QUESTIONS 405 Review & Summry Density Te ensity r of ny mteril is efine s te mteril s mss per unit volume: r m (14-1) V. Usully, were mteril smple is muc lrger tn tomic imensions, we cn write Eq. 14-1 s r m V. (14-2) Flui Pressure flui is substnce tt cn flow; it conforms to te bounries of its continer becuse it cnnot witstn sering stress. It cn, owever, exert force perpeniculr to its surfce. Tt force is escribe in terms of pressure p: p F (14-3), in wic F is te force cting on surfce element of re. If te force is uniform over flt re, Eq. 14-3 cn be written s p F. (14-4) Te force resulting from flui pressure t prticulr point in flui s te sme mgnitue in ll irections. Guge pressure is te ifference between te ctul pressure (or bsolute pressure) t point n te tmosperic pressure. Pressure Vrition wit Heigt n Dept Pressure in flui t rest vries wit verticl position y. For y mesure positive upwr, p 2 p 1 rg(y 1 y 2 ). (14-7) Te pressure in flui is te sme for ll points t te sme level. If is te ept of flui smple below some reference level t wic te pressure is p 0, ten te pressure in te smple is p p 0 rg. (14-8) Pscl s Principle cnge in te pressure pplie to n enclose flui is trnsmitte uniminise to every portion of te flui n to te wlls of te contining vessel. rcimees Principle Wen boy is fully or prtilly submerge in flui, buoynt force F : b from te surrouning flui cts on te boy. Te force is irecte upwr n s mgnitue given by F b m f g, (14-16) were m f is te mss of te flui tt s been isplce by te boy (tt is,te flui tt s been puse out of te wy by te boy). Wen boy flots in flui, te mgnitue F b of te (upwr) buoynt force on te boy is equl to te mgnitue F g of te (ownwr) grvittionl force on te boy. Te pprent weigt of boy on wic buoynt force cts is relte to its ctul weigt by weigt pp weigt F b. (14-19) Flow of Iel Fluis n iel flui is incompressible n lcks viscosity, n its flow is stey n irrottionl. stremline is te pt followe by n iniviul flui prticle. tube of flow is bunle of stremlines.te flow witin ny tube of flow obeys te eqution of continuity: R V v constnt, (14-24) in wic R V is te volume flow rte, is te cross-sectionl re of te tube of flow t ny point, n v is te spee of te flui t tt point.te mss flow rte R m is R m rr V rv constnt. (14-25) Bernoulli s Eqution pplying te principle of conservtion of mecnicl energy to te flow of n iel flui les to Bernoulli s eqution long ny tube of flow: 1 p 2rv 2 rgy constnt. (14-29) Questions 1 We fully submerge n irregulr 3 kg lump of mteril in certin flui. Te flui tt woul ve been in te spce now occupie by te lump s mss of 2 kg. () Wen we relese te lump, oes it move upwr, move ownwr, or remin in plce? (b) If we next fully submerge te lump in less ense flui n gin relese it, wt oes it o? 2 Figure 14-21 sows four situtions in wic re liqui n gry liqui re in U-tube. In one sitution te liquis cnnot be in sttic equilibrium. () Wic sitution is tt? (b) For te oter tree sit- (1) (2) (3) (4) Figure 14-21 Question 2. utions, ssume sttic equilibrium. For ec of tem, is te ensity of te re liqui greter tn, less tn, or equl to te ensity of te gry liqui? 3 bot wit n ncor on bor flots in swimming pool tt is somewt wier tn te bot. Does te pool wter level move up, move own, or remin te sme if te ncor is () roppe into te wter or (b) trown onto te surrouning groun? (c) Does te wter level in te pool move upwr, move ownwr, or remin te sme if, inste, cork is roppe from te bot into te wter, were it flots? 4 Figure 14-22 sows tnk fille wit wter. Five orizontl floors n ceilings re inicte; ll ve te sme re n re locte t b istnces L, 2L, or 3L below te top of te tnk. Rnk tem ccoring to te force on tem ue to te wter, gretest first. Figure 14-22 Question 4. c e
406 CHPTER 14 FLUIDS 5 Te tepot effect. Wter Spout poure slowly from tepot spout cn ouble bck uner te spout for b consierble istnce (el tere by tmosperic pressure) before Wter etcing n flling. In Fig. 14-23, c flow te four points re t te top or bottom of te wter lyers, insie or Figure 14-23 Question 5. outsie. Rnk tose four points ccoring to te guge pressure in te wter tere, most positive first. 6 Figure 14-24 sows tree ienticl open-top continers fille to te brim wit wter; toy ucks flot in two of tem. Rnk te continers n contents ccoring to teir weigt, gretest first. () (b) (c) 2.00R R 2.00R (1) Figure 14-24 Question 6. 7 Figure 14-25 sows four rrngements of pipes troug wic 3.00R 2.00R R (2) wter flows smootly towr te rigt. Te rii of te pipe sections re inicte. In wic rrngements is te net work one on unit volume of wter moving from te leftmost section to te rigtmost section () zero, (b) positive, n (c) negtive? 8 rectngulr block is puse W pp fce-own into tree liquis, in turn. Te pprent weigt W pp of te block versus ept in te tree liquis is plotte in Fig. 14-26. b Rnk te liquis ccoring to teir weigt per unit volume, gretest first. c 9 Wter flows smootly in orizontl Figure 14-26 Question 8. pipe. Figure 14-27 sows te kinetic energy K of wter element K s it moves long n x xis tt runs long te pipe. Rnk te tree lettere sections of te pipe B C x ccoring to te pipe rius, gretest Figure 14-27 Question 9. first. 10 We ve tree continers wit ifferent liquis. Te guge pressure p g versus ept is plotte in Fig. 14-28 for te liquis. In ec continer, we will fully submerge rigi plstic be. Rnk te plots ccoring to te mgnitue of te buoynt force on te be, gretest first. p g b c 2.00R R 3.00R (3) R Figure 14-25 Question 7. 3.00R (4) R Figure 14-28 Question 10. Problems SSM Tutoring problem vilble (t instructor s iscretion) in WileyPLUS n Webssign Worke-out solution vilble in Stuent Solutions Mnul WWW Worke-out solution is t Number of ots inictes level of problem ifficulty ILW Interctive solution is t itionl informtion vilble in Te Flying Circus of Pysics n t flyingcircusofpysics.com ttp://www.wiley.com/college/lliy Moule 14-1 Fluis, Density, n Pressure 1 ILW fis mintins its ept in fres wter by justing te ir content of porous bone or ir scs to mke its verge ensity te sme s tt of te wter. Suppose tt wit its ir scs collpse, fis s ensity of 1.08 g/cm 3. To wt frction of its expne boy volume must te fis inflte te ir scs to reuce its ensity to tt of wter? 2 prtilly evcute irtigt continer s tigt-fitting li of surfce re 77 m 2 n negligible mss. If te force require to remove te li is 480 N n te tmosperic pressure is 1.0 10 5 P, wt is te internl ir pressure? 3 SSM Fin te pressure increse in te flui in syringe wen nurse pplies force of 42 N to te syringe s circulr piston, wic s rius of 1.1 cm. 4 Tree liquis tt will not mix re poure into cylinricl continer.te volumes n ensities of te liquis re 0.50 L, 2.6 g/cm 3 ; 0.25 L, 1.0 g/cm 3 ; n 0.40 L, 0.80 g/cm 3. Wt is te force on te bottom of te continer ue to tese liquis? One liter 1 L 1000 cm 3. (Ignore te contribution ue to te tmospere.) 5 SSM n office winow s imensions 3.4 m by 2.1 m. s result of te pssge of storm, te outsie ir pressure rops to 0.96 tm, but insie te pressure is el t 1.0 tm.wt net force puses out on te winow? 6 You inflte te front tires on your cr to 28 psi. Lter, you mesure your bloo pressure, obtining reing of 120/80, te reings being in mm Hg.In metric countries (wic is to sy,most of te worl),tese pressures re customrily reporte in kilopscls (kp). In kilopscls, wt re () your tire pressure n (b) your bloo pressure?
PROBLEMS 407 7 In 1654 Otto von Guericke, inventor of te ir pump, gve emonstrtion before te noblemen of te Holy Romn Empire in R F F wic two tems of eigt orses coul not pull prt two evcute brss emisperes. () ssuming Figure 14-29 Problem 7. te emisperes ve (strong) tin wlls, so tt R in Fig. 14-29 my be consiere bot te insie n outsie rius, sow tt te force F : require to pull prt te emisperes s mgnitue F pr 2 p, were p is te ifference between te pressures outsie n insie te spere. (b) Tking R s 30 cm, te insie pressure s 0.10 tm, n te outsie pressure s 1.00 tm, fin te force mgnitue te tems of orses woul ve to exert to pull prt te emisperes. (c) Explin wy one tem of orses coul ve prove te point just s well if te emisperes were ttce to stury wll. Moule 14-2 Fluis t Rest 8 Te bens uring fligt. nyone wo scub ives is vise not to fly witin te next 24 becuse te ir mixture for iving cn introuce nitrogen to te bloostrem. Witout llowing te nitrogen to come out of solution slowly, ny suen ir-pressure reuction (suc s uring irplne scent) cn result in te nitrogen forming bubbles in te bloo, creting te bens, wic cn be pinful n even ftl. Militry specil opertion forces re especilly t risk. Wt is te cnge in pressure on suc specil-op solier wo must scub ive t ept of 20 m in sewter one y n prcute t n ltitue of 7.6 km te next y? ssume tt te verge ir ensity witin te ltitue rnge is 0.87 kg/m 3. 9 Bloo pressure in rgentinosurus. () If tis longnecke, gigntic suropo e eigt of 21 m n ert eigt of 9.0 m, wt (yrosttic) guge pressure in its bloo ws require t te ert suc tt te bloo pressure t te brin ws 80 torr (just enoug to perfuse te brin wit bloo)? ssume te bloo ensity of 1.06 10 3 kg/m 3. (b) Wt ws te bloo pressure (in torr or mm Hg) t te feet? 10 Te plstic tube in Fig. 14-30 s cross-sectionl re of 5.00 cm 2. Te tube is fille wit wter until te sort rm (of lengt 0.800 m) is full. Ten te sort rm is sele n more wter is grully poure into te long rm. If te sel will pop off wen te force on it excees 9.80 N, wt totl eigt of wter in te long rm will put te sel on te verge of popping? Figure 14-30 Problems 10 n 81. 11 Girffe bening to rink. In girffe wit its e 2.0 m bove its ert, n its ert 2.0 m bove its feet, te (yrosttic) guge pressure in te bloo t its ert is 250 torr.ssume tt te girffe stns uprigt n te bloo ensity is 1.06 10 3 kg/m 3. In torr (or mm Hg), fin te (guge) bloo pressure () t te brin (te pressure is enoug to perfuse te brin wit bloo, to keep te girffe from finting) n (b) t te feet (te pressure must be countere by tigt-fitting skin cting like pressure stocking). (c) If te girffe were to lower its e to rink from pon witout splying its legs n moving slowly, wt woul be te increse in te bloo pressure in te brin? (Suc ction woul probbly be letl.) 12 Te mximum ept mx tt iver cn snorkel is set by te ensity of te wter n te fct tt umn lungs cn func- tion ginst mximum pressure ifference (between insie n outsie te cest cvity) of 0.050 tm.wt is te ifference in mx for fres wter n te wter of te De Se (te sltiest nturl wter in te worl, wit ensity of 1.5 10 3 kg/m 3 )? 13 t ept of 10.9 km, te Cllenger Deep in te Mrins Trenc of te Pcific Ocen is te eepest site in ny ocen. Yet, in 1960, Donl Wls n Jcques Piccr rece te Cllenger Deep in te btyscp Trieste. ssuming tt sewter s uniform ensity of 1024 kg/m 3, pproximte te yrosttic pressure (in tmosperes) tt te Trieste to witstn. (Even sligt efect in te Trieste structure woul ve been isstrous.) 14 Clculte te yrosttic ifference in bloo pressure between te brin n te foot in person of eigt 1.83 m. Te ensity of bloo is 1.06 10 3 kg/m 3. 15 Wt guge pressure must mcine prouce in orer to suck mu of ensity 1800 kg/m 3 up tube by eigt of 1.5 m? 16 Snorkeling by umns n elepnts. Wen person snorkels, te lungs re connecte irectly to te tmospere troug te snorkel tube n tus re t tmosperic pressure. In tmosperes, wt is te ifference p between tis internl ir pressure n te wter pressure ginst te boy if te lengt of te snorkel tube is () 20 cm (stnr sitution) n (b) 4.0 m (probbly letl sitution)? In te ltter, te pressure ifference cuses bloo vessels on te wlls of te lungs to rupture, relesing bloo into te lungs. s epicte in Fig. 14-31, n elepnt cn sfely snorkel troug its trunk wile swimming wit its lungs 4.0 m below te wter surfce becuse te membrne roun its lungs contins connective tissue tt ols n protects te bloo vessels, preventing rupturing. 17 SSM Crew members ttempt to escpe from mge submrine 100 m below te surfce. Wt force must be pplie to pop-out tc, wic is 1.2 m by 0.60 m, to pus it out t tt ept? ssume tt te ensity of te ocen wter is 1024 kg/m 3 n te internl ir pressure is t 1.00 tm. 18 In Fig. 14-32, n open tube of lengt L 1.8 m n cross-sectionl re 4.6 cm 2 is fixe to te top of cylinricl brrel of imeter D 1.2 m n eigt H L 1.8 m. Te brrel n tube re fille wit wter (to te top of te tube). Clculte te rtio of te yrosttic force on te bottom of te brrel to te grvittionl force on te wter contine in te brrel. Wy is tt rtio not equl to 1.0? (You nee not consier te tmosperic pressure.) H 19 lrge qurium of eigt 5.00 m is fille wit fres wter to ept of 2.00 m. One wll of te qurium consists of tick plstic 8.00 m wie. By ow muc oes te totl force on tt wll increse if te qurium is next fille to ept of 4.00 m? Figure 14-31 Problem 16. FRESH WTER SUITBLE FOR DRINKING D Figure 14-32 Problem 18.
408 CHPTER 14 FLUIDS 20 Te L-spe fis tnk sown in Fig. 14-33 is fille wit wter n is open t te top. If 5.0 m, wt is te (totl) 2 force exerte by te wter () on fce n (b) on fce B? 3 21 SSM Two ienticl cylinricl vessels wit teir bses t te sme level ec B contin liqui of ensity 1.30 10 3 kg/m 3. Te re of ec bse is 4.00 cm 2, 2 but in one vessel te liqui eigt is 0.854 Figure 14-33 m n in te oter it is 1.560 m. Fin te Problem 20. work one by te grvittionl force in equlizing te levels wen te two vessels re connecte. 22 g-loc in ogfigts.wen pilot tkes tigt turn t ig spee in moern figter irplne, te bloo pressure t te brin level ecreses, bloo no longer perfuses te brin, n te bloo in te brin rins. If te ert mintins te (yrosttic) guge pressure in te ort t 120 torr (or mm Hg) wen te pilot unergoes orizontl centripetl ccelertion of 4g, wt is te bloo pressure (in torr) t te brin, 30 cm rilly inwr from te ert? Te perfusion in te brin is smll enoug tt te vision switces to blck n wite n nrrows to tunnel vision n te pilot cn unergo g-loc ( ginuce loss of consciousness ). Bloo ensity is 1.06 10 3 kg/m 3. 23 In nlyzing certin geologicl fetures, it is often pproprite to ssume tt te pressure t some orizontl level of compenstion, Mountin H eep insie Ert, is te sme over lrge region n is equl to te pressure ue to te Continent 2.9 g/cm 3 T grvittionl force on te overlying mteril. Tus, te pressure on Mntle Root 3.3 g/cm 3 D y te level of compenstion is given Compenstion by te flui pressure formul. Tis moel requires, for one ting, tt b level mountins ve roots of continentl Figure 14-34 Problem 23. rock extening into te enser mntle (Fig. 14-34). Consier mountin of eigt H 6.0 km on continent of tickness T 32 km. Te continentl rock s ensity of 2.9 g/cm 3, n benet tis rock te mntle s ensity of 3.3 g/cm 3. Clculte te ept D of te root. (Hint: Set te pressure t points n b equl; te ept y of te level of compenstion will cncel out.) 24 In Fig. 14-35, wter stns t ept D 35.0 m bein te verticl upstrem fce of m of W wit W 314 m. Fin () te net D orizontl force on te m from te guge pressure of te wter n O (b) te net torque ue to tt force Figure 14-35 Problem 24. bout orizontl line troug O prllel to te (long) wit of te m.tis torque tens to rotte te m roun tt line, wic woul cuse te m to fil. (c) Fin te moment rm of te torque. Moule 14-3 Mesuring Pressure 25 In one observtion, te column in mercury brometer (s is sown in Fig. 14-5) s mesure eigt of 740.35 mm. Te temperture is 5.0 C, t wic temperture te ensity of mercury r is 1.3608 10 4 kg/m 3.Te free-fll ccelertion g t te site of te brom- eter is 9.7835 m/s 2.Wt is te tmosperic pressure t tt site in pscls n in torr (wic is te common unit for brometer reings)? 26 To suck lemone of ensity 1000 kg/m 3 up strw to mximum eigt of 4.0 cm, wt minimum guge pressure (in tmosperes) must you prouce in your lungs? 27 SSM Wt woul be te eigt of te tmospere if te ir ensity () were uniform n (b) ecrese linerly to zero wit eigt? ssume tt t se level te ir pressure is 1.0 tm n te ir ensity is 1.3 kg/m 3. Moule 14-4 Pscl s Principle 28 piston of cross-sectionl re is use in yrulic press to F exert smll force of mgnitue f on f te enclose liqui. connecting pipe les to lrger piston of crosssectionl re (Fig. 14-36). () Wt force mgnitue F will te lrger piston sustin witout moving? (b) If Figure 14-36 Problem 28. te piston imeters re 3.80 cm n 53.0 cm, wt force mgnitue on te smll piston will blnce 20.0 kn force on te lrge piston? 29 In Fig. 14-37, spring of spring Bem constnt 3.00 10 4 Continer N/m is between Spring rigi bem n te output piston of yrulic lever. n empty continer wit negligible mss sits on te input piston.te input piston s re i, n te output piston s re 18.0 i. Initilly te spring is t its rest lengt. Figure 14-37 Problem 29. How mny kilogrms of sn must be (slowly) poure into te continer to compress te spring by 5.00 cm? Moule 14-5 rcimees Principle 30 5.00 kg object is relese from rest wile fully submerge in liqui. Te liqui isplce by te submerge object s mss of 3.00 kg. How fr n in wt irection oes te object move in 0.200 s, ssuming tt it moves freely n tt te rg force on it from te liqui is negligible? 31 SSM block of woo flots in fres wter wit two-tirs of its volume V submerge n in oil wit 0.90V submerge. Fin te ensity of () te woo n (b) te oil. 32 In Fig. 14-38, cube of ege lengt L 0.600 m n mss 450 kg is suspene by rope in n open tnk of liqui of ensity 1030 kg/m 3. L/2 Fin () te mgnitue of te totl ownwr force on te top of te L cube from te liqui n te tmospere, ssuming tmosperic pressure is 1.00 tm, (b) te mgnitue of te totl upwr force on te bottom of te cube, n (c) te tension Figure 14-38 Problem 32. in te rope. () Clculte te mgnitue of te buoynt force on te cube using rcimees principle. Wt reltion exists mong ll tese quntities? 33 SSM n iron ncor of ensity 7870 kg/m 3 ppers 200 N ligter in wter tn in ir. () Wt is te volume of te ncor? (b) How muc oes it weig in ir? 34 bot floting in fres wter isplces wter weiging
PROBLEMS 409 35.6 kn. () Wt is te weigt of te wter tis bot isplces wen floting in slt wter of ensity 1.10 10 3 kg/m 3? (b) Wt is te ifference between te volume of fres wter isplce n te volume of slt wter isplce? 35 Tree cilren, ec of weigt 356 N, mke log rft by lsing togeter logs of imeter 0.30 m n lengt 1.80 m. How mny logs will be neee to keep tem () flot in fres wter? Tke te ensity of te logs to be 800 kg/m 3. W s 36 In Fig. 14-39, rectngulr block is grully puse fce-own into liqui. Te block s eigt ; on te bottom n top te fce re is 5.67 cm 2. Figure 14-39b gives te pprent 0 1 2 weigt W pp of te block s function of te ept of its lower (b) (cm) fce. Te scle on te verticl xis is set by W s 0.20 N. Wt is te Figure 14-39 Problem 36. ensity of te liqui? 37 ILW ollow spericl iron sell flots lmost completely submerge in wter.te outer imeter is 60.0 cm, n te ensity of iron is 7.87 g/cm 3. Fin te inner imeter. K s 38 smll soli bll is relese from rest wile fully submerge in liqui n ten its kinetic energy is mesure wen it s move 4.0 cm in te liqui. Figure 14-40 gives te results fter mny liquis re use: 0 1 2 3 ρ Te kinetic energy K is plotte versus liq (g/cm3 ) te liqui ensity r liq, n K s 1.60 J Figure 14-40 Problem 38. sets te scle on te verticl xis. Wt re () te ensity n (b) te volume of te bll? 39 SSM WWW ollow spere of inner rius 8.0 cm n outer rius 9.0 cm flots lf-submerge in liqui of ensity 800 kg/m 3. () Wt is te mss of te spere? (b) Clculte te ensity of te mteril of wic te spere is me. 40 Lurking lligtors. n lligtor wits for prey by floting wit only te top of its e expose, so tt te prey cnnot esily see it. One wy it cn just te extent of Figure 14-41 Problem 40. sinking is by controlling te size of its lungs. noter wy my be by swllowing stones (gstrolites) tt ten resie in te stomc. Figure 14-41 sows igly simplifie moel ( romboeron gter ) of mss 130 kg tt roms wit its e prtilly expose. Te top e surfce s re 0.20 m 2. If te lligtor were to swllow stones wit totl mss of 1.0% of its boy mss ( typicl mount), ow fr woul it sink? 41 Wt frction of te volume of n iceberg (ensity 917 kg/m 3 ) woul be visible if te iceberg flots () in te ocen (slt wter, ensity 1024 kg/m 3 ) n (b) in river (fres wter, ensity 1000 kg/m 3 )? (Wen slt wter freezes to form ice, te slt is exclue. So, n iceberg coul provie fres wter to community.) 42 flottion evice is in te spe of rigt cyliner, wit eigt of 0.500 m n fce re of 4.00 m 2 on top n bottom, n its ensity is 0.400 times tt of fres wter. It is initilly el fully submerge in fres wter, wit its top fce t te wter surfce.ten W pp (N) K (J) it is llowe to scen grully until it begins to flot. How muc work oes te buoynt force o on te evice uring te scent? 43 Wen resercers fin resonbly complete fossil of inosur, tey cn etermine te mss n weigt of te living inosur wit scle moel sculpte from plstic n bse on te imensions of te fossil bones. Te scle of te moel is 1/20; tt is, lengts re 1/20 ctul lengt, res re (1/20) 2 ctul Figure 14-42 Problem 43. res, n volumes re (1/20) 3 ctul volumes. First, te moel is suspene from one rm of blnce n weigts re e to te oter rm until equilibrium is rece. Ten te moel is fully submerge in wter n enoug weigts re remove from te secon rm to reestblis equilibrium (Fig. 14-42). For moel of prticulr T. rex fossil, 637.76 g to be remove to reestblis equilibrium. Wt ws te volume of () te moel n (b) te ctul T. rex? (c) If te ensity of T. rex ws pproximtely te ensity of wter, wt ws its mss? 44 woo block (mss 3.67 kg, ensity 600 kg/m 3 ) is fitte wit le (ensity 1.14 10 4 kg/m 3 ) so tt it flots in wter wit 0.900 of its volume submerge. Fin te le mss if te le is fitte to te block s () top n (b) bottom. 45 n iron csting contining number of cvities weigs 6000 N in ir n 4000 N in wter. Wt is te totl cvity volume in te csting? Te ensity of soli iron is 7.87 g/cm 3. 46 Suppose tt you relese smll bll from rest t ept of 0.600 m below te surfce in pool of wter. If te ensity of te bll is 0.300 tt of wter n if te rg force on te bll from te wter is negligible, ow ig bove te wter surfce will te bll soot s it emerges from te wter? (Neglect ny trnsfer of energy to te splsing n wves prouce by te emerging bll.) 47 Te volume of ir spce in te pssenger comprtment of n 1800 kg cr is 5.00 m 3. Te volume of te motor n front weels is 0.750 m 3,n te volume of te rer weels,gs tnk,n trunk is 0.800 m 3 ; wter cnnot enter tese two regions. Te cr rolls into lke. () t first, no wter enters te pssenger comprtment. How muc of te cr, in cubic meters, is below te wter surfce wit te cr floting (Fig. 14-43)? (b) s wter slowly enters, te cr sinks. How mny cubic meters of wter re in te cr s it isppers below te wter surfce? (Te cr, wit evy lo in te trunk, remins orizontl.) Figure 14-43 Problem 47. 48 Figure 14-44 sows n iron bll suspene by tre of negligible mss from n uprigt cyliner tt flots prtilly submerge in wter. Te cyliner s eigt of 6.00 cm, fce re of 12.0 cm 2 on te top n bottom, n ensity of 0.30 g/cm 3, n 2.00 cm of its eigt is bove te wter surfce.wt is te rius of te iron Figure 14-44 bll? Problem 48.
410 CHPTER 14 FLUIDS Moule 14-6 Te Eqution of Continuity 49 Cnl effect. Figure 14-45 b i sows n ncore brge tt extens cross cnl by istnce 30 m n into te wter by istnce b 12 m. Te cnl s v i D wit D 55 m, wter ept H 14 m, n uniform wter-flow spee v i 1.5 m/s. ssume tt te b v flow roun te brge is uniform. s H i te wter psses te bow, te wter level unergoes rmtic ip Figure 14-45 Problem 49. known s te cnl effect. If te ip s ept 0.80 m, wt is te wter spee longsie te bot troug te verticl cross sections t () point n (b) point b? Te erosion ue to te spee increse is common concern to yrulic engineers. B 50 Figure 14-46 sows two? sections of n ol pipe system tt runs troug ill, wit B istnces B 30 m n D D 110 m. On ec sie of Figure 14-46 Problem 50. te ill, te pipe rius is 2.00 cm. However, te rius of te pipe insie te ill is no longer known. To etermine it, yrulic engineers first estblis tt wter flows troug te left n rigt sections t 2.50 m/s. Ten tey relese ye in te wter t point n fin tt it tkes 88.8 s to rec point B. Wt is te verge rius of te pipe witin te ill? 51 SSM gren ose wit n internl imeter of 1.9 cm is connecte to (sttionry) lwn sprinkler tt consists merely of continer wit 24 oles, ec 0.13 cm in imeter. If te wter in te ose s spee of 0.91 m/s, t wt spee oes it leve te sprinkler oles? 52 Two strems merge to form river. One strem s wit of 8.2 m, ept of 3.4 m, n current spee of 2.3 m/s. Te oter strem is 6.8 m wie n 3.2 m eep, n flows t 2.6 m/s. If te river s wit 10.5 m n spee 2.9 m/s, wt is its ept? 53 SSM Wter is pumpe steily out of flooe bsement t 5.0 m/s troug ose of rius 1.0 cm, pssing troug winow 3.0 m bove te wterline. Wt is te pump s power? 54 Te wter flowing troug 1.9 cm (insie imeter) pipe flows out troug tree 1.3 cm pipes. () If te flow rtes in te tree smller pipes re 26, 19, n 11 L/min, wt is te flow rte in te 1.9 cm pipe? (b) Wt is te rtio of te spee in te 1.9 cm pipe to tt in te pipe crrying 26 L/min? Moule 14-7 Bernoulli s Eqution 55 How muc work is one by pressure in forcing 1.4 m 3 of wter troug pipe ving n internl imeter of 13 mm if te ifference in pressure t te two ens of te pipe is 1.0 tm? 56 Suppose tt two tnks, 1 n 2, ec wit lrge opening t te top, contin ifferent liquis. smll ole is me in te sie of ec tnk t te sme ept below te liqui surfce, but te ole in tnk 1 s lf te cross-sectionl re of te ole in tnk 2. () Wt is te rtio r 1 /r 2 of te ensities of te liquis if te mss flow rte is te sme for te two oles? (b) Wt is te rtio R V1 /R V2 of te volume flow rtes from te two tnks? (c) t one instnt, te liqui in tnk 1 is 12.0 cm bove te ole. If te tnks re to ve equl volume flow rtes, wt eigt bove te ole must te liqui in tnk 2 be just ten? 57 SSM cylinricl tnk wit lrge imeter is fille wit wter to ept D 0.30 m. ole of cross-sectionl re 6.5 cm 2 in te bottom of te tnk llows wter to rin out. () Wt is te ringe rte in cubic meters per secon? (b) t wt istnce below te bottom of te tnk is te cross-sectionl re of te strem equl to one-lf te re of te ole? 58 Te intke in Fig. 14-47 s cross-sectionl re of 0.74 m 2 n wter flow t 0.40 m/s. t te outlet, istnce D 180 m below te intke, te cross-sectionl re is smller tn t te intke n te wter flows out t 9.5 m/s into equipment. Wt is te pressure ifference between inlet n outlet? Reservoir Intke D Genertor builing Outlet Figure 14-47 Problem 58. 59 SSM Wter is moving wit spee of 5.0 m/s troug pipe wit cross-sectionl re of 4.0 cm 2. Te wter grully escens 10 m s te pipe cross-sectionl re increses to 8.0 cm 2. () Wt is te spee t te lower level? (b) If te pressure t te upper level is 1.5 10 5 P, wt is te pressure t te lower level? 60 Moels of torpeoes re sometimes teste in orizontl pipe of flowing wter, muc s win tunnel is use to test moel irplnes. Consier circulr pipe of internl imeter 25.0 cm n torpeo moel ligne long te long xis of te pipe.te moel s 5.00 cm imeter n is to be teste wit wter flowing pst it t 2.50 m/s. () Wit wt spee must te wter flow in te prt of te pipe tt is unconstricte by te moel? (b) Wt will te pressure ifference be between te constricte n unconstricte prts of te pipe? 61 ILW wter pipe ving 2.5 cm insie imeter crries wter into te bsement of ouse t spee of 0.90 m/s n pressure of 170 kp. If te pipe tpers to 1.2 cm n rises to te secon floor 7.6 m bove te input point, wt re te () spee n (b) wter pressure t te secon floor? 62 pitot tube (Fig. 14-48) is use to etermine te irspee of n irplne. It consists of n outer tube wit number of smll oles B (four re sown) tt llow ir into te tube; tt tube is connecte to one rm of U-tube. Te oter rm of te U-tube is connecte to ole t te front en of te evice, wic points in te irection te plne is ee. t te ir becomes stgnnt so tt v 0.t B, owever, te spee of te ir presumbly equls te irspee v of te plne. () Use Bernoulli s eqution to sow tt 2rg v, r ir were r is te ensity of te liqui in te U-tube n is te ifference in te liqui levels in tt tube. (b) Suppose tt te tube contins lcool n te level ifference is 26.0 cm. Wt is te plne s spee reltive to te ir? Te ensity of te ir is 1.03 kg/m 3 n tt of lcool is 810 kg/m 3. ρ ir v Hole Figure 14-48 Problems 62 n 63. B B Liqui ir ρ
PROBLEMS 411 63 pitot tube (see Problem 62) on ig-ltitue ircrft mesures ifferentil pressure of 180 P. Wt is te ircrft s irspee if te ensity of te ir is 0.031 kg/m 3? 64 In Fig. 14-49, wter flows troug orizontl pipe n ten out v 2 v 1 2 1 into te tmospere t spee v 1 15 m/s. Te imeters of te left n rigt sections of te pipe re 5.0 cm n 3.0 Figure 14-49 Problem 64. cm. () Wt volume of wter flows into te tmospere uring 10 min perio? In te left section of te pipe, wt re (b) te spee v 2 n (c) te guge pressure? 65 SSM WWW venturi meter is use to mesure te flow spee of flui in pipe. Te meter is connecte between two sections of te pipe (Fig. 14-50); te cross-sectionl re of te entrnce n exit of te meter mtces te pipe s cross-sectionl re. Between te entrnce n exit, te flui flows from te pipe wit spee V n ten troug nrrow trot of crosssectionl re wit spee v. mnometer connects te wier portion of te meter to te nrrower portion. Te cnge in te flui s spee is ccompnie by cnge p in te flui s pressure, wic cuses eigt ifference of te liqui in te two rms of te mnometer. (Here p mens pressure in te trot minus pressure in te pipe.) () By pplying Bernoulli s eqution n te eqution of continuity to points 1 n 2 in Fig. 14-50, sow tt 2 2 p V, ( 2 2 ) were r is te ensity of te flui. (b) Suppose tt te flui is fres wter, tt te cross-sectionl res re 64 cm 2 in te pipe n 32 cm 2 in te trot, n tt te pressure is 55 kp in te pipe n 41 kp in te trot. Wt is te rte of wter flow in cubic meters per secon? Meter entrnce V Pipe 1 Venturi meter v 2 Mnometer Figure 14-50 Problems 65 n 66. Meter exit Pipe 66 Consier te venturi tube of Problem 65 n Fig. 14-50 witout te mnometer. Let equl 5. Suppose te pressure p 1 t is 2.0 tm. Compute te vlues of () te spee V t n (b) te spee v t tt mke te pressure p 2 t equl to zero. (c) Compute te corresponing volume flow rte if te imeter t is 5.0 cm. Te penomenon tt occurs t wen p 2 flls to nerly zero is known s cvittion.te wter vporizes into smll bubbles. 67 ILW In Fig. 14-51, te fres wter bein reservoir m s ept D 15 m. orizontl pipe 4.0 cm in imeter psses troug te m t ept 6.0 m. plug secures te pipe opening. () Fin te mgnitue of te frictionl force between plug n pipe wll. (b) Te plug is remove. Wt wter volume exits te pipe in 3.0? D 68 Fres wter flows orizontlly from pipe section 1 of cross-sectionl re 1 into pipe section 2 of cross-sectionl re 2. Figure 14-52 gives plot of te pressure ifference p 2 p 1 versus Figure 14-51 Problem 67. te inverse re squre 1 2 tt woul be expecte for volume flow Δp s rte of certin vlue if te wter flow were lminr uner ll circumstnces. 0 Te scle on te verticl xis is set by 16 32 Δp s 300 kn/m 2. For te conitions of te figure, wt re te vlues of Δp s 2 () 2 n (b) te volume flow rte? 1 (m 4 ) 69 liqui of ensity 900 kg/m 3 Figure 14-52 Problem 68. flows troug orizontl pipe tt s cross-sectionl re of 1.90 10 2 m 2 in region n cross-sectionl re of 9.50 10 2 m 2 in region B. Te pressure ifference between te two regions is 7.20 10 3 P. Wt re () te volume flow rte n (b) te mss flow rte? 70 In Fig. 14-53, wter flows steily from te left pipe section (rius r 1 2.00R), troug te mile section (rius R), n into te rigt section (rius r 3 3.00R). Te spee of te wter in te mile section is 0.500 m/s. Wt is te net work one on 0.400 m 3 of te wter s it moves from te left section to te rigt section? 71 Figure 14-54 sows strem of wter flowing troug ole t ept v 10 cm in tnk oling wter to eigt H 40 cm. () t wt istnce x oes te strem strike te H floor? (b) t wt ept soul secon ole be me to give te sme vlue of x? (c) t wt ept soul x ole be me to mximize x? Figure 14-54 Problem 71. 72 very simplifie scemtic of te rin ringe system for ome is sown in Fig. 14-55. Rin flling on te slnte roof runs off into gutters roun te roof ege; it ten rins troug ownspouts (only one is sown) into min ringe pipe M below te bsement, wic crries te wter to n even lrger pipe below te street. In Fig. 14-55, floor rin in te bsement is lso connecte to ringe pipe M. Suppose te w following pply: (1) te ownspouts ve eigt 1 11 m, (2) te floor rin s eigt 2 1.2 m, (3) pipe M s rius 3.0 cm, (4) te ouse s sie wit w 30 m n front lengt L 60 m,(5) ll 1 p 2 p 1 (kn/m 2 ) r 1 R r 3 Figure 14-53 Problem 70. M 2 Floor rin Figure 14-55 Problem 72.
412 CHPTER 14 FLUIDS te wter striking te roof goes troug pipe M, (6) te initil spee of te wter in ownspout is negligible, n (7) te win spee is negligible (te rin flls verticlly). t wt rinfll rte, in centimeters per our, will wter from pipe M rec te eigt of te floor rin n treten to floo te bsement? itionl Problems 73 bout one-tir of te boy of person floting in te De Se will be bove te wterline. ssuming tt te umn boy ensity is 0.98 g/cm 3, fin te ensity of te wter in te De Se. (Wy is it so muc greter tn 1.0 g/cm 3?) 74 simple open U-tube contins mercury. Wen 11.2 cm of wter is poure into te rigt rm of te tube, ow ig bove its initil level oes te mercury rise in te left rm? 75 If bubble in sprkling wter ccelertes upwr t te rte of 0.225 m/s 2 n s rius of 0.500 mm, wt is its mss? ssume tt te rg force on te bubble is negligible. 76 Suppose tt your boy s uniform ensity of 0.95 times tt of wter. () If you flot in swimming pool, wt frction of your boy s volume is bove te wter surfce? Quicksn is flui prouce wen wter is force up into sn, moving te sn grins wy from one noter so tey re no longer locke togeter by friction. Pools of quicksn cn form wen wter rins unergroun from ills into vlleys were tere re sn pockets. (b) If you flot in eep pool of quicksn tt s ensity 1.6 times tt of wter, wt frction of your boy s volume is bove te quicksn surfce? (c) re you unble to brete? 77 glss bll of rius 2.00 cm sits t te bottom of continer of milk tt s ensity of 1.03 g/cm 3. Te norml force on te bll from te continer s lower surfce s mgnitue 9.48 10 2 N. Wt is te mss of te bll? 78 Cugt in n vlnce, skier is fully submerge in flowing snow of ensity 96 kg/m 3. ssume tt te verge ensity of te skier, cloting, n skiing equipment is 1020 kg/m 3. Wt percentge of te grvittionl force on te skier is offset by te buoynt force from te snow? 79 n object ngs from spring blnce.te blnce registers 30 N in ir, 20 N wen tis object is immerse in wter, n 24 N wen te object is immerse in noter liqui of unknown ensity.wt is te ensity of tt oter liqui? 80 In n experiment, rectngulr block wit eigt is llowe to flot in four seprte liquis. In te first liqui, wic is wter, it flots fully submerge. In liquis, B, n C, it flots wit eigts /2, 2/3, n /4 bove te liqui surfce, respectively. Wt re te reltive ensities (te ensities reltive to tt of wter) of (), (b) B, n (c) C? 81 SSM Figure 14-30 sows moifie U-tube: te rigt rm is sorter tn te left rm. Te open en of te rigt rm is eigt 10.0 cm bove te lbortory benc. Te rius trougout te tube is 1.50 cm. Wter is grully poure into te open en of te left rm until te wter begins to flow out te open en of te rigt rm. Ten liqui of ensity 0.80 g/cm 3 is grully e to te left rm until its eigt in tt rm is 8.0 cm (it oes not mix wit te wter). How muc wter flows out of te rigt rm? 82 Wt is te ccelertion of rising ot-ir blloon if te rtio of te ir ensity outsie te blloon to tt insie is 1.39? Neglect te mss of te blloon fbric n te bsket. 83 Figure 14-56 sows B sipon, wic is evice for removing liqui from continer. 1 Tube BC must initilly be fille, but once tis s been one, liqui will flow troug te tube until te liqui surfce in te continer is level wit te tube opening t. Te liqui s ensity 1000 kg/m 3 n negligible viscosity. Te istnces sown re 1 25 cm, 2 12 cm, n 2 40 cm. () Wit wt spee oes te liqui emerge C from te tube t C? (b) If te tmosperic pressure is 1.0 10 5 P, Figure 14-56 Problem 83. wt is te pressure in te liqui t te topmost point B? (c) Teoreticlly, wt is te gretest possible eigt 1 tt sipon cn lift wter? 84 Wen you coug, you expel ir t ig spee troug te trce n upper bronci so tt te ir will remove excess mucus lining te ptwy.you prouce te ig spee by tis proceure:you brete in lrge mount of ir, trp it by closing te glottis (te nrrow opening in te lrynx), increse te ir pressure by contrcting te lungs, prtilly collpse te trce n upper bronci to nrrow te ptwy, n ten expel te ir troug te ptwy by suenly reopening te glottis. ssume tt uring te expulsion te volume flow rte is 7.0 10 3 m 3 /s. Wt multiple of 343 m/s (te spee of soun v s ) is te irspee troug te trce if te trce imeter () remins its norml vlue of 14 mm n (b) contrcts to 5.2 mm? 85 tin cn s totl volume of 1200 cm 3 n mss of 130 g. How mny grms of le sot of ensity 11.4 g/cm 3 coul it crry witout sinking in wter? 86 Te tension in string oling soli block below te surfce of liqui (of ensity greter tn te block) is T 0 wen te continer (Fig. 14-57) is t rest. Wen te continer is given n upwr ccelertion of 0.250g, wt multiple of T 0 gives te tension in te string? Figure 14-57 Problem 86. 87 Wt is te minimum re (in squre meters) of te top surfce of n ice slb 0.441 m tick floting on fres wter tt will ol up 938 kg utomobile? Tke te ensities of ice n fres wter to be 917 kg/m 3 n 998 kg/m 3, respectively. 88 8.60 kg spere of rius 6.22 cm is t ept of 2.22 km in sewter tt s n verge ensity of 1025 kg/m 3. Wt re te () guge pressure, (b) totl pressure, n (c) corresponing totl force compressing te spere s surfce? Wt re () te mgnitue of te buoynt force on te spere n (e) te mgnitue of te spere s ccelertion if it is free to move? Tke tmosperic pressure to be 1.01 10 5 P. 89 () For sewter of ensity 1.03 g/cm 3, fin te weigt of wter on top of submrine t ept of 255 m if te orizontl cross-sectionl ull re is 2200.0 m 2. (b) In tmosperes, wt wter pressure woul iver experience t tis ept? 90 Te sewge outlet of ouse constructe on slope is 6.59 m below street level. If te sewer is 2.16 m below street level, fin te minimum pressure ifference tt must be crete by te sewge pump to trnsfer wste of verge ensity 1000.00 kg/m 3 from outlet to sewer.