Question as to whether the gas in the tank is oxygen or helium. Which do you think it is? Explain how you arrived at your answer. ' . id/j t = tJ. go IJ, 1= #x. volwme (.J2z-Pj.. )6.. fe) Since. ( ;: -trno.sther,c ,;{h wftn jOYe.JStlre as.,Sumed -h, T:::. (J'IJor + If.iJ) OR (2/,,7 ty::: -3 / 1.t, )( /0 oS wl/S H3 (121'" /'1':7) tS/ h( II/-: 7 ,..r/a ) ti .ft, /fellj 1:hll b 3 Ttt/,Ic I. 7 R :: / 5"SIf)( If) /OY A of ; = /. 2 t;.Z )( /0 If Ii, /), ./-0;- Sf/.(9 ' Dj ::: 9. 81X/O-a..J!V1 (Jlbj(s/vJfl/S2)) = Q.82X10-;Wff . s" Hence, 'W == 9.f2XIO-;(68,.ooofP) ,;: 668 /b /-33 34. J-- Master Typing Sheet I00( Reduct{)I 8 1/:2 x I I tnm size - I *1.43 Develop a computer program for calculating the density of an ideal gas when the gas pressure in pascals (abs), the tem perature in degrees Celsius, and the gas constant in J/kg' K are specified. Plot the density of helium as a function of temperature from 0 C to 200 C and pressures of 50, 100, ISO, and 200 kPa (abs). I I --...., .....- . I I T I I I (')htl'< -r iJ IIl.j,,/"j. ;oY'usJ kl1h 9AS aJ..,s J.11 t anA T i-(lbs()/",,-k -iempua-blre. Ti-t-'ws 1-1 1ht! i:mJ cuye Is 111 "C I --tn1el1 - 1 ,1 I -+--1-+1 --fl. .2.05''I,c/O h">. );::: 1.3x/O-Z'' (8G"" /-36 iJ.5 Tl; "" ... 37. /. /f7 I 1.41 One type of capillary-tube viscometer is shown in Video V 1.5 and in Fig. Pl.41 . For this device the liquid to be tested is drawn into the tube to a level above the top etched line. The time is then obtained for the liquid to drain to the bottom etched line. The kinematic viscosity, v, in m'ts is then obtained from the equation v = KR4t where K is a constant, R is the radius of the capillary tube in mm, and t is the drain time in seconds. When glycerin at 20 C is used as a calibration fluid in a particular viscometer the drain time is 1,430 s. When a liquid having a density of 970 kglml is tested in the same viscometer the drain time is 900 s. What is the dynamic viscosity of this liquid? Glass strengthening - bridge -."1:>Etched lines Capillary --'rn Tt, 6/ 8,2. /n ApndiJl B : (.f.r/r /Vafe,. ai fpo') jA- = It. ;""5 )LIO-If j Thus.) -'I- /'H..() If. r..r..5 J{. /0 = 3,7= /II;' I. fIT ;( I()- L() -7 if. 71f!i )I. 10 -2 :: = :l.!J5")I.J0 "Y.tti,. /. ek ;(/0-5" 40. Master Typing: Sheet lOCk Reduction 8 1/2 x I I trilll size /,:50 I I I==J====;!========'========I==========- ---- I-- r- - + - -- /,IsI 1.50 The viscosity of a certain fluid is 5 x 10-' poise. Determine its viscosity in both SI and BG units. t:lne/ Frp/?f TctbJ 1.1;- /''> 9 ) v = b '4 51;" 20 = 0.1 mm gap FIGURE p1.6'1- (0.000I /)n HIOJ.;)/f.JI..Ys/ lDo) ( O. H N.S )({). l tm2) /1'>1 '" J - 55 56. 1. 6 5 1.65 A layer of water flows down an inclined fixed surface with the velocity profile shown in Fig. P1.6S. Detennine the magnitude and direc tion of the shearing stress that the water exerts on the fixed surface for U = 2 mls and h = 0.1 m. Tht/' ;, a.1: -th C)Fo So fixe,! sur/dee = dl O h / - 5 6 FIGURE PI-55 57. 1.6b Standard air flows past a flat surface and velocity measurements near the surface indicate the following distribution: y (ft) 10.005 10.01 10.02 10.04 1 0.06 1 0.08 u (ft/s) 0.74 1.51 3.03 6.37 10.21 14.43 The cuordinate y is measured normal to the sur face and u is the velocity parallel to the surface. (a) Assume the velocity distribution is of the form u = C,y + C,y' and use a standard curve-fitting technique to de termine the constants C, and C,. (b) Make use of the results of part (a) to determine the mag nitude of the shearing stress at the wall (y = 0) and at y = 0.05 ft. ( It) Use I1M/;;'ertr rejrSSI';" proghlm (6) -fo OUI:tIh &JefHC/Mi::s (I tmti C.z. . The prt:J/Jrr:lm PNJrluc&s Iells t slp'tlrt's est/males "I /he ptlY'lIl11ei:frs of tl ntJl1itll/?4r rt/1Pt/e/. FbI'" -the dlt/;a. J/l/fJ1) C = 153 5 - ' 1 SIYl C e., du t=r d !1 ;f .k1/()UlS 1h,rt t =j' ( t 3 C L ) Thus, at- the wil li ('1 = 0) Ifi /- 5 7 - 5' II:, = 5: 7:J. x IO it.. 58. t, 67 1.67 A new computer drive is proposed t o have a disc, as shown in Fig. P1.67. The disc is to rotate at 10,000 rpm, and the reader head is to be positioned 0.0005 in. above the surface of the disc. Estimate the shearing force on the reader head as result of the air between the disc and the head. IIll F I G U R E P1.67 Stationary reader head Rotating disc Q,2in,dia. -j f-- 0.0005 in. F '" ..rheal' force on head. CA ) whenJ if Ihe ve/oc/ly prolJle if} fhe qap he/ween fhe Jire anJ head ir /iYJfrir a/ld {/11I"f{Jl'm tI (jIGSs fhe hetlrJ.J 1hen au U (:= r Ty =)A- b ) where rr'" (,() R :: 10 aDo!!!.. ( !min)(21l''A!) (.!- 1-1) :: / 75" 1t,/ min 60-I rev 1'2- s Thv # r "'(3.7IfX/O-7) / 75 -:s W ( O',o:.s;0) $0 fh",f F :: ,...,1 = (1,5"7#-.. )* (W=-Nt :: 3. '13 x IO-If16 59. 1 . 68 1.68 The space between two 6-in.-Iong concentric cylinders is filled with glycerin (viscosity = 8.5 x 10-3 Ib . S/ft2). The inner cylinder has a radius of 3 in. and the gap width between cylinders is 0.1 in. Determine the torque and the power required to rotate the inner cylinder at 1 80 rev/min. The outer cylinder is fixed. As sume the velocity distribution in the gap to be linear. Tortuf; d du -/-0 11eIIr;"j smss on /nnt'r c:;/in c/o- ,j qual .f" d 'T: . i dA wh-er cjA .= (1::. de) -f .c d 'J :: :z. . J T dB and Ivr3H! regu;"rrd to I n ne r 01f/tlder is 2 Tr CO? view Fixed outer cylinder 1I 1 ):: !ride() (J. ... CfjllfJdrr lenqt"h ) ve /Oc./.j. disfribw.f../ol1 / n fhe 3fA. /> S o -fhtl. !: R.. W R() - R.. .27i R/}.f cu Re> - R,' (/80 r.. )(e3lTm lJ, w = rAg )(/ n1l;'):. 6 rr re v t-, o s Yad- s . =: Cons t:Ql1t {'-Ie -P, . ,pF t' rv In;hAJ .rhte where tind p. 1, * f. hr1tJ/ s k-ce .L .f- So -inA} -41050 i !} _ = C(nc/ 1- - --e> r 7f : -fr - frR 7 (' 5 R ( .it )(Ilflf i!2.t )7C> 111. ). +-t:... ('1.25" )f./D-B S/lIfJ )(3.offx 10 $ -1& 11. )h3 sJuf . D 7(P 5 oR - /.jjpCJ = 305 of } - 1 1 72. 1.8 3 I 1.B3 Compare the isentropic bulk modulus of air at 101 kPa (abs) with that ofwater at the same pressure. r ti lt (E''g. /./7 )) Fy -k f = (I.Jfo ) (10/ x /,:?t. ) = 1. 11/ x / 5" I='bl- Ultl-ier ( TaI.J I.J, ) 13,., = ,1. /5" ,>( 10 1 ,q Thus) Ev (Wit--ter ) ", (cur ) ,;(. /5" ;< /0 'iA. I. If/ ,I( 15"1} / -72. - 1. 5";l ,x/o i' 73. 4/. 8if I " 1.elf D-;ePacomputer program for cal- culating the final gage pressure of gas when the initial gage pressure, initial and final volumes, atmospheric pressure. and the type of process (isothermal or isentropic) are specified. Use BG units. Check your program against the results ob tained for Problem 1.7'1. ? = (!tMs-toni. fA wheye -h= / trw isothN11Q/ PI''' cess ) and k = .:Jj'ecific. heLl 1-"4. 1:10 lOr 1.st'nfrtJp'c procss. THus J -I>. = 1}. ;:..,. ;;..p, where '" In/flll/ kc.t.1 .f'""' /ihq/ .5hik1 So th,;i; 1; = ft.)"!:.. fhen = 'It. fL' fj. w hel"e .) ) tire Thus) Irm 131 /1) 3 r 1;.ttn ;: Cal1 be. U./"i ffen a s if, = ()-k (j T tCIh in ) t E''$ua/s the va-I'0'" pressure . /;;- car};on td....ac./oy;d ai :LIfe :: I] R.. (,ds ) 1hu) 13 Ie PI0Y fYs. s,.trc o/- wilier 0 6 3S'C 1.5 S. gl ....t (;,5$) (-/I'4n7 To!'//! 8. 2 ,,, /ip?"d" j3 uSI"7 1/",,"; l;,krfo/lJi;(f) J. Titus, ;,c &Vie,. bo,"/s at 1l1is fempr dl(re f11e 4tm".spHPrtC p,.'.I5ure. !nus!: .he eftlDI i S. i/ .lJ.f'a.. (/,s ) I;' :5I t(l'1ih. In f.J6 l/'1i fs) (S.J'/.xI03::"Z.)(/''15"PxJt)-'f-: ) = O. !If.;L pi (o"s) 7: /- 79 80. / , q'f I 1.94 When a 2-mm-diameter tube is inserted into a liquid in an open tank. the liquid is observed to rise 10 mm above the free sur face of the liquid. the contact angle between the liquid and the tube is zero. and the specific weight of the liquid is 1 .2 X 10' N/m'. Determine the value of the surface tension for this liquid. ThvsJ 2 rJ c os e O' R - 0.0 6 0 % J where e 0 'f N ( -3 ) -3 1. 2 XIO ;;j3 1 0 '1- 1 0 m (2X/V m12 ) 2- eN 0 81. /. qS I Lq 5 Small droplets ofcarbon tetrachloride at 68 OF are formed with a spray nozzle. If the av erage diameter of the droplets is 200 I,m what is t,he difference in pressure between the inside and outside of the droplets? 5ince p= - :z. rr = .J. b '? A IO it..... == j- 8 1 (t 1. :2.1 ) 82. I. q 6 I 1 .9 6 A l2-mm diameter jet of water discharges vertically into the atmosphere. Due to surface tension the pressure inside the jet will be slightly higher than the surrounding atmospheric pressure. Determine this difference in pressure. 'For elIi//6riUII1 fsf' !/jtlt"'e ),; t(zU):: rr(z tl.) SD 1/Ia t 1> == = 12 '" Jb- .3 Mt -z = 12. 2 Pa. 83. / 9 7 I 1.97 As shown in Video VI.9, surface tension forcescan be strong enough to allow a double-edge steel razor blade to "float" on wa- ter, but a single-edge blade will sink. Assume that the surface ten sion forces act at an angle 8 relative to the water surface as shown in Fig. P1.97. (a) The mass of the double-edge blade is 0.64 x 10-3 kg, and the total length of its sides is 206 mm. De termine the value of 8 required to maintain equilibrium between the blade weight and the resultant surface tension force. (b) The mass of the single-edge blade is 2.61 X 10-3 kg, and the total length of its sides is 154 mm. Explain why this blade sinks. Sup port your answer with the necessary calculations. I (a. ) L F =- 0 Vr+1 Ca I , tow '1;J = T S in B lu heve ttJ ::: (YyI x cHI d T = CT x. iel'lfhl of. 5 1 cie5_ blode. (o. lP )( ID-3--k ) (. I fYYI/sl.): 0.n I.)D-2..!j;,) ({J. 20 !)n) 5'1 ,, 8 :5 111 &- =- D . Lf-15 [;) = :2.. 4-. 5 ( b) For slnrle-edJ n a lY'r'I a X: / m tarn Va. l u e +o y- l n e I S I ,'+ followsI fi1cd CZU :> T SIr, e Cl n d jn:J( -ec15e hlade w ; I I sill k . 84. I. 98 I ( ) 1 . q S To measure the water depth in a large open tank with opaque walls, an open vertical glass tube is anached to the side of the tank. The height of the water column in the tube is then used as a measure of the depth of water in the tank. (a) For a true water depth in the tank of 3 ft, make use of Eq. 1 .22 (with e = 0) to determine the percent error due to capillarity as the diameter of the glass tube is changed. Assume a water temperature of 80 oF. Show your results on a graph of percent error versus tube diameter, D, in the range 0.1 in. < D < 1 .0 in. (b) If you want the errono be less than 1 0/0, what is the smallest tube diameter allowed? Th eX CeSS hljh t I h) caused 6( h = 2 cr G 'oR 1J,e, surfr" c. I:-enf,/n /s (EZ . j, '2z. ) f;?r G-::: 0" tv; th b = 2. R. h = if 0- rD Prt9r"n TAJ,/, /3, ( / 11 A-ppendl X 8 /Dr tVo.1:ev a.,i. fT= Jf. 9/ xIf)- 3 fb/Pi (;111&/ r = ' Z, 2. z lob/ft:". Ths .fnm Pq. ( J )I P -J I I. ) h (F-1:) :: If (if.fit x: 10 -:;:L (z lZ. l.!!. ) D (,'rI.) . k ' ' 2. I.f.f.c - 3 ::l.l q )( 1 0 .D ( (n.) 0 ) %O"F 010 f'rror =- h t+t J )( 1 0 0 3 ft (toI 7lt -The frue. c.1eptn = 3 ft-) ('r toJJ0 Ws frc>WI E l ) -tJ.../lf: _ 3 /o e y rt'Y = 3, 7tf X If> :;( 10 0 3 D (ln. ) A- plot of io tvr,pr vusus t:Wbe dlt1tt1e.fer IS S/1()W/1 "n 17" I1ft-t pa 'l e . / - 8 1f c ) 85. I. 9 8 I (Ci:JI'/t ) Diameter % Error of tube, in. 0.1 1 .26 0 . 1 5 0.84 0.2 0.63 0.3 0.42 0.4 0.32 0.5 0.25 0.6 0.21 0.7 0. 1 8 0.8 0. 1 6 0.9 0.14 1 0 . 1 3 " Values obtained from Eq. (3) (b) For Jio 1 1 .50 1 .000 w 0 0.50 0.00 0 0.2 0.4 0.6 0.8 1 1 .2 Tube diameter, in. j eYYtJY ;;'PI11 g . O) ) = 6. /2b tx/".J D -= O. / 2 "" in . / - 85 86. /. (/q I 1.q q Under the right conditions. it is possible. due to surface tension. to have metal objects float on water. (See " ide" Vl .q.) Consider placinr, a short length of a small diameter steel (sp. wI. = 490 lb/ft ) rod on a surface of water. What is the maximum diameter that the rod can have before it will sink? Assume that the surface tension forces act vertically upward. NOle: A standard paper clip has a diameter of 0.036 in. Partially unfold a paper clip and see if you can get it to float on water. Do the results of this experiment support your analysis? In "cIty Ivr yo .J-.o -float (se (',?ille) I i .ft>/Iows Pta t 1. 0-1 ::: CW .:: r-)(n4) tt'eI Thus ) #'r 1J1( /,m;hnJ ca.se :l :z.. rr.l- DmRI. - [) mao(, . 0 . 0 "" '+ I n . g cr rrl 'V1. -3 u.. 5 l l x l b t'l St'nct. a. t.tlf1t1lfYd ieel p"-pty dip hils 4 dl4mdrr D f tJ. 3/' in. ) wh,'c), I So /(55 fr..a.J1 O. D'-/f/. ;'n.) It 5nol{M f/o tL /;- . ,4 /mp/( e;t..painJflti f.,t) t // V-ev;.f Tht.!. . Yes . /- 86 87. /. I D O I I. 101 I 1. 1 0 0 An open, clean glass tube. having a diameter of 3 mm, is insened venically into a dish of mercury at 20 'C. How far will the column of mercury in the tube be depressed? = '2 cr (!i95 f) ?r R WI // be del'resseel 1. 101 An open, clean glass tube (8 = 0') is inserted veltically into a pan of water. What tube diameter is needed if the water level in the tube is to rise one tube diameter (due to surface tension)? For ---h = -It = ZR. J.. R : '2 :t. Lf .tt J - 3 R :: . 9' X ) D +1:. d Ia rn e be j.- - .2.. R ::- l. g o x ) 0- 2 II:- (g. I. 22 ) - 3 3. 00 x /D tm 3. 0 0 ,.,.,., m? 88. 1 . 102.. I 1 ./01. Determine the height water at 60 'F will rise due to capillary action in a clean. !in.-di ameter tube. What will be the height if the di ameter is reduced to 0.01 in.o 2 rT cos G '!' R TJ,,, with (9 : 0 J / S/rn//tl rl'J ) ( lor R =- 19. W!i" In. ) I ' )(C>,J:Z.5"/. )r tJ. /Kb lh. . = o, oO S' In. 89. 1. /03 1.1113 (See Fluids in the News article titled "Walking on water," Section l.9.) (a) The water strider bug shown in Fig. Pl.l03 is supported on the surface of a pond by surface tension acting along the interface between the water and the bug's legs. Determine the minimum length of this interface needed to support the bug. As sume the bug weighs 10-' N and the surface tension force acts vertically upwards. (b) Repeat part (a) if surface tension were to support a person weighing 750 N. (0..) -eIII L bl'l;"1r J f7UJ :: rrj. C1lv - 3 1 . 3 )( 1D fWI 11 F I G U A IE P1 .103 4.v r"V W-e'18 ht- a- rv SII....tac .J..r.,SIOI1 f I'J It'nj"tn 61 "f)m.c!... (,=1I. )(IO-3tyl) (ID3) ;; (.1) If-. 0 2 )( I D f{YI 90. /. /OIJ 1.lO't Fluid Characterization by Use of a Stormer Viscometer Objective: As discussed in Section 1.6, some fluids can be classified as Newtonian flu ids; others are non-Newtonian. The purpose of this experiment is to determine the shearing stress versus rate of strain characteristics of various liquids and, thus, to classify them as Newtonian or non-Newtonian fluids. Equipment: Stormer viscometer containing a stationary outer cylinder and a rotating, concentric inner cylinder (see Fig. PJ.lO'lj; stop watch; drive weights for the viscometer; three different liquids (silicone oil, Latex paint, and corn syrup). Experimental Procedure: Fill the gap between the inner and outer cylinders with one of the three fluids to be tested. Select an appropriate drive weight (of mass m) and attach it to the end of the cord that wraps around the drum to which the inner cylinder is fastened. Release the brake mechanism to allow the inner cylinder to start to rotate. (The outer cylinder remains stationary.) After the cylinder has reached its steady-state angular velocity, measure the amount of time, I, that it takes the inner cylinder to rotate N revolutions. Repeat the measurements us ing various drive weights. Repeat the entire procedure for the other fluids to be tested. Calculations: For each of the three fluids tested, convert the mass, m, of the drive weight to its weight, W = mg, where g is the acceleration of gravity. Also determine the angular ve locity of the inner cylinder, w = Nil. Graph: For each fluid lested, plot the drive weight, W, as ordinates and angular velocity, w, as abscissas. Draw a best fit curve through the data. Results: Note that for the flow geometry of this experiment, the weight, W, is propor tional to the shearing stress, T, on the inner cylinder. This is true because with constant an gular velocity, the torque produced by the viscous shear stress on the cylinder is equal to the torque produced by the weight (weight times the appropriate moment arm). Also, the angu lar velocity, w, is proportional to the rate of strain, duldy. This is true because the velocity gradient in the fluid is proportional to the inner cylinder surface speed (which is proportional to its angular velocity) divided by the width of the gap between the cylinders. Based on your graphs, classify each of the three fluids as to whether they are Newtonian, shear thickening, or shear thinning (see Fig. 1,7). Data: To proceed, print this page for reference when you work the problem and c/i" k I,,'rl' to bring up an EXCEL page with the data for this problem. ,4f---Re,tating Inner cylinder .:I'I--Ol.ter cylinder Drive weIght F I G U R E P l .IOlf 91. /. / OIf I Problem 1 . 104- Weight, W, vs Angular Velocity, (0 for Silicone Oil 4.50 ,----,------,---..,-----, 4.00 +----+---+----l.-----I /3.50 +---+---1--/ 3.00 Vz 2.50 +----f---'-----+--___1 ;: 2.00 / W=2.5 '" ./1 .50 +----_l---+_---I 1 .00 ./ 0.50 I ...... 0.00 ---+---_I---+----I Problem 1 . JOy. Weight, W, vs Angular Velocity, tn' 1= (;lJ./j(ID"3:!;J{S'XI03hr =50.5 ,4./$0I t=(50.5 2-3 = 50.5" 1'1 p... 97. ;J.. 7 I 2.7 For the great depths that may be en countered in the ocean the compressibility of sea- . water may become an important consideration. (a) Assume that the bulk modulus for seawater is constant and derive a relationship between pressure and depth which takes into account the change in fluid density with depth. (b) Make use (a..) Thus) '" -6' =-f3 '!.:1: :: - i dr f' 1ft's a. fttnd'/lP/1 0 f p) W(, 111 fe'lI't1f-ln? lit (I ). :s Inee) p- !if. df/f (J = fv /7 - E 1;,v t: of part (a) to determine the pressure at a depth of 6 km assuming seawater has a bulk modulus of 2.3 x 10' Pa, and a density of 1030 kg/m' at the surface. Compare this result with that ob tained by assuming a constant density of 1030 kg/m'. ( g. Vf) (r) (Eg. 1./3) a.t p=o t.Jhere 98. 2.7 I (can'l) (c) h:,,, UJI?S /:anI: densi P=?fJ.. =;;3- J.. =(t.fJ3JD3)(?,f/;..)({,/1>3rm) = fa tJ. t. f.1R.. 99. 2.8 I 2.8 Sometimes when riding an elevator or driving up or down a hilly road a person's ears "pop" as the pressure difference between the inside and outside of the ear is equalized. Determine the pressure difference (in psi) associated with this phenomenon if it occurs during alSO ft elevation change. bf ::: tDh ::: 0.0765 }J (ISFIJ Ib I H _) '"' II,,05 1P' (I'H in.'- 0.0797 pSI . 2.q Develop an expression for the pressure variation in a liquid in which the specific weight increases with depth, h, as y = Kh + Yo, where K is a constant and Yo is the specific weight at the free surface. :!1 = _ dr Let -p..::];o - Z So -mat d-P. : -eli: and 1 :: v l" II 7 / I 100. "'2.10 J ;j1m) = S9. g::'--= S fl-kFA. b) To etJIml(J" JCl/ pYJSUYc. 1, hl/rfJlYt heart. Co/1 Vt:yt;- Pr'S.sIlI'