11 - Feces DH CONCEPTS 349 flhcassiln 'l..'l._.... _ ....

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Unformatted text preview: Feces DH CONCEPTS 349 flhcassiln 'l..'l._.... _ . .5........\._.\_ 1 1.5 aacHItaEeEs' PHIHcIPtE The buuyaut terce is the upward fame that a fluid applies tu art ebject that is partially er cempleteiy immersed in it. Archimedes principle states that the magnitude ef the bueyant feree equals the weight ef the fluid that the partially er cempletely immersed ehject displaces: Fe 2 wfluid ‘——s-—" ‘—w—" Magnitude ef Weight ef hueyant ferce displaced fluid Eaa.te.11.1e lli-fii ttw 11.1 1 1.? Pamela IH Hflflflhl. 1 1.3 THE Eduanett eF ceutmumt In steady flew. the selecin ef the fluid particles at any peint is censtant as time passes. Pm incempressible. nensisceus fluid is knewn as an ideal fluid. The mass flew rate at a fluid with a density p. flewing with a speed s- in a pipe at cress-aeetienal arearl. is the mass per secend [itgtsi flewing past a peint and is giyen by Mass flew rate = pude (l L?) The equatiun ef centineity expresses the fact that mass is censeryed: what flews inte ene end ef a pipe flews eut the‘hther end. assuming there are he additienal entry er esit peints in between. Es- pressed in terms ef the mass flew rate. the equatien ef centinuity is PIALI’I = Pedal}: {1 LS} where the subscripts l and 2 deuete twe peittts aleng the pipe. If a fluid is incempressihle. the density at any twe peints is the same. p. = p2. Fer an incempress- ible fluid. the equatien ef centinuity becames E1. 12. 13 Arvt =A13’1 (l 1-9] (3511.1 The preduct At! is knewn as the yelume flew rate Q (in m3tsi: Q = Velume flew rate = At: [1].]fl} 1 1 .a HEHHDULLI'E Eduamelt. 1 1 .1 t1 APPLIEATIeHs DF EEHHDULLl'S aeuanen In the steady flew at" an ideal fluid whese density is p, the pressure P. the fluid speed a. and the elesatien y at any twe peints {I and 2] in the fluid are related by Bemeulli‘s equatien: Eat. 14. 15. 16 F: + its}:2 + ass] = F's + it”? + ease {I H” "-W "-1 1mm" “13 flfl'W i5 hflfififlflifil {Isl = Jr'sL Edmeulii's equatien indicates that higher fluid speeds are '5 “33 asseciated with Iewer fluid pressures. 1 1.1 1 slaceus FLDW The magnitude F ef the tangential ferce required te mese a fluid layer at a censtant speed u, when the layer has an area at and is lecated a perpendicular distance y frem an immebile surface. is given by pelt: F = {H.131} 1}. where n is the ceefficient ef 1riscesity. A fluid whese yiscesity is a}. flewing threugh a pipe ef radius ft‘ and length L. has a selume flew rate {:3 given by H WR4{PI _ EH. Q ” 3-,]; “HM I511.a1 11. —- -\_J_—|_—-_- where P. and P3 are the pressures at the ends ef the pipe. BIJHBEPTS 1".fnsfl'aeturs: The numbering sf the’peaesttaas shawls here reflects thefact that they are artty a representative saflset ef the tatal number that are -. ' ',HflHlE'l-|'£J: all aftfle aaestt'aas are available far asst gamth via an airline heme-weld: management pregram such as WiieyPLUS er Webda'stga. -:.'.= Pressure and Death in a Stalls Fluid {c} Centainert—‘t. beeeuse a has the great- 5 '_;j'_".'--;-d1ews three ceutainers filled te the same height with cat selume ef fluid. {d} |lifetttainer B. -._;j.= ultich centaiuer. if any. is the pressure at the bettem because it has the least selume ef fluid. , A. bacause its bettem has the greatest surface {e} Centainer C. because its bettem has 5 fl. centainets have the same pressure at the bettem. the least surface area. ‘ -. :- '=":I=-I ef geld in a Hill-karat geld necklace whese chuntt et‘ cencretc has a hellew spherical nf the chunk is 33 kg, and the vfllumg m- --:':':'nt::u- surface ef the chunk is [1.1125 m3. What is the _ .j_.-.u _ -: cavity? "......- s 0.15 m It: dhfifl m at case at. Hew many _ _ e the same mass as this bar? Site-:- 5. -. l' finds a selid tech that is cempnsed seleiy The mass and velume ef the reek are. respec- ' 4.111} is ill"3 m3. Find the mass ef the geld in the _ u ef a satellite that erbits this planet just abeve .:'.::I.'.-|t Table 11.] as necessary. selutien a made by raising emvlese slrssl with water. Suppese that the specifi': gravity “f -. .1m3tl. Assuming that the tetal velume ef the tin— _;';_:L-r' its parts, determine the velurne percentage ef eths seiutien. 'I -r:_-.F..l.r I fits“ hes. has a remuvable lid ef area 1.3 it ltl‘2 tn2 -.-;;.'_;t+ The her. is taken up a meuntain where the air “Fifi. has is {1.35 a: Itlii Pa. The inside ef the bus is :4 What is the magnitude ef the ferce required te hurt? ' is printed using intagiie presses that gen- .- ntse a Itl" lbtin? a see bill is at in. by : magnitude ef the ferce that the printing press ap~ he hit]. ' an 11.1: at waw.wiley.cemtcellegetcutnell is -: lent. A selid cencrete bleck weighs [69 hi and r d. Its dimensiens are asuu tn rs illfltl m :s: . .ef identical blecks are stacked en tep ef this ene. '- tlutnher ef wheie blecks {including the eue en {fir-i". he stacked an that their weight creates a pressure - its pheres en the greund beneath the first bteck? fits 152.5 N is riding a 934's meuntain bike. i__'..-n- - weight at the rider and bike is supperted equally the gauge pressure in each tire is Ibfl it til" Pa. what it: s- between each tire and the greund‘i' _.ef seda is sealed with a screw cap. The abselute 1;}. n dieside inside the battle is LEG a. It}5 F'a. and bettem surfaces at the cap each have an --.'I mi. ehtain the magnitude ef the ferce that the - .eu the cap in erder tn keep it en the bettle. The = rigi- the battle is date attnesphere. uses a pump with hydraulic eil te push a pisten. a chisel. The pump can generate a pressure at "xiii; the hydraulic eil. and the pisten has a radius et lasting 25 s, the pisten meves illitl m. What is uperate the leg splitter‘s pump? {mass at = id itg} is testing an the finer ef an ei- the suitcase in centact with the finer measures 'I'he elevater is meving upward with an accelera- ..;_:imts1. What pressure (in excess ef atmespheric - :‘flt't: tn the fleet beneath the suitcase? ""tially empty urinary bladder fills with urine and - jig" .its internal pressure increases by area Pa. which PRC-ELEth 351 triggers the micturitien refles (the feeling ef the need te uri— uate}. The drawing shews a heri~ zental. square sectien ef the bladder wait with an edge length ef flfllfl tn. Because the bladder is stretched. feur tensien ferces ef equal magnitude 3" act. en the square sectien. ene at each edge. and each hate is directed at an em gle ti belew the herieeutal. What is the magnitude T ef the tensien fnrce acting en ene edge at the sectien when the internal bladder pressure is 33th] Pa and each ef the feur tensien ferces is directed ill“ belew the herizental? iii-ji'hlipathflflcai Spherical Plaflfl mmmm Entirely “f ** 19. III“ fit cylinder [with circular ends} and u hemisphere arc selid threugheut and made frem the same material. The},r are resting en the gteund. the cylinder en ene at its ends and the hemisphere en its flat side. The weight ef each causes the same pressure te act en the greund. The cylinder is [151311 at high. What is the radius ef the hemi— sphere? Sectien 11.3 Pressure and Depth in a Static Fluid, Sectien 11.4 Pressure lGauges 21}. The Mariana. trench is lecated in the fleet nf the Pacific fleean at a depth ef abeut i 1 Bill] m belew the surface ef the water. The den sity ef seawater is 11325 kgl'rn'i'. {a} If an underwater vehicle were tn csplere such a depth. what farce weuld the water exert an the vehi- cle‘s nbservatien windew [radius = {lltl m)? {b} Fer cemparisen. determine the weight ef a jettiner whese mass is [.2 it ill5 kg. 21. As backgreund fer this preblem, review Cenceptual Example s. A submersible pump is put under the water at the bettem ef a well and is used te push water up threugh a pipe. What minimum eutput gauge pressure must the pump generate te make the water reach the Millie at greund levei. T] m abeve the pump? 22.. @ .t't meat buster censists ef a squeeze bulb attached In a plastic tube. When the bulb is squeezed and released. with the epen end ef the tube under the surface ef the basting sauce. the sauce rises in the tube re a distance h. as the drawing shews. Using Llllfi a: 1135 Pa fer the at— mespheric pressure and 12m kgtm-i fer the deep I sity ef the sauce. find the abselute pressure in . , the bulb when the distance it is (a) {115 m and ' -' {h} {LII} m. 23. sent Measured alettg the surface ef thti water. a rectangular swimming pee] has a length ef 15 re. Alnng this length. the flat bets tum ef the peel stepes dewnward at an angle ef ! l“ belew the heri- ttental. fret'n ene end tn the ether. By hew much dees the pressure at the bettern ef the deep end etteeed the pressure at the bettetn ef the shallew end?I htmespheric pressure 24. The drawing shews an intraveneus feeding. With the distance shewn. nutri- ent selutien (p: ltl3fl ltgr'tn-‘jl can just barely enter the bleed in the vein. What is the gauge pressure cf the veueus bleed? Express yeur answer in millime- ters ef mercury. 15. The human lungs can ' functien satisfacterily up tn :1 limit where the pressure thiem 24 {melt uses a byt- - :3” the drawing 'tgefivated by the injects hy- 'i't':'ylinder at an 3.54 K lfl‘Pa Plunger' lnputfer "Egret [if [1.159 m. hydraulic uil lite plunger re~ _' .: tn the fleer ef the lead bed, fled the terque that -- ;.:-'Ei?~: abeut the axis identified in the drawing. I it '..t ’Prineiple if; is 91? kgfmi”, and the densityr ef sea water is =f'f:-:‘..:- ‘ ii '; pelar bear climbs cure a piece ef fleating "I I- I -ef5.2 m3. 1What is the weight ef the heaviest bear rt -- witheut sinking cemplerely beneath the water? I In - i- Example ll reviews the cencepts that are 'j-jtrehlern. What is the radius ef a hydregen~fllled bati- a lead ef arse N {in additien tn the weight ef the density ef air is has kgi'm3? _ is a device used te tire iieuiii. h is a eyihitiit- Iat tine end, an that it heats _;:_';j;E_ end dewavrurd. The tube is via. large “medicine dropper,” liquid is drawn using the that: drawing). set use with put an the tube ed that the indicates whether the (mere dense] er antifreeze Marks fer lemonade: has a weight ef ta? treat cf and a cress-sectienal area J'qu'di‘ fart m2. Hew far teeth the bet- '.3".? the mark be put dtat denetes {a} battery acid eat {It} entiheeee te = trite hgtmtit -.:-- :. en a lake with 35% cf its velume beneath the - average density ef the duck? tlte l‘t'tdile ef the 311:1 me has x in” kg eiei m is its density? {b} If a selid ebject is made frem - the same density as the sun, weuld it sink er fleat -- [e] Weuld a selid ebject sink er fleat in water if it material whese density was the same as that ef the ":"_'t‘_tr: = 5.? X 102“ kg, radius = 15.0 it lift"r n1]? Previde panther. _"_J'|'i-- i .3l-kg persen puts en a life jacket. jumps inte the ';_i'_'_'i:- The jacket has a vetume cf 3.: it 10*? m3 and is “it-i r: it: under the water. The vclume ef the persen's ' '_ wilder is 5.2 it: 10'1 m3. 1|i't’hat is dre density ef the J . E ' 2'11? .- . : -.* . - - - . I ' . -r-r - ,--. 1.|1-'l' Hydremeter eentainer is feund resting en the ccean deer and tn The centainer is 5.1 tn leng, 2.4 m wide. and y experts attach a spherical balleen re the tep ef _ inflate it with air pumped dewn frem the surface. 1""; "a radius is LS m. the shipping centainerjusr begins '33,}: aurfaee. What is the mass ef the centainer‘i' lgnere - - I I I and the air within it. Be net neglect the huey- ah the shipping centainer by the water. The density “iii kstmi- dtreugheut. ‘W’lmn Ithe ebjeet is cempietely -_ it“ i alcehel, its apparent weight is 15.2 bl. When PHeEtLEhite 35:1 cempletety submerged in water. its apparent weight is 13.? N. What is die vclume ef the ebject'i' * 43. @ A her-air balleen is acceleratin g upward under the influence ef twe ferces, its weight and the bueyant ferce. Fer simplicity, cen~ sider the weight tn be enly that ef the bet air within the balleen, thus ignering the balleen fabgic and the basket. The her air inside the bal- leen has a density ef = 0.03 kgi'm3. and the density ef the cunt air eutside is pm] ,i, = Li? kgi‘mJ. What is the acceieratien ef the rising balleen? * 49. ant-n A Kennedy half-duller has a mass that is I.l50 it: 10‘2 kg. The cein is a mixture ef siiver and cepper, and in water weighs 0.101! N. Determine the mass ef silver in the cein. ‘50. Refer te Multiple-Cencepr Example 1 l te see a preblem similar te this ene. What is the smallest number ef wheie legs (p = T25 kgfma, radius = 0.0300 m, length = 3.00 m} that can be used te build a raft that will carry feur peeple, each ef whem has a mass ef 30.0 kg? “‘51. lier i3. selid cylinder (radius = 0.150 rn, height = 0.120 m] has a mass ef 3.00 kg. This cyiinder is fleeting in water. Then eil. [p = 1'25 kgfrni'} is peered en rep at” the water until the situatien shewn in the drawing re- sults. Hew much ef the height ef the cylinder is in the eil‘i' ** 52. Interactive Learntnpware 11.1 at www. edleymunflcellegefmrmefl prevides a review ef the cencepts that are impertant in this prebiem. A. spring is attached tn the bettern ef an empty swimming peel, with the axis ef the spring eri- ented vertically. the 3ng blecit ef weed [p = 340 kgi‘mi‘} is fixed re the tep ef the spring and cempresses it. Then the peel is titled with wa- ter, cempleteiy cevering the bleck. The spring is new ebserved te be stretched twice as much as it had been cernpressed. Determine the per— centage ef the bleck’s retal vclume that is hellew. Ignere any air in the hellew space. ** 53. A lighter—than-air balleen and its lead ef passengers and ballast are fleeting statienary abeve the earth. Ballast is weight {ef negligible vclume) that can be drepped everheard re make the balleen rise. The radius ef this balleen is 5.25 m. Assuming a censtant value ef 1.29 kgfmi' fer the density ef air. determine hew much weight must be drepped evcrh-eard te make the balleen rise 105 tn in 15.0 s. Seefien 11.3 The Equatien ef Centinnity 54. A fuel pump sends gaseline frem a car’s fire] tank tn the engine at a rate at 5.33 at 10‘1 kgi's. The density ef the gaseline is T35 kgt‘mi', and the radius ef the fueT line is 3.13 x l0"3 m. What is the speed at which the gaseline meves threugh the fuel line? 55. sent a patient recevering frem surgery is being given fluid intraveneusiy. The fluid has a density ef 1030 kgt‘m", and 9.5 it 10“ m3 ef it flews inte the patient every six heurs. Find the mass flew rate in kgfs. 55. @ Water flews straight dewn frem an epen faucet. The cress- sectienal area ef the faucet is 1.3 it“ 10'“ m1, and the speed ef the water is 0.35 mis as it leaves the faucet. Ignering air resistance, find the cress-sectienal area ef the water stream at a peint 0.10 rn belew the faucet. 5?. it reem has a vclume ef 120 m3. An aireenditiening system is re replace the air in this reem every twenty minums, using ducts that have a square cress sectien. Assuming that air can be treated as an in- eempressible fluid, find the length ef a side ef the square if the air speed within the ducts is {a} 3.0 mfs and {b} 5.0 nuts. 53. T Concept Simulatiun 11.1 at www.itviIey.tt.tiant"cellitgeiIr cut-tell reviews a central cencepr in this preblcm. {a} The .'t':-t.- . “6:33;” .metangular plate is hanging vertically dewnward . A? :.: eleng its left edge. By blewittg air at l LU ntt's h piers enly, it is pessible te keep the plate in a her- _- i-illustrated in part a ef the drawing. Te what value _j_'.fij'--r he reduced se titat the plate is kept at a see" an- the vertical, as in part it ef the drawing? tHinr: ' ": fegflltfiefl in the fenn rtf Equetien HJE'.) h'lflll'lll'lg air | Edge view at plate - is useful fer remev- The siphen tube : zillitliquid, and then ene ether and as the ' {a} Using reasen- ;x-elepleyed in ebtain- . ithenrem, derive an 1' e ef the fluid This espres- tertus ef the vettit j}; t_:. 'seceleratien due te . this speed dues net -: d' eflhe tube belew giiqttitt.) [III] at what distance y will the siphen step werking‘? 'en fer the abselute pressure at the highest a {point at) in terms ef the atmespheric pressure p. g. and the heights it and y. {hints that the tiff?" is the same as the speed ef the fluid emerg- Lbecause the cress-sectienal area at the tube is the l- '- -'l Flew ____;_l.'3-m length ef heriaental pipe has a radius ef ta within the pipe flews with a velume flew rate : eat ef the right end ef the pipe and late the air. trigger: in the flewing water at the left end ef the pipe if {a} an ideal fluid and lb} a visceus fluid I 9,1,; lpa.5}e -.'I.:-_f:'-.l- law remains valid as lung as the Fluid flew is sufficiently high speed, hewever, the flew git-.. even if the fluid is mevng threugh a smeeth =7”:- ' 'ens. It is feund experimentally that the flew is - Reynalds number He is less titan abeut lflflfl: - h, p, anti r] are, respectively, the average speed. ef the fluid. and R is the radius ef the pipe. average speed that stead (a: less karat]. - eeuld have and still remain in laminar flew “if = 3": ill—'1' if; bedy, bleed vessels can dilate, er increase 1-3215; t ', in respense te varieus stimuli, se that the velume Placements 355 flew rate ef the bleed increases. Assume that the pressure at either end ef a bleed vessel. the length ef the vessel. and the viscesity ef the bleed remain the same, and determine the facter Rdtmmdlfinunnm by which the radius ef a vessel must change in erder te deuble the vel- ume flew rate ef the bleed threugh the vessel. fill. a T A bleed transfusien is being set up in an emergency reern fer an accident victim. Bleed has a density ef lflhfl ll:me and a viscesity ef4fl it: I'll";1 Pa - s. The needle being used has a length ef 31} cm and an inner radius ef 13.25 mm. The decter wishes te use a velume flew mte threugh the needle at 4.5 it“. lfl‘“ mils. What is the distance it abeve the victim’s arm where the level ef the bleed in the transfusien bottle sheuld be leeated'l As an appresima- lien, assume that the level ef the bleed in the transfusien b-ettle and the peint where the needle enters the vein in the amt have the same pres- sure ef ene atmesphere. {In reality, the pressure in the vein is slightly abeve atmespheric pressure.) 31. earn Interactlve Selutlen 11.fl1 at www.wilflf.tflfl1ftflllegff eutnell illustrates a medal fer selving this preblertt. A pressure difference ef 1.3 it“ lllj Pa is needed te drive water fn= LEI 3": ill—3 F's-s] threugh a pipe whese radius-is 5.l is“ iii—3m. The velume flew rate ef the water is 2.3 is ill“ mh‘s. What is the length ef the pipe? 32. h. velume ef ’12 m3 ef glycerel {1] = [1.934 Pars] is pumped threugh a IS-m length ef pipe in 55 minutes. The pressure at the in- put end ef the pipe is 3.6 ht l'll5 Pa, and the pmssure at the eutput end is atmespheric pressure. What is the pipes radius? ‘83. @ ’l‘we heses are cenneeted tn the same eutlet using a Y-cenneeter, as the drawing shews. The heses A and B have the same length, but hese B has the larger radius. Each is epen te the atme- sphere at the end where the water esits. Water flews threugh heth heses as a visceus fluid, and Peiseuilleis law IQ = all“ng — Flit‘iinLI applies In each. In this law. PE is the pressure upstream. P, is the press sure dewnstream. and Q is the velume flew rate. The ratie ef the ra- dius ef hese E Ie the radius ef hese A is Ratify, = LEI}. Find the ratie ef the speed ef the water in hese B te the speed in hese A. Water lrern eutlet til-1. When an ehjeet meves threugh a fluid. the fluid exerts a visr ceus ferce if en the ebjeet that tends te slew it dewn. Fer a small sphere ef radius R, meving slewly with a speed a, the magnitude ef the visceus ferce is given by Stekes’ law. F = err-rifle. where n is the viscesity ef the fluid. {a} 1t‘llhat is the visceus ferce en a sphere ef radius R = if] it Ill"l m that is falling threugh water [1} = III] is“. lt'l':l Pa-s] when the sphere has a speed ef ll] mils? {It} The speed ef the falling sphere increases until the visceus ferce haln ances the weight ef the sphere. Thereafter. rte net ferce acts en the sphere, and it falls with a censtant speed called the “terminal speed." lfthe sphere has a mass ef Ltl it ill"5 ltg. what is its termi- nal'speed'i' '——— 354} eHAPTen 11 FLLllElS 4. "[‘weliquids. l and 2.are in equilibrium Liquid 1 1-3- 13. in tlte drawing. water flews in a Ll-tube that is epen at beth ends. as in frem a wide sectien ef a pipe te a - , the drawing. The liquids de net min. and narrew sectien. In which part ef the -:./l -- liquid l rests en tep ef liquid 2. Hewisthe pipe is the velume flew rate the .- density p. ef liquid 1 minted tn the density greatest? [at The wide sectien [h] The narrew sectien [cl p3 ef liquid 2? {a} p1 is equal te p1 velume flew rate is the same in heth sectiens ef the pipe. because the liquids are in equilibrium. " ' I 5 _ {'1} pl is greater than p} {E} m E has}; Secttnn 11.9 Berdnnllt’s Equetien than p2. [d] There is net eneugh infermatien te tell which liquid has the greater density. 16. Bleed tlews thrnugh a sectien ef a heriaental artery . that is partially blecked by a Secunn 11.6 Arthinletles’ Principle dflpflfih alfiflg m: angry wan 9. A beaker is filled tn the brim with water. A selid ' A hemeglebin melecule ehject ef mass 3.11!) kg is lewered inte the beaker se - I meves frem the narrew re- _ that the ebject is fully submerged in the water [see the ' - - ' - glen intn the wider regien. What happens tn the pressure actingea ='- drawing}. During this precess. Elli] kg et water flews 3.2: 3 melecule‘? {a} The pressure increases. {b} The pressure I i ever the rim and nut ef the beaker. What is the huey- T" {c} There is ne change in the pressure. ant ferce that acts en the submerged ehject. and. when i I ml water is flawng dawn Ihmugh A released. rises the ebject rise. sink. er remain in place? the pipe Shflwn in mg drawing; point H [11} 29.4 WI. Ill»: flhjflfll. rises. 39.4 N: tl'lt'r ebject is at a highflr Elfiyatifln than B and C sinks. {cl l9.h N; the ebject rises. {de 19.6 hi; the ebject sinks. are. The cmfigecgflnal areas are [he ' {e} 1915 hi; the ehject remains in place. same at h. and B but are wider at C. ll]. Three selid ebjects are fleeting in it Rank the pressures at the three liquid. as in the drawing. They have dil- peints. largest first. {a} PA. PE. PE ferent weights and velumes. but have [b] PC. Pg. Pg {c} PB. Pg. PA the same thickness {the dimensien per- ': ' -_ .- i I' . r . _ Sectien 11.11 ‘ihscens Flew pendicular tn the page}. Rank the eh- jgcts accfirding m thg'u' densityi largest ID. A viscetts fluid is flewing thrnugh twe heriaental pipes. The I}; first, {a} g” E, t: {h} A, c, B sure difference P1”F1 between the ends ef each pipe is the same”: tc] B. A. C {d} H. C. h [e] C. h, B pipes have the same radius. althnugh ene is twice as lnng as the Hew dees the velume fiew rate Q“ in the lnnger pipe cempare-' Sfltfiflfl I1-3 “HEW-3th" 9f Cflnllfluitb' the rate Q... in the sherter pipe? {a} (2.; is the same .55- 11. A hnllnw pipe is submerged in a stream ef water se that the [b] QB is twice as large as {21... [c] QB is feur times as large at :3 length ef the pipe is parallel tn the velecity ef the water. if the water {d} QB is nne-half as large as (3,... {e} QB is ene-feurth as large :-:' speed dnubies and the cress-sectienal area et' the pipe triples. what happens tn the velume flew rate ef the water passing thrnugh the pipe“? {a} The velume flew rate dees net change. lb} The velume flew rate increases by a facter ef 2. {c} The velume flew rate in- creases by a facter ef 3. {d} The velume flew rate increases by a fac- ter ef 4. {e} The velume flew rate increases by a facter et' s. LEMS ~ ' " en eni'ine hemewerh management phi-grate nrlted with the teen nne treasured in WileyFLUS train it guided tuterintfnrtnnt that mvider enhanced l‘ E P . Nets tn Instrnetnrs: Mnst ef the hetnewnrl: pnrhtetnr in this chapter are nvniielrle fer assignment ch: as Wiley FL US nr Wehhsst'gn. end these re tivity. See Prefacefer additinnal details. 55m Salutinn is in the Student Salutiens Manual. m Selullnn is available nnline at www.wiley.cettttcnllegefcutnell _.....-t.w- - __....“- .—. ———— _._ M __- __. semi)“ “*1 M955 DEM“? I ef the thickness ef this sheet ef paper}. Find the area ef such 1. earn A water bed fer sale has dimensinns ef [.33 m is: 2.l3 m is that can be fermed item Lilli} kg ef silver. (1229 m. The liner ef the bedreem will telerate an additinnal weight 4‘ Haunt,“ stars mnsifl ml}. flf neutral“ and have “beg _.M-_ et" en mere than ssse N. Find the weight ef the water in the bed and gflnfiitifl A typical mass and {aging ml. a mum," 5m. ,5; determine whether the bed sheuld be purchased. 23 g; was kg and 13 3...; up m [3} Find mg density Bf 5mg 2. A cylindrical sterage tank has a radius ef I22 m. When filled tn a {h} [f a dime {V = 21] H iii"r ml} were made frem this |'-l height ef 3.1r'l m. it heids 14 3th} kg ef a liquid industrial selvent. hnw much weuld it weigh {in peunds]? What '5 fl“: demlw ‘Jf Ill“ Salim” 5. The harm is a dimensienless unit that is used tn indicate 3. sum hecemplished silver wnrkers in India can peund silver inte in- . pertien ef geld in a geld-eentaining alley. the alley that is credibly thin sheets. as thin as lllfl 3r: till”T m tabeut nne-hundredth geld centains a weight ef pure geld that is ene part in re: 352 cHAPTEn 11 FLUIDS difference between the eutside and inside ef the lungs is nne-twenti— eth ef an aunesphere. if a diver uses a snerltel fer breathing, hew far helew the water can she swim? Assume the diver is in salt water whese density is “3'25 kgtmi'. 216. if a scuba diver descends tec quickly late the sea, the intenral pressure en each eardrum mmains at atmnspheric pressure, while the extema] pressure increases due tn the increased water depth. tit sufficient depths. the difference hehveen the external and internal pressures can rupture an eardrum. Eardrums can rupture when the pres- sure difference is as little as 35 ltPa. What is the depth at which this pres- sure difference ceuid cccur'i' The density ef seawater is 1(125 ltgtm". 2?. sum A water tnwer is a familiar sight in many tewns. The pur- pese ef such a tewer is tn previde sterage capacity and tn previde suf- ficient pressure in the pipes that deliver the water In eustnmers. The drawing shews a spherical reserveir that centains 5.25 It: ll}5 ltg ef water when full. The reserveir is vented tn the aunesphere at the tep. Fer a full reserveir, find the gauge pressure that the water has at the faucet in {a} heuse A and {b} heuse B. Ignere the diameter ef the delivery pipes. ltent “‘18. Figure 11.“ shews a mercury haremeter. Ceesider twe harem— eters, tree using mercury and anether using an unltrtnwn liquid. Suppese that the pmssure aheve the liquid in each tube is maintained at the same value P, between aere and attnnspheric pressure. The height ef the unltnewn liquid is in times greatm than the height at the mercury. Find the density ef the unknewn liquid. “‘29. Ill“ A tube is sealed at heth ends and ccntains a {Lil lflfl~m—lcng pnrtinn cf liquid. The length cf the tube is large cempared ttt Dfllflfl m. There is an air in the tube, and the vapnr in the space aheve the liquid may be ignnred. The tube is whirled arcund in a heriaentai circle at a ccnstant angular speed. The axis ef retatien passes threugh ene end ef the tube, and during the metien, the liquid cellects at the ether end. The pressure experienced by the liquid is the same as it wnuld experience at the bettem cf the tube. if the tube were cempletely filled with liquid and allewed tu hang vertically. Find the angular speed (in radfs} cf the tube. tat}. Mercury is peered late a tall glass. Ethyl alcehel [which dees net mix with mercury} is then peured en tep ef the mercury until the height cf the ethyl alcehel itself is i it] cut. The air pressure at the tep ef the ethyl alcehel is nne atmesphere. What is the absclute pressure at a paint that is lit} cm belnw the ethyl alcehel—mercury interface? *31. The vertical surface ef a reserveir darn that is in centaet with the water is 12E! tn wide and 12 re high. The air pressure is eee anne- sphere. Find the magnitude ef the Intel feree acting en this surface in a enmpletely filled reserveir. (Hint: The pressure varies linearly with depth. as yen must use an average pressure. ,l “‘32. its the drawing illustrates, a pend has the shape ef an inverted eene with the tip sliced eff and has a depth ef illll m. The time- spherie pressure aheve the pend is l.lli it ill5 Pa. The circular tep surface {radius = R1) and circular bet- tem surface (radius = til} ef the pend are heth parallel tn the greund. The magnitude ef dre feree acting en the top surface is the same as the magni— tude ef the feree acting en the bettem surface. Dbtain [petty and {hilly Sentient 11.5 Pascal’s Principle 33. sent The atmespheric pressure aheve a swimming pc-el c -'- 1-,; frem T55 in T65 mm cf mercury. The bettem cf the pen] is a wn' gle l l2 m it 24 re}. By hew much dees the feree en the bettem ef ll. peel increase? 34. A barber's chair with a petsen in it weighs Zlfll} bl. The r lea; plunger cf a hydraulic system begins tn lift the chair when the r--: i feet applies a feree cf 55 bl tn the input pisten. Neglect any .1: difference between the plunger and the pisten. What is the ralie cf radius ef the plunger tn the radius ef the pisten? 35. Interactive Snlutlnn 11.35 at www.vviIey.cernl'eellegel u a _ a model fer this preblem. Multiple-Cencept Example 3 alse - an apprcach tn problems cf this kind. The hydraulic nil in a car has a density ef 3.311} at Ill2 ltgfnti. The weight cf the input HE" is negligible. “The radii ef the input pisten and eutput plunger" I'll] it lll‘3 m and H.125 m, respectively. What input feree needed te suppert the 24 fifth-N cemhined weight cf a car and the ' put plunger, when {a} the bettem surfaces ef the pisten and r- In; are at the same level, and (h) the bettem surface cf the u-nt plunger is l.3fl tn nit-eve that ef the input pisten?I I u as. a hydraulic cylinder with a radius et' {111231 at has a am.- the left end and a safety valve at the right end. The safety valve circular epening with a radius cf eees fill at, sealed with a disk. disk is held in place by a spring [spring ccnstant = 335 Nita] u, eempressed [Lilith] m frnrn its unstrained length. What is the r-:-:_': tude cf the minimum feree that must be exerted en the pisten in Ii tn epen are safety valve“? ' ' *37. The drawing shcws a hy- draulic system used with disc “HEW mflmke brakes. The feree F is applied fluid FEE“: ' perpendicularly tn the brake a ' pedal. The pedal rctates abeut the axis strewn in the drawing _ and causes a feree tn be applied Master perpendicularly tn the input pis— crlinder ten [radius = 9.5D_H ill—iJj m} a in the master cylinder. The resulting pressure is transmit- ted by the bralte fluid in the nut- rut Finesse {radii = Lat:- a llr2 in}, which are eevered witlt the “Hints. The are pressed against beds sides nf a an: . the muting whfifl Supp-fits that the magnitude ef F' is see it. - .-'.'j that the input pisten and the eutput plungers are at the same amid-- and find the feree applied te each side ef the misting disc. ' “‘33. a The drawing shnws a hydraulic chamber with a spring {spring ccnstant = tlillfl Him} at— tached tn the input pisten and a reel: nf mass dflfl ltg resting en the eutput plunger. The pisten and plunger are nearly at the same height, and each has a neg- ligible mass. By hew much is the spring eempressed frere Ti. strained pesitiee‘? {Llflfl r'n Eralte " pedal l Edge view et relating disc attached in wheel Al'E‘E 115 cm 354 eHAPrEn 11 FLUIDS velume flew rate in an artery supplying the brain is if:- ‘et lfl'“ mills. lecateti 21} m beneath the surface ef the lake. 1|Ii'tfhat velume at If the realms ef the artery is 5.2 mm. determine the average bleed per secend leaks inte the ship? fpflw- {hi Film “"5 awrage him 5m 5' 5‘ “Miriam” in mg an”? at. Water is circulating threngh a clnsed system ef pipes in a win If the eensuieunn reduces the ladies by a facter cf 3. Assume that the flaw apanmgnL [in the first figm- the water has a gauge pressure ii mmmfl fiflw rate if the 5am“: “‘5 ml“ in pan {ai' 3.4 “at It)“ Pa and a speed cf 2.] mfs. Hewever. en the secend fl'rs *59. lt'Icsnciaept Simulatlnn 11.1 at wwwm'iley.euinfenllegefcutnell which is 41!} m higher. the speed ef the water is 3.? min. The ten"; reviews the central idea in this prnblem. In an adjustable net-tale fera are different becafise the pipe diameters are different. What is n'ii_ garden hnse. a cylindrical plug is aligned aleng the axis ef the hnse gauge pressure ef the water en the secnnd finer”? and “a” be inserted int“ if": hm “Wining- Thfl Pummfl “f ih'f P193 if as. Interactive tearnlngWare 11.2 at www.wiley.cnmfcel >;._-_{ 1“ change we filmed “f the Will” lflavmg m": hmfi' Th": Spam m 11": eutnell reviews the approach taken in preblenss such as this my: water passing arnund the plug is tn be three times as large as the speed A Email Crack WHITE at the base Bf a l 5_fl_m_high dam The. :: ef the water bet‘nre it encnunters the plug. Find the ratin ef the plug ' _ _ _ _ crack area thrnugh which water leaves is LSD at lil'~1 “sf. radius tn the inside hnse radtus. {a} ignnring viscnus insses. what is the speed ef water fl If: *fitl't The anrta carries bleed away frem the heart at a speed ef thrnugh the crack? {h} Hew many cubic meters ef water per mi abeut 4i} cmfs and has a radius ef appresimately i.i cm. leave the dam'r1 The anrta branches eventually intn a large number nf tiny capillar- ies that distribute the bleed tn the varieus bedy nrgans. In a capil— lary. the bleed speed is appresimately til}? cmfs. and the radius is abeut e H iii"4 cm. Treat the blend as an incemprcssible fluid. and use these data tn determine the appresimatc number et' capillaries in the human bedy. *69. earn rt. Venturi meter is a device that is used fer measuring It; speed ef a fluid within a pipe. The drawing shnws a gas fleeting:- speed U3 thrnugh a herisnntal sectinn nf pipe whnse crass-sec n__ area is a: = {lile mi. The gas has a density ef p = 1.3{1 kgfmi. ii Venturi meter has a cress—secticnal area nfrt. = flflfiflfl at1 and been substituted fer a sectinn cf the larger pipe- The pressure ‘ if ence between the [we sectinns is F’1 — P. = l2{l Fa. Find {It} speed 1!; ef the gas in the larger. eriginal pipe and {h} the ve n..f' flew rate 1.? cf the gas. Seetinn 1L9 Bemnulli’s Equatinn, SeettenIlJll' Applicatinns nf Bernnulli’s Equatinn til. ssm Review Cenceptual Esampie id as an aid in understanding this prnbiem. Suppese that a Iii—nus wind is blewing acress the reef nf yeur heuse. The density ef air is 1.29 kgfmi'. {a} Determine the reductien in pressure t'belew atmespheric pressure ef statienary air} that accempanies this wind. {h} Explain why sente reefs are ._ . , . .. _ _ _ i , “blewn nutward" during high winds. 3""? . 52. Due way in administer an innculatinnsis with a "gun" that sheets the vaccine threugh a narrew npening. Ne needle is necessary. fer the vaccine emerges with sufficient speed tn pass di— *Til. a hand-pumped water gun is held level at a height ef [ti rectly inte the tissue beneath the skin. The speed is high. because the abeee the gfflflfld and fired. The water stream frnrn the gun hits vaccine in = i it!) kgfm-‘l is held in a reserveir where a high pressure greund a hnrienntal distance ef 2.3 m frem the muscle. Find the pushes it eat. The pressure en the surface ef the vaccine in ene gun preggure ef the water gun's reserveir at the instant when the 1 _ is 4.] at it)" Pa abnvc the atmnspheric pressure eutside the narrew iii-ed. Assume that the speed at" the water in the reserveir is we .' npening. The desage is small ennugh that the vaccine‘s surface in the that the water flew is. steady Igniting hum air mgigtanee and the _. reserveir is nearty statinnary during an inecuiatien. The vertical difference between the reserveir and the mantle. ' height between the vaccine's surface in the reserveir and the npening can he ignered. Find the speed at which the vaccine emerges. VIE l'IILII'i l'l'lE‘Iti'r' *‘r'l. In a very large clesed tank. the abseiute pressure cf the air :-'r"I_ the water is Etfll at 1-35 Pa. The water leaves the hettem cf the r-" '63. um he airplane wing is designed se that the speed ef the air threugh a nezeie that is directed straight upward. The epening acress the tap ef the wing is 25] nus when the speed ef the air belew nnesle is 4H] m helnw the surface nf the water. ta} Find the ;~. the wing is 225 rats. The density cf the air is [.29 kgfmi. What is the at which the water leaves the neeele. {‘bl lgnnring air reestaues lifting fnrce en a wing at area 24h m3? visceus effects. determine the height In which the water rises. I54. @ Censult Multiple—Cencept Esarnple IS tn review the cen- “‘12. An airplane has an effective wing surface area ef in at1 if cepts cm which this prnblem depends. Water flewing nut nf a herienn- genemting the lift fnrce. [n level flight the air speed ever the tap u _' tal pipe emerges threugh a nnaale. The radius ef the pipe is I]? cm. wings is fill] mils. While the air speed bedeath the wings is Sill} :I: and the radius nf the neeale is [143 cm. The speed ef the water in the What is the weight nf the plane”.JI I pipe is 9.62 nus. Treat the water as an idea] fluid. and determine the #11 Internal“ Euluflun ":3 m www‘wiler‘mnflmuw absnlute pressure nf the water in the pipe. ' presents nne methed fer mndeling this preblem. The censt - In]. {55. See Multiple—Cnucept Esample [5 tn review the cnncepts a flat ractangular reef {if} m is” 6.3 ml allnws it tn withstands: mm are Pertinent hit this prehlem. The blend speed in a nnr- intum net eutward fnrce that is 22 [tilt] N. The density cf the rnal segment ef a heriacnta] artery is ill 1 rats. An ahnnnnai segment L29 Itgr‘mf. At what wind speed will this rnnf blew eutward? nf the artery is nan'nwed dnwn by an arteriesclemtic plaque te ene- fnurth the nnrrnal crnss-seetiena] area. What is the dilt‘erence in blend pressures between the nerrnal and censuicted segments cf the artery? *74. The cnncepts that play reles in this prettier-n are similar tn 4.. in Multiple-Cnncept Esample IS. except that the fluid here I".!" upward rather than remaining heriaental. rt. liquid is fiewing u- L: as. @ a ship is Heating en a lake. [is held is the interinr space he a hnnanntal pipe whnse radius is ll.tl2flt] m. The pipe bends if? neath its deck: the held is empty and is npen tn the atmesphere. The upward threugh a height ef lflfl m and jnins anether het'ieental 5;” ball has a hate in it. which is belew the water line. se water leaks intn whnse radius is nests) n1. What vnlume flew rate will keep the If t the held. The effective area nf the hnle is hit a: It] "imi- and is sures in thetwe hnrieental pipes the same'.’ 355 eHAFTEH 11 FLUIDS -._;_ 1.,ttnsit Psuettns 35. sum The main water line enters a heuse en the first hear. The line has a gauge pressure ef 1.90 Ia: iii“i Fa. {a} A faucet en the secend fleet. are in aheve the first fleer. is turned eff. What is the gauge pressure at this faucet? {b} Hew high ceuld a faucet be befere ne water weuld flew frem it. even if the faucet were epen‘.l air circuiatien. The animals maintain a difference in the shapes ef twe entrances te the burrew. and because ef this difference. the air I.“ p = l.29 itgi'mi'] hlews past the epenings at different speeds. as the drawing indicates. Assuming that the epenings are at the same verti~ cal level. find the difference in air pressure between the epenings and indicate which way the air circulates. HA = 3.5 this LE: 1*: lil“ Pa. if an artery in the brain is I145 m abeve the heart. what is the pressure in the artery? Ignere any pressure changes due te bleed flew. 39. fine ef the cencrete pillars that suppert a heuse is 2.2 rn tail and has a radius ef [infill rn. The density ef cencrete is abeut 2.2 is“ lilat kgfnr‘. Find the weight ef this pillar in peunds [l N = £12243 lb}. 99. An undergreund pump initially ferces water threugh a heriaental pipe at a flew rate ef "Mil gallens per minute. After several years ef ep— eratien. cerresien and mineral deposits have reduced the inner radius ef the pipe te lll9 m fretn {1.24 m. but the pressure difference between the ends ef the pipe is the same as it was initially. Find the final flew rate in the pipe in gallens per minute. Treat water as a visceus fluid. 9]. fine and ef a wire is attached tn a ceiling. and a selid brass hall is tied tn the lewer end. The tensien in the wire is lit:- N. What is the radius ef the hrass hall?I 92. A cylindrical air duct in an air cenditiening system has a length ef 5.5 m and a radius ef 12 is: Ill"I m. A fan ferces air in: 1.3 :s lll‘5 Pa-s] threugh the duct. se that the air in a reem {velume = 239 m3} is replenished every ten minutes. Determine the difference in pressure between the ends ef the air duct. 93. Review Cenceptuai Esample e as an aid in understanding this preblern. Censider the pump en the right side ef Figure 1 Lil}. which acts te reduce the air pressure in the pipe. The air pressure eutside the pipe is nne atmesphere. Find the masimum depth frern which this pump can estract water frem the well. 94. A paperweight. when weighed in air. has a weight ef W = 15.9 H. When cnmpletely immersed in water. hewever. it has a weight ef 1.39.“...3...l = 4.3 H. Find the velume ef the paperweight. “‘95. sum A water line with an internal radius ef fi.5 h: iii—3‘ n1 is cen- nected te a sbewer head that has I? hnles. The speed ef the water in the line is 1.2 this. {a} What is the velume flew rate in the If: {h} At what speed dees the water leave ene ef the heles {effecti hele radius = 4.15 it: iii“1i tn} in the head? *9ti. A lid-kg skiefis geing dewn a siepe eriented 35“ abeve the m”. ieental. The area ef each siti in centact with the snew is 13.13 .-'E Determine the pressure that each ski exerts en the shew. *91 A hellew cubical her: is 9.30 m en an edge. This her is fleeting a lake with ene-third ef its height bmeadi the surface. The walisef bent have a negligible thickness. Water is peured inte the hes. What- the depth ef the water in the hes at the instant the bes begins in 1:5 *98. Twe identical centainers are epen at the tep and are cen- nected at the bettem via a tube ef negligible velume and a valve that is clesed. Beth centainers are filled initially te the same height ef Lilli] m. ene with 1water. I the ether with mercury. as the drawing indicates. The valve is I-:_ epened. Water and mercury are immiscible. Determine the fluid . in the left centainer when equilibrium is reestablished. *99. earn w A Lilli-m-tall centainer is filled tn the brim. -: -__ with mercury and the rest ef the way with water. The centainer; epen tn the atmesphere. What must be the depth ef the mercury that the ahselute pressure en the bettem ef the centainer is twice '3 atmespheric pressure? * Iii-ll. A full can ef black cherry seda has a mass ef [Ls-let kg. it n tains 3.54 is: if!"1 m3 ef liquid. Assuming that the seda has the -::" density as water. find the velume et' aluminum used In make the v: - * 191. A feuntain sends a stream ef water straight up inte the air maximum height ef 5.90 m. The effective cress-sectienal area of :' pipe feeding the feuntain is 5.99 is: ltl“4 m3. Neglecting air resi :._i_' and any visceus effects. determine hew many gallens per minute being used by the feuntain. (Hem: 1 gal = 3.?9 h: ltl‘:l mi} ' rates. ene kilegratn ef glass (p: ase a let agile-i} is shaped a hellew spherical shell that just barely fleats in water. What are If} inner and enter radii ef the shell“.l De net assume that the shell.- thin. “193. A heuse has a met" with the dimensiens shewn in the drawing. Determine the magnitude and directien ef the net ferce that the atmesphere applies te the reef when the eutside pressure rises suddenly by HM] rnm ef mercury. befere the pressure in the attic can adjust. MErCury “194. Twe circular heles. ene larger than the ether. are cut in the side ef a large water tank whese tep is epen te rnesphere. The center ef ene ef these heles is iecated twice as neath the surface ef the water as the ether. The velume flew :--'i;' the water ceming eut ef the heles is the same. {a} Deeide hele is iecated nearest the surface ef the water. {b} Calculm; ratie ef the radius ef the larger hele tn the radius ef the smaller ::'_ thfem L93 ...
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