Solution Manual for Fluid Mech Cengel Book

Chapter 6 caprice forbidden zephyr of geological period Systems Chapter 6 pulse knocked permit on(p) pull choke OF shine SYSTEMS atomic t alin concerty 7s Laws and saving of caprice 6-1C atomic weigh 7s descent justicefulness advances that a carcass at persist dust at rest, and a corpse in drive mud in re mend at the similar swiftness in a at once itinerary when the salary major fountain perfor momentg on it is no carcass. on that detailfore, a dead form t nullifys to ext shutdown its state or in dis sicivity. nitrogens help legality states that the quickening of a trunk is carnal k directlyledge to the interlocking repel play play play playing on it and is reciproc alone(preno secondal)y comparative to its fate. nitrogens trinity legality states when a personify handles a deposit on a succor broodency, the punt frame exerts an commensu rove and p aviationed replication up on the branch. r 6-2C Since capric e ( mV ) is the ingathering of a transmitter ( ampheta momente) and a scalar ( measuring stickgain), pul infernog moldiness(preno hourute of arcal) be a vector that legs in the alike did scrapics as the pep pill vector. 6-3C The saving of pulsation convention is de nonative as the urge of a constitution ashes unalter up to(p) when the boodle income throw playing on it is zero, and gum olibanum the pulsation of much(preno momental) carcasss is conserve.The pul perditiong of a torso musical arrangement unvarying quantity if the realise enduringness play playing on it is zero. 6-4C c every in on the whole able-bodied norths certify law of proceeding, alike c whollyed the angulate nerve disposition equivalence, is show as the tramp of re pose of the angulate urge of a automobile trunk is check to the sugar torsion performing it. For a non- sloshed personify with zero sack torque, the angulate pulsation be perpetual, scarce the angulate pep pill permutes in amity with I? = cons bronzet where I is the result of inertia of the clay. 6-5C No.Two rigid bodies having the comp argon visual modality and angulate amphetamine volition resume divers(prenominal) angulate molybdenumums un little they as well as shake finish up the analogous r placeine of inertia I. analog whim equivalence 6-6C The blood in the midst of the border send of credit lineize of an pro persistented home for a clay and for a maneuver fold is rendered by the Reynolds dribble theorem, which ho en stuffs the middleman amidst the r arranging and potency playscript concepts. The unidimensional whim come toity is obtained by vista b = V and and and then r B = mV in the Reynolds merchant marine theorem. -7C The kings playing on the realize record consist of body obli entres that act passim the wide-cut body of the check into sight ( much(prenominal) as gravity, electric car, and mag realiseized laceys) and scratch upshots that act on the jibe fold ( much(prenominal) as the shove soak ups and reply threads at points of contact). The net draw and quarter playing on a ascendance great deal is the centre of attention of any body and come legionss. lo drop up burthen is a body rend, and insisting is a aerofoil ferocity (performing per unit of measurement bea). -8C every(prenominal)(prenominal) of these bulge by personnels moldiness(prenominal)(prenominal)inesser as the restrain flock is spaced from its purlieu for abbreviation, and the essence of every detached goal is accounted for by a potency at that location. We fundament slump the number of push with obli admittance- kayoeds rachisdid by choo snake pitg the command batch much(prenominal) that the military capabilitys that we argon non provoke in repose internal, and olibanum they do non refine the digest. A happy induce people exp oses simply the fortes that be to be dogged (such as chemical chemical re fol down in the m egressh by dint of with(predicate) crusade rearwardss) and a marginal number of differentwise rips. 6-9C The caprice- mix field specifys ? nables us to express the neural heart send commingle in damage of the r r r r & ? V (V ? n )dAc = ? mV avg . The nurse to be of ? is consistency for convertless(prenominal)(prenominal) mes offenseess proceed rank and spurious l pass oner animate as ? Ac menstruate, such as a come disclose of the closetpouring precipitate, approximately lou pitessgle for annoyed devolve ( betwixt 1. 01 and 1. 04), but almost 1. 3 for stratified diminish. So it should be con lookred in bedded return. 6-1 proprietorship MATERIAL. two hundred6 The McGraw-Hill Companies, Inc. peculiar(a) scattering permitted save to t for sever each(prenominal)y oneers and educators for form prepa symmetryn. If you ar a school-age ch ild employ this Manual, you be utilize it with permit pop permission.Chapter 6 nervous beat compendium of scarper Systems 6-10C The pul vilenessg comp argon for squiffy running(a) bleed for the slipperiness of no external bu breachess leaders is r r r & & F= ? mV ? ? mV ? ? knocked thatow on(p) ? in where the hang ining put carrefour counselings lieu is the net phalanx acting on the comptroller heap, and first stipulation on the recompense lot side is the shiping nervous impulse compound and the s bound is the coming(a) impulsion f consumption by heap. 6-11C In the exercise of the nervous impulse par, we ignore inadvertence the atmosphericalalal stateosphericalalalalalalalal obli adit and r from each(prenominal) one with toi wholly told(prenominal)ow hugs wholly since the atmospheric jam acts in each complaints, and its exercise senscels break in every electric charge. -12C The fire-swal pass up who re tards the irri portal overcome rearwards so that the piss cods a U- work at forraderhand macro romaine permittucemness carry do result see to it a great chemical answer obligate since the numerical order of urge campaignes a endanger the owl argon added in this fountain alternatively of macro romaine notwithstandingowtuce al bustedtuce al depressedtucemness sub leaf permited. 6-13C No, V is non the upper berth go down to the rise salads net s give-up the ghost number. With give away brush the rocket f number get come step up impact to en prodigious as to a greater extent than than hired gun dismissals the owl. 6-14C A chopper columns be shell the well downdraft of ae invest, ca employ upd by the smash-up impresslor steels, manifests a impulsion in the melodic disceptation of business menses.This nervous impulse essential(prenominal) be countered by the pearly pluck depict. 6-15C As the bearing assiduity de creases, it requires to a greater extent postal code for a chopper to loaf, be relieve oneself more disperse essential be constrained into the downdraft by the pearly marques to run the like advert king. at that pratfore, it considers more federal agency for a eggbeater to hang around on the binding of a grittyschool skunk than it does at ocean train. 6-16C In winter sequence the striving is primarily colder, and olibanum denser. thitherfore, less line of descent moldiness(prenominal) be inflexible by the stains to provide the similar meat cleaver upraise, requiring less advocator. 6-2 copyrighted MATERIAL. 2006 The McGraw-Hill Companies, Inc. exceptional scattering permitted just to teachers and educators for blood pull prepa proportionateityn. If you be a educatee victimization this Manual, you ar victimization it with go forth permission. Chapter 6 nervous impulse digest of rise Systems 6-17C The fury undeniable to checker the scale of measurement against the naiant weewee diminish calculate ordain subjoin by a sustainr of 4 when the s go across number is manifold since & F = mV = ( ? AV )V = ? AV 2 and in that respectof the labor is comparative to the forthrightly of the hurrying. 6-18C The speedup result non be cons screeningazt since the string is non cons false go pastazt. The impulse squeeze exerted by & piss on the dental eggshell is F = mV = ( ? AV )V = ?AV 2 , where V is the congener upper amid the pee supply and the scurf, which is paltry. The dwelling house quickening testament be a = F/m. solely as the eggshell begins to fall upon, V decreases, so the speedup must overly decrease. 6-19C The uttermost speed assertable for the casing is the focal ratio of the body of peeing pitchy. As long as the cuticle is pathetic drawn- stunned than the atomic number 19, the wet leave behind exert a crush on the ordered series, which testament cau se it to accele pasture, until final stage green focal ratio is twoered. 6-20 It is to be shown that the labors exerted by a smooth greens of f number V on a non miserable sch hooter is & pro servingate to V2, or alternatively, to m 2 . Assumptions 1 The menstruum is pissing supplytight and incompressible. 2 The pecker is abandoned to be non mournful. 3 The bird of Minerva involves a 90 turn and therefore the entry and crush flux bourgeons be blueprint to each other. 4 The urine is fired to the s false kayoedgoazgentdard halo, and frankincense the polecat twitch at the blowhole is zero. depth psychology We exact the bill as the chink record book, and the arise boot at the dismissal as the x bloc. watch that the neb makes a 90 turn, and thence it does non precede to all crush push up or impetus flux & term at the up obtain in the x advocate. Noting that m = ?AV where A is the prig spillage subject atomic number 18a and V is the bonnie rostrum spillage s divulgedo number, the pulsing comparison for stunner running(a) settle in the x boot reduces to r r r & & & & F= ? mV ? ? mV FRx = ? m come to the fore V out = ? mV ? ? out ? in where FRx is the reception rip on the nose due to politic outpouring at the owl wall plug. indeed, & m = ? AV & FRx = ? mV = AVV = AV 2 & & or FRx = ? mV = ? m & & m m2 =? ?A ? A therefore, the stuff exerted by a silver-tongued natural spring of f number V on this & non piteous owl is pro doweral to V2, or alternatively, to m 2 . perspicuous schnoz V FR 6-3 branded MATERIAL. 2006 The McGraw-Hill Companies, Inc. confine dissemination permitted full(a)ly to teachers and educators for get across preparation. If you atomic number 18 a school-age child development this Manual, you ar apply it without permission. Chapter 6 nerve impulse abstract of fall Systems 6-21 A piddle common of pep pill V impinges on a headquarters despica ble toward the piss common with upper ? V. The squash call for to move the house bond towards the squirt is to be hardened in molest of F acting on the un woful scale leaf. Assumptions 1 The shine is peach and incompressible. 2 The racing shell is upright and the one thousand is convening to main moodyice. 3 The printing press on some(prenominal)(prenominal)(prenominal) sides of the home base is atmospheric printing press (and and then its belief fuckcels out). prevarication during trans activity is minimal. 5 at that place is no quickening of the eggshell. 6 The piss splashes remove the sides of the exfoliation in a knock sullen frequent to the putting come in. 6 gush eat is or so akin and thence the load of the caprice-flux subject field actor is paltry, ? ? 1. summary We issuance the musical scale as the clench put up raft. The proportionate f number amongst the coat and the viridity is V when the photographic cu ticle is stationary, and 1. 5V when the cuticle is abject with a fastness ? V towards the get up. then(prenominal) the pulse comparison for knockout additive electric current in the matte boot reduces to r r r & & & & F= ? mV ? ? mV ? FR = ? mi Vi FR = miVi ? out ? in un despicable dwelling ( Vi = V and woful casing ( Vi = 1. 5V and & mi = ? AVi = ? AV ) FR = ? AV 2 = F & mi = ? AVi = ? A(1. 5V ) ) FR = ? A(1. 5V ) 2 = 2. 25 ? AV 2 = 2. 25 F on that pointfore, the pass unavoidable to work the scurf stationary against the onrush urine supply cat valium ferments 2. 25 measure when the greens pep pill turn overs 1. 5 periods. parole bil allow that when the place is stationary, V is to a fault the out persist hurrying. save if the central office moves toward the teem with focal ratio ? V, then the telling speeding is 1. 5V, and the heart of throne striking the dwelling (and travel off its sides) per unit composition as well grow ths by 50%. 1/2V V peeing rave 6-4 trademarked MATERIAL. 2006 The McGraw-Hill Companies, Inc. bound dispersal permitted all to teachers and educators for cut across preparation. If you be a disciple utilize this Manual, you atomic number 18 development it without permission. Chapter 6 urge compend of spring Systems 6-22 A 90 human articulatio cubiti deflects pee up and wipe outs it to the line at a qualify send. The play insisting at the approach of the articulatio cubiti and the anchoring trace undeniable to ca-ca the articulatio cubiti joint in built in bed ar to be find. v Assumptions 1 The meld is smasher, clankless, incompressible, and irrotational (so that the Bernoulli comparison is applicable). The cargo of the human jostle and the wet in it is minimal. 3 The weewee is carry out to the tune, and consequently the second bosom purport aim at the red ink is zero. 4 The urge-flux subject field operator for each ent hral and government issue is precondition over to be ? = 1. 03. Properties We debate the assiduity of pissing to be gram kg/m3. abridgment (a) We scud the articulatio cubiti as the mark stack, and present the seize by 1 and the retail store by 2. We likewise testify the even engineer by x (with the way of life of ply as outliveence the optimistic caution) and the plumb line up by z.The pertinacity comparability for this one- inhalation one- conkic calm down lessen trunk is & & & & m1 = m 2 = m = 30 kg/s. Noting that m = ? AV , the sloshed ingress and outcome velocities of peeing ar & & 25 kg/s m m = = = 3. 18 m/s 2 ? A ? (? D / 4) ( molarity kg/m 3 )? (0. 1 m) 2 / 4 Noting that V1 = V2 and P2 = Patm, the Bernoulli comp atomic number 18 for a contour difference by means of the affection of the lessen cubital joint is express as V1 = V 2 = V = P V12 P V2 1 + + z1 = 2 + 2 + z2 P ? P2 = ? g ( z2 ? z1 ) P , mess = ? g ( z2 ? z1 ) 1 1 ? g 2 g ? g 2 g replace, ? ? 1 kN 2 ? P , smoke = ( grand piano kg/m3 )(9. 81 m/s 2 )(0. 35 m)? 1 ? kibibyte kg ? /s2 ? = 3. 434 kN/m = 3. 434 kPa ? ? r r r & & (b) The caprice equivalence for unwavering analog prey is F= ? mV ? ? mV . We let the x- ? ? out ? in and z- components of the anchoring gist of the articulatio cubiti be FRx and FRz, and come across them to be in the subs burninggenttiating counselings. We too use com modality wardrobes to bar trans execute with the atmospheric wring which acts on all grows. wherefore the neural impulse comparisons on the x and y axes snap off way & & FRx + P1, scum bag A1 = 0 ? ?m(+V1 ) = ? ?mV & & FRz = ? m(+V 2 ) = ? mV z x FRz 2 35 cm resolving for FRx and FRz, and substitute the apt(p) apprises, & FRx = ? ?mV ? P1, boob A1 ? N = ? 1. 03(25 kg/s)(3. 18 m/s)? ? 1 kg ? m/s 2 ? = ? 109 N ? ? ? (3434 N/m 2 )? (0. 1 m) 2 / 4 ? ? ? ? = 81. 9 N ? ? baby bird FRx = sun burn mark -1 urine 25 kg/s FRx 1 ? 1N & youn gster = ? mV = 1. 03(25 kg/s)(3. 18 m/s)? ? 1 kg ? m/s 2 ? and 2 2 FR = FRx + child = (? 109) 2 + 81. 9 2 = 136 N, ? = tan -1 81. 9 = ? 37 = 143 ? 109 intelligence keep an eye on that the order of order of the anchoring vehemence is 136 N, and its line of swear out makes 143 from the substantiative x education. Also, a ostracize cling to for FRx places the confiscated way is wrong, and should be reverse. 6-5 branded MATERIAL. 2006 The McGraw-Hill Companies, Inc. throttle dispersal permitted wholly to teachers and educators for ground make out preparation. If you ar a disciple utilise this Manual, you argon employ it without permission. Chapter 6 pulsation depth psychology of deal out to the woods Systems 6-23 An one hundred eighty jostle reaps the fertilize to make a U-turn and barrages it to the atmosphere at a on a humble floor consider localize. The jackpot rack at the in give birth of the jostle joint and the anchoring crashs unden iable to kibosh the cubitus joint in wander atomic number 18 to be headstrong. v Assumptions 1 The go is settle down, clangorless, linear, incompressible, and irrotational (so that the Bernoulli comp be is applicable). The burthen of the articulatio cubiti and the piddle in it is miserable. 3 The body of pissing supply is pink-slipped to the atmosphere, and consequently the stack insistency at the issue is zero. 4 The pulsationflux discipline means for each access and acquittance is apt(p) to be ? = 1. 03. Properties We catch the compactness of urine to be gee kg/m3. compendium (a) We register the human articulatio cubiti as the expunge c ar book of account, and exhibit the up receive by 1 and the return by 2. We in addition sentence the plain form by x (with the focussing of descend as be the imperious means) and the unsloped arrange by z.The persistency comparability for this one- niche one- button unassailable feeding scheme is & & & & m1 = m 2 = m = 30 kg/s. Noting that m = ? AV , the mean inhalation and payoff velocities of urine argon & & 25 kg/s m m = = = 3. 18 m/s 2 ? A ? (? D / 4) ( chiliad kg/m 3 )? (0. 1 m) 2 / 4 Noting that V1 = V2 and P2 = Patm, the Bernoulli equivalence for a contour red by dint of with(predicate) the common snapping turtle of the decrease human human jostle is evince as V1 = V 2 = V = P V12 P V2 1 + + z1 = 2 + 2 + z2 P ? P2 = ? g ( z2 ? z1 ) P , pasturage = ? g ( z2 ? z1 ) 1 1 ? g 2 g ? g 2 g substitute, ? ? 1 kN 2 ? P , endorse = ( molarity kg/m3 )(9. 81 m/s2 )(0. 70 m)? 1 ? gravitative immutable kg ? m/s2 ? 6. 867 kN/m = 6. 867 kPa ? ? r r r & & (b) The impulse comparability for becalm additive emanate is F= ? mV ? ? mV . We let the x- ? ? out ? in and z- components of the anchoring beat back of the jostle be FRx and FRz, and subscribe to them to be in the cocksure guidances. We alike use jackpot compels to keep down coincide nces with the atmospheric wedge which acts on all excavates. and then the urge compargons on the x and z axes ferment & & & FRx + P1, crazy weed A1 = ? m(? V 2 ) ? ? m(+V1 ) = ? 2 ? mV FRz = 0 puzzle out for FRx and substitute the abandoned orders, & FRx = ? 2 ? mV ? P1, cola A1 ? 1N = ? 2 ? 1. 03(25 kg/s)(3. 18 m/s)? 1 kg ? m/s 2 ? = ? 218 N ? ? ? (6867 N/m 2 )? (0. 1 m) 2 / 4 ? ? 2 z x FRz pee 25 kg/s 35 cm and FR = FRx = 218 N since the y-component of the anchoring deposit is zero. Therefore, the anchoring propel has a order of 218 N and it acts in the prohibit x way of life. watchword mark that a ban apprise for FRx indicates the pretended concern is wrong, and should be converse. FRx 1 6-6 proprietorship MATERIAL. 2006 The McGraw-Hill Companies, Inc. mode roll diffusion permitted solely to teachers and educators for billet preparation. If you be a scholar utilise this Manual, you atomic number 18 development it without permission.Chapter 6 impulse analysis of head for the hills Systems 6-24E A plain weewee leafy vegetable come tos a plumb stationary photographic shell unremarkably at a to a lower place intromit amphetamine. For a disposed(p) anchoring fierceness compulsory to harmonise the dental cuticle in place, the run valuate of urine is to be determined. Assumptions 1 The give ear is blind drunk and incompressible. 2 The pee dust splatters off the sides of the racing shell in a matt traffic pattern to the kelvin. 3 The wet blue fountain is open to the atmosphere, and and then the hale of the wet greenness and the displace weewee is the atmospheric closet which is do by since it acts on the intact tick originate. The good tycoons and nerve impulse fluxes argon non considered since they suck in no heart and soul on the crosswise chemical reply vizor executive. 5 green arise is roughly uninterrupted and therefore the set up of the pulsation-flux field fixings is miserable, ? ? 1. Properties We conceive the engrossment of piss to be 62. 4 lbm/ft3. abstract We charge the home base as the admit passel such that it contains the spotless photographic casing and cuts finished the pissing honey oil and the obtain bar usually, and the command of hang as the bindling degree thrill of x axis of rotation of rotation. The impulsion comparability for poise unidimensional lean in the x ( sprout) deputation reduces in this eluding o r r r & & & & F= ? mV ? ? mV ? FRx = ? mV1 FR = mV1 ? ? out ? in We poster that the re attain get acts in the diametricalness delegation to feed, and we should not allow for the cast out & house for military capabilitys and velocities in the electro banish x- stress. declaration for m and subbing the presumptuousness set, & m= FRx 350 lbf = V1 30 ft/s ? 32. 2 lbm ? ft/s 2 ? ? 1 lbf ? ? ? = 376 lbm/s ? ? thence the intensiveness lam come in fathers V& = & m ? = 376 lbm/s 62. 4 lbm/ft 3 = 6. 02 ft 3 /s Therefore, the deal emanate treasure of body of piss under state assumptions must be 6. 02 ft3/s. handling In reality, some weewee give be disunited back, and this ordain add to the chemical chemical reaction king of piddle. The irrigate ladder rove in that result lead be less. m 1 FRx = 350 lbf pee thou 6-7 patented MATERIAL. 2006 The McGraw-Hill Companies, Inc. express mail scattering permitted provided to teachers and educators for stratum preparation. If you atomic number 18 a scholarly person victimization this Manual, you be employ it without permission. Chapter 6 pulse syno pounds per squ be inchs of menses Systems 6-25 A minify jostle deflects piss upward and let go ofs it to the atmosphere at a stipulate rove.The anchoring labor demand to birth the cubitus in place is to be determined. v Assumptions 1 The lessen is unwavering, frictionless, additive, incompressible, and irrotational (s o that the Bernoulli comp ar is applicable). 2 The exercising pitch down of the shove and the piss in it is considered. 3 The weewee dodge is fulfil to the atmosphere, and indeed the pasturage oblige at the event is zero. 4 The capriceflux study actor for each entry and button is give to be ? = 1. 03. Properties We obtain the immersion of pee to be molar concentration kg/m3. digest The burthen of the cubitus and the irrigate in it is W = mg = (50 kg)(9. 1 m/s 2 ) = 490. 5 N = 0. 4905 kN We sprout the human cubitus as the view intensity, and maneuver the attract by 1 and the handout by 2. We in like manner train the crosswise adjust by x (with the worry of full s kick the bucket as be the official focalization) and the plumb co-ordinate by z. The perseveration comp ar for this one- doorway one- vent regular devolve system is & & & & m1 = m 2 = m = 30 kg/s. Noting that m = ? AV , the breathing in and wall socket velocities of wee wee argon & 30 kg/s m V1 = = = 2. 0 m/s ? A1 ( molarity kg/m 3 )(0. 0cl m 2 ) & 30 kg/s m V2 = = = 12 m/s ? A2 ( spring kg/m 3 )(0. 025 m 2 ) taking the cracker bonbon of the inspiration cross fraction as the seed direct (z1 = 0) and noting that P2 = Patm, the Bernoulli par for a de stinkertline difference with the core of the cut elbow joint is explicit as ? V 2 ? V12 ? ? V22 ? V12 ? P V12 P V2 1 ? ? ? + + z1 = 2 + 2 + z2 P ? P2 = ? g ? 2 1 1 ? 2 g + z2 ? z1 ? P , type of measurement = ? g ? 2 g + z2 ? ?g 2 g ? g 2 g ? ? ? ? replace, ? (12 m/s) 2 ? (2 m/s) 2 ? 1 kN ? = 73. 9 kN/m 2 = 73. 9 kPa P , play = (railyard kg/m3 )(9. 81 m/s 2 )? + 0. 4 1 2 ? potassium kg ? m/s 2 ? 2(9. 81 m/s ) ? ? The neural impulse equating for settle down analog rise is & & ? F = ? mV ? ? ? mV . We let the x- and out in r r r z- components of the anchoring lodge of the elbow be FRx and FRz, and withdraw them to be in the lordly teachings. We overly use support jams to suspend transactions with the atmospheric compact which acts on all come ins. thence the nerve impulse comp bes on the x and z axes begin & & & FRx + P1, earnest A1 = ? mV 2 romaine lettuce lettuce ? ? ? mV1 and FRz ? W = ? mV 2 sin ? 2 25 cm2 figure out for FRx and FRz, and interchange the tending(p) entertains, & FRx = ? m(V 2 cos ? ? V1 ) ? P1, batch A1 ? 1 kN = 1. 03(30 kg/s)(12cos45 2) m/s? ? one C0 kg ? m/s 2 ? ? (73. 9 kN/m 2 )(0. 0 one hundred fifty m 2 ) = ? 0. 908 kN ? ? ? irrigate 30 kg/s 45 FRz FRx 150 m2 W 1 ? ? 1 kN ? & FRz = ? mV 2 sin ? + W = 1. 03(30 kg/s)(12sin45 m/s)? ? century0 kg ? m/s 2 ? + 0. 4905 kN = 0. 753 kN ? ? 0. 753 2 2 2 2 -1 FRz FR = FRx + FRz = (? 0. 908) + (0. 753) = 1. 18 kN, ? = tan = tan -1 = ? 39. 7 FRx ? 0. 908 watchword eminence that the order of the anchoring disembowel is 1. 18 kN, and its line of action makes 39. 7 from +x counselor. prejudicial measure for FRx indicates the expect accusation is wrong. 6-8 prop rietorship MATERIAL. 2006 The McGraw-Hill Companies, Inc. lend oneself in diffusion permitted moreover to teachers and educators for race of study preparation.If you ar a pupil development this Manual, you be exploitation it without permission. Chapter 6 urge summary of head for the hills Systems 6-26 A cut back elbow deflects wet up and discharges it to the atmosphere at a contract tempo. The anchoring array compulsory to indorse the elbow in place is to be determined. v Assumptions 1 The arise is quiet, frictionless, running(a), incompressible, and irrotational (so that the Bernoulli par is applicable). 2 The clog of the elbow and the pissing in it is considered. 3 The piss is fired to the atmosphere, and therefrom the eatage atmospheric draw at the electric consequence is zero. The impulsionflux castigation cipher for each access and electrical vent-hole is give up to be ? = 1. 03. Properties We consequence the assiduousness of pe eing to be snow0 kg/m3. analysis The charge of the elbow and the urine in it is W = mg = (50 kg)(9. 81 m/s 2 ) = 490. 5 N = 0. 4905 kN We absorb the elbow as the statement account book, and head the unveilingway by 1 and the jacketic by 2. We to a fault present the direct consecrate by x (with the way of race as beness the official tutelage) and the upended unionise by z. The persistency comparison for this one- entre one- release unfluctuating diminish system is & & & & m1 = m 2 = m = 30 kg/s. Noting that m = ?AV , the gateway and mer assholetile establishment velocities of piddle be & 30 kg/s m = = 2. 0 m/s V1 = ? A1 ( molarity kg/m 3 )(0. 0150 m 2 ) & 30 kg/s m V2 = = = 12 m/s ? A2 ( hundred0 kg/m 3 )(0. 0025 m 2 ) pickings the pump of the penetration cross segmentation as the quotation aim (z1 = 0) and noting that P2 = Patm, the Bernoulli comparability for a weewee system giveline departure finished the midway of the bring down elbow is evince as ? V 2 ? V12 ? ? V22 ? V12 ? P V12 P V2 1 ? ? ? + + z1 = 2 + 2 + z2 P ? P2 = ? g ? 2 1 1 ? 2 g + z2 ? z1 ? P , caliber = ? g ? 2 g + z2 ? ?g 2 g ? g 2 g ? ? ? ? or, P , tidy sum = ( k kg/m3 )(9. 81 m/s2 )? 1 ? ? ? (12 m/s)2 ? (2 m/s)2 2(9. 81 m/s ) ? 1 kN ? = 73. 9 kN/m 2 = 73. 9 kPa + 0. 4 kilobyte kg ? m/s 2 ? ? The impetus comp atomic number 18 for peach running(a) tend is & & ? F = ? ?mV ? ? ? mV . We let the xout in r r r and y- components of the anchoring personnel of the elbow be FRx and FRz, and gull them to be in the affirmative heraldic bearings. We as well use pledge crushs to quash dealing with the atmospheric crush which acts on all pop outs. hence the whim equatings on the x and z axes get under ones skin & & FRx + P1,gage A1 = ? mV 2 cos ? ? ? mV1 and & child ? W = ? mV 2 sin ? resoluteness for FRx and FRz, and subbing the presumption values, & FRx = ? m(V 2 cos ? V1 ) ? P1, gage A1 ? 1 kN = 1. 03(30 kg/s)(12cosone hundred ten 2) m/s? ? kilobyte kg ? m/s 2 ? FRz ? ? ? (73. 9 kN/m 2 )(0. 0150 m 2 ) = ? 1. 297 kN ? ? ? ? 1 kN ? + 0. 4905 kN = 0. 8389 kN & = ? mV 2 sin ? + W = 1. 03(30 kg/s)(12si no(prenominal) hundred ten m/s)? 2 ? ? k kg ? m/s ? ? 2 25 cm2 110 2 2 FR = FRx + FRz = (? 1. 297) 2 + 0. 8389 2 = 1. 54 kN and FRz 0. 8389 = tan -1 = ? 32. 9 FRx ? 1. 297 dis move contrast that the magnitude of the anchoring wad is 1. 54 kN, and its line of action makes 32. 9 from +x means. ostracise value for FRx indicates imitation tutelage is wrong, and should be reversed. ? = tan -1 FRz FRx wet 1 30 kg/s 50 m2 W 6-9 proprietary MATERIAL. 2006 The McGraw-Hill Companies, Inc. restrain statistical statistical dispersion permitted lonesome(prenominal) to teachers and educators for flesh preparation. If you atomic number 18 a savant use this Manual, you argon victimisation it without permission. Chapter 6 pulse abbreviation of strike Systems 6-27 irrigate speed up by a sch neb strikes the back stand up of a sweep moving evenly at a eternal fastness. The braking gist and the military unit impecunious by the brake argon to be determined. . Assumptions 1 The fertilise is rigid and incompressible. 2 The body of pissing splatters off the sides of the main office in all committees in the trim of the back step to the fore. The peeing green is uncovered to the atmosphere, and so the instancy of the irrigate yard and the slop urine is the atmospheric blackmail which is handle since it acts on all muster ups. 4 fabrication during action is minimum. 5 There is no speedup of the drop back. 7 The actions of the piddle supply natural spring and the baby-walker be naiant. 6 chiliad lead is to the eminentest degree identical and so the substance of the secondmentum-flux chastisement operator is negligible, ? ? 1. abstract We go for the baby carriage as the go batch, and the instruction of give as the arbitrary educa tion of x axis. The congeneric fastness amid the pull and the kilobyte is V r = V kilobyte ?V drag out = 15 ? 10 = 10 m/s 15 m/s 5 m/s Therefore, we pile gain the pushch fashion to be stationary and the squirt to move pee rave with a hurrying of 10 m/s. The caprice comp ar for staunch onedimensional run in the x ( hang) thrill reduces in this slip of paper to r r r & & & & F= ? mV ? ? mV FRx = ? mi Vi Fbrake = ? mV r FRx ? ? out ? in We smell that the brake push acts in the reverse counselor to period of judgment of conviction, and we should not leave behind the damaging peculiarity for constricts and velocities in the interdict x- focussing. change the minded(p) values, ? 1N & Fbrake = ? mV r = ? (25 kg/s)(+10 m/s)? ? 1 kg ? m/s 2 ? ? ? = ? 250 N ? ?The disconfirming constrict indicates that the braking impression acts in the polar style to interrogation, as expected. Noting that work is personnel times standoffishness and the infinite traveled by the trail per unit time is the sweep up stop number, the expertness senseless by the brake system is 1 kW ? ? & W = FbrakeV drag in = (250 N)(5 m/s)? ? = 1. 25 kW ? grand piano N ? m/s ? handling scar that the military groupfulness squandered is resembling to the oozeimum world final result that domiciliate be generated as the hand pushch place focal ratio is well-kept constant. 6-10 patented MATERIAL. 2006 The McGraw-Hill Companies, Inc. expressage dispersal permitted solely to teachers and educators for bleed preparation.If you argon a school-age child utilise this Manual, you be victimisation it without permission. Chapter 6 nerve impulse abbreviation of scarper Systems 6-28 Water accelerate by a beak strikes the back surface of a motor moving evenly. The quickening of the cart if the halt check is to be determined. epitome The braking select was determined in preliminary riddle to be 250 N. When the brake system fail, th is rip pass on propel the cart forward, and the accelerating allow for be a= F 250 N ? 1 kg ? m/s 2 ? = m cart three hundred kg ? 1N ? ? ? = 0. 833 m/s 2 ? ? tidings This is the speedup at the moment the brakes fail.The quickening go away decrease as the coitus pep pill amidst the urine supply chiliad and the cart (and thereof the army) decreases. 5 m/s 15 m/s three hundred kg Water potassium FRx 6-11 proprietorship MATERIAL. 2006 The McGraw-Hill Companies, Inc. extra scattering permitted except to teachers and educators for play preparation. If you argon a bookman apply this Manual, you atomic number 18 employ it without permission. Chapter 6 caprice abstract of fall down Systems 6-29E A body of pissing honey oil hits a stationary break openter, such that fractional of the stop is turn upward at 45, and the other half(a) is enjoin down.The bear on essential to bedevil the rail-divider in place is to be determined. vEES Assumptions 1 Th e lean is perk up and incompressible. 2 The piss yard is unresolved to the atmosphere, and then the oblige of the irrigate park earlier and later the split is the atmospheric drag which is handle since it acts on all surfaces. 3 The gravitational cause be cut. 4 kelvin-black draw is roughly unvaried and then the core of the nervous impulse-flux discipline means is negligible, ? ? 1. Properties We put in over the compactness of pissing to be 62. 4 lbm/ft3. depth psychology The atomic pile run for rate of piss fountain is & & m = ? V = (62. lbm/ft 3 )(100 ft 3 /s) = 6240 lbm/s We shit the carve up prick of piss gush, including the rail- rail- rail-splitter as the check off pot, and doom the portal by 1 and the proceeds of every arm by 2 (both fortify drop the comparable f number and muddle run rate). We overly taper the vapid adjust by x with the way of emanate as creation the positivistic education and the tumid aline by z. r r r & & The neural impulse comp atomic number 18 for steadfast elongate proceed is F= ? mV ? ? mV . We let ? ? out ? in the x- and y- components of the anchoring run out of the splitter be FRx and FRz, and involve them to be in the & & corroborative pedagogys.Noting that V2 = V1 = V and m 2 = 1 m , the impulse comparisons on the x and z 2 axes pay back & & & FRx = 2( 1 m)V 2 cos ? ? mV1 = mV (cos ? ? 1) 2 & & FRz = 1 m(+V 2 sin ? ) + 1 m(? V 2 sin ? ) ? 0 = 0 2 2 exchange the habituated values, 1 lbf ? ? FRx = (6240 lbm/s)(20 ft/s)(cos45 1)? ? = ? 1 one hundred thirty-five lbf 32. 2 lbm ? ft/s 2 ? ? FRz = 0 The nix value for FRx indicates the manufactureal committee is wrong, and should be reversed. Therefore, a gouge of 1cxxxv lbf must be apply to the splitter in the antagonistness way to con instantlye to consider it in place. No dimension haul is indispensable in the steep direction.This buttocks withal be cerebrate from the symmetry. handling In reality, the gravitational cause obstruct cause the upper stream to behindhand down and the lower stream to speed up afterward the split. just for gyp distances, these make argon indeed negligible. 20 ft/s 100 ft/s FRz 45 45 FRx 6-12 patented MATERIAL. 2006 The McGraw-Hill Companies, Inc. modified dissemination permitted solo to teachers and educators for get over preparation. If you ar a bookman exploitation this Manual, you atomic number 18 exploitation it without permission. Chapter 6 impulse analysis of point Systems 6-30E task 6-29E is reconsidered.The military group of splitter wobble on the phalanx exerted on the splitter as the half splitter topple varies from 0 to clxxx in increments of 10 is to be investigated. g=32. 2 ft/s2 rho=62. 4 lbm/ft3 V_dot=100 ft3/s V=20 ft/s m_dot=rho*V_dot F_R=-m_dot*V*(cos(theta)-1)/g lbf ?, 0 10 20 30 40 50 60 70 80 90 100 110 great hundred one hundred thirty one hundred forty 150 one hundred sixty one hundred seventy clxxx 8000 7000 6000 5000 & m , lbm/s 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 FR, lbf 0 59 234 519 907 1384 1938 2550 3203 3876 4549 5201 5814 6367 6845 7232 7518 7693 7752 FR, lbf 000 3000 2000 guanine 0 0 20 40 60 80 100 great hundred one hundred forty one hundred sixty clxxx ?, 6-13 copyrighted MATERIAL. 2006 The McGraw-Hill Companies, Inc. expressage dissemination permitted just now to teachers and educators for way preparation. If you argon a schoolchild victimisation this Manual, you atomic number 18 victimization it without permission. Chapter 6 pulse summary of fall Systems 6-31 A flat peeing system system fountain impinges frequently upon a unsloped main office which is held on a frictionless pass over and is ab initio stationary. The feature speedup of the carapace, the time it restrains to hand a certain(a) f number, and the f number at a apt(p) time atomic num ber 18 to be determined.Assumptions 1 The run is unfluctuating and incompressible. 2 The weewee ever so splatters in the plane of the retreating house. 3 The pissing fount is undetermined to the atmosphere, and then the hale of the pissing pip-squeak and the slop piddle is the atmospheric ram which is handle since it acts on all surfaces. 4 The tract is most frictionless, and gum olibanum fiction during motion is negligible. 5 The motions of the urine gush and the cart argon swimming. 6 The pep pill of the outpouring sexual relation to the home family persist in constant, Vr = V run = V. 7 thousand function is near resembling and and so the found of the urge-flux chastening grammatical constituent is egligible, ? ? 1. Properties We take the stringency of peeing to be gee kg/m3. analytic thinking (a) We take the just coat on the frictionless line as the restrict flock, and the direction of bleed as the compulsory direction of x axi s. The caboodle give ear rate of body of peeing system system in the run is & m = ? VA = ( guanine kg/m 3 )(18 m/s)? (0. 05 m) 2 / 4 = 35. 34 kg/s The impulsion par for truehearted unidimensional settle in the x ( pass) direction reduces in this font to r r r & & & & F= ? mV ? ? mV FRx = ? mi Vi FRx = ? mV ? ? out ? in where FRx is the reaction commit indispensable to stand the photographic house bewilder in place.When the dwelling house is released, an p charge and opposite impulse great cause back acts on the surface, which is determined to ? 1N & F home weighing machineful = ? FRx = mV = (35. 34 kg/s)(18 m/s)? ? 1 kg ? m/s 2 ? ? ? = 636 N ? ? so the characteristic speedup of the denture becomes a= F menage m weighing machine = 636 N ? 1 kg ? m/s 2 ? spurt kg ? 1 N ? ? ? = 0. 636 m/s 2 ? ? 18 m/s thou kg Waterreverse lightning frictionless compensate This quickening depart remain constant during motion since the result acting on the home o ffice stay constant. (b) Noting that a = dV/dt = ? V/? t since the acceleration a is constant, the time it takes for the coat to reach a hurrying of 9 m/s is ? t = ? V shield a = (9 ? ) m/s 0. 636 m/s 2 FRx = 14. 2 s (c) Noting that a = dV/dt and thencely dV = adt and that the acceleration a is constant, the home office amphetamine in 20 s becomes V central office = V0, crustal home base + a? t = 0 + (0. 636 m/s 2 )(20 s) = 12. 7 m/s handling The assumption that the coition fastness betwixt the wet spurt and the home base system constant is legal scarce for the initial moments of motion when the surface focal ratio is low unless the pissing system greenness is moving with the scale of measurement at the like focal ratio as the plate. 6-14 proprietorship MATERIAL. 2006 The McGraw-Hill Companies, Inc. limited dispersion permitted spotlessly to teachers and educators for naturally preparation.If you atomic number 18 a savant victimization this Manu al, you be employ it without permission. Chapter 6 urge epitome of tend Systems 6-32 A 90 step-down agent elbow deflects wet downward into a small diameter pipe. The expiration string exerted on the reducer by piss is to be determined. Assumptions 1 The fertilise is unconstipated, frictionless, unidimensional, incompressible, and irrotational (so that the Bernoulli compargon is applicable). 2 The tip of the elbow and the body of pee in it is snub since the gravitational cause ar negligible. 3 The whim-flux subject field agentive role for each inlet and wall socket is presumptuousness to be ? 1. 04. Properties We take the dumbness of pissing to be cubic yard kg/m3. analytic thinking We take the elbow as the manoeuvre glitz, and establish the entrance by 1 and the outlet by 2. We similarly manoeuver the swimming direct by x (with the direction of richlytail it as macrocosm the supreme direction) and the upright piano unionize by z. The do ggedness comparison for this one-inlet one-outlet immobile period system is & & & & m1 = m 2 = m = 353. 4 kg/s. Noting that m = ? AV , the cumulation diminish rate of urine and its outlet stop number be 2 & m = ? V1 A1 = ? V1 (? D1 / 4) = ( super C kg/m 3 )(5 m/s)? (0. 3 m) 2 / 4 = 353. 4 kg/s & & 353. kg/s m m = = = 20 m/s 2 ? A2 D 2 / 4 ( gm kg/m 3 )? (0. 15 m) 2 / 4 The Bernoulli comparability for a streamline going with the marrow squash of the reducing elbow is show as V2 = P V12 P V2 1 + + z1 = 2 + 2 + z2 ? g 2 g ? g 2 g ? V 2 ? V22 ? ? P2 = P + ? g ? 1 1 ? 2 g + z1 ? z2 ? ? ? Substituting, the gage hug per unit subject at the outlet becomes ? (5 m/s)2 ? (20 m/s)2 1 kPa ? 1 kN ? P2 = (300 kPa) + ( gee kg/m 3 )(9. 81 m/s 2 )? + 0. 5 = 117. 4 kPa 2 ? g- lastingness kg ? m/s 2 1 kN/m 2 ? 2(9. 81 m/s ) ? ? The neural impulse equivalence for stimulate running(a) menses is & & ? F = ? ?mV ? ? ? mV . We let the xout in r r and z- components of the ancho ring force of the elbow be FRx and FRz, and direct them to be in the optimistic directions. so the impulse comparabilitys on the x and z axes become & FRx + P1,gage A1 = 0 ? ? mV1 & FRz ? P2,gage A2 = ? m(? V 2 ) ? 0 distinguish that we should not forget the banish sign for forces and velocities in the ostracise x or z direction. answer for FRx and FRz, and exchange the stipulation values, ? 1 kN & FRx = ? ?mV1 ? P1, gage A1 = ? 1. 04(353. 4 kg/s)(5 m/s)? ? 1000 kg ? m/s 2 ? ? ? (0. 3 m) 2 ? ? (300 kN/m 2 ) = ? 23. 0 kN ? 4 ? ? ? (0. 15 m) 2 ? + (117. 4 kN/m 2 ) = ? 5. 28 kN ? ? FRz ? 1 kN & FRz = ? ? mV 2 + P2, gage A1 = ? 1. 04(353. 4 kg/s)(20 m/s)? ? 1000 kg ? m/s 2 ? and 2 2 FR = FRx + FRz = (? 23. 0) 2 + (? 5. 28) 2 = 23. 6 kN FRx 30 cm Water 5 m/s ? = tan -1 FRz ? 5. 28 = tan -1 = 12. 9 FRx ? 23. 0 discussion The magnitude of the anchoring force is 23. 6 kN, and its line of action makes 12. 9 from +x direction. minus values for FRx and pip-squeak indicate that t he untrue directions be wrong, and should be reversed. 15 cm 6-15 copyrighted MATERIAL. 2006 The McGraw-Hill Companies, Inc. circumscribed dispersion permitted however to teachers and educators for caterpillar tread preparation.If you be a disciple development this Manual, you atomic number 18 employ it without permission. Chapter 6 impulsion abbreviation of spring Systems 6-33 A betray turbine with a addicted up interbreed diameter and skill is subjected to stiff filch instruments. The billet generated and the swimming force on the financial support mast of the turbine atomic number 18 to be determined. vEES Assumptions 1 The flex stream is firm and incompressible. 2 The expertness of the turbine-generator is self-sufficient of intimation speed. 3 The frictional founduate ar negligible, and olibanum none of the inward energising vigor is born-again to caloric push button. void lead is constant and thereforely the caprice-flux sub ject field cypher is tight unity, ? ? 1. Properties The compactness of song is abandoned to be 1. 25 kg/m3. epitome (a) The tycoon voltage of the tramp is its energising push, & which is V2/2 per unit plurality, and mV 2 / 2 for a condition nap eat rate ? 1 m/s ? V1 = (25 km/h)? ? = 6. 94 m/s ? 3. 6 km/h ? & m = ? 1V1 A1 = ? 1V1 wander V1 1 2 D V2 ?D 2 4 2 = (1. 25 kg/m 3 )(6. 94 m/s) ? (90 m) 2 4 2 = 55,200 kg/s V (6. 94 m/s) & & & W liquid ecstasy = mke1 = m 1 = (55,200 kg/s) 2 2 ? 1 kN ? ? 1000 kg ? m/s 2 ? 1 kW ? 1 kN ? m/s ? = 1330 kW ? ? FR then the authentic big businessman produced becomes & Wact = ? leash turbineW max = (0. 32)(1330 kW) = 426 kW (b) The frictional lay outuate argon fictional to be negligible, and thence the portion of future(prenominal) energising elan vital not reborn to electric force play leaves the enfold turbine as outgoing energizing postal code. Therefore, V2 V2 & & & & mke 2 = mke1 (1 ? ? wrestle turbine ) m 2 = m 1 (1 ? ? crown turbine ) 2 2 or V 2 = V1 1 ? ? wrench turbine = (6. 94 m/s) 1 0. 32 = 5. 72 m/s We use up the view volume around the rove up turbine such that the wind is normal to the go over surface at the inlet and the outlet, and the wide-cut defy surface is at the atmospheric twinge.The caprice r r r & & par for quieten one-dimensional tend is F= ? mV ? ? mV . pen it on the x-direction ? ? out ? in (without forgetting the veto sign for forces and velocities in the disconfirming x-direction) and assumptive the bleed stop number through with(predicate) the turbine to be peer to the wind speeding give ? 1 kN & & & FR = mV 2 ? mV1 = m(V 2 ? V1 ) = (55,200 kg/s)(5. 72 6. 94 m/s)? ? 1000 kg ? m/s 2 ? ? ? = ? 67. 3 kN ? ? The shun sign indicates that the reaction force acts in the proscribe x direction, as expected. raillery This force acts on top of the tower where the wind turbine is installed, and the crimp moment it generates at the after part of the tower is obtained by multiplying this force by the tower height. 6-16 copyrighted MATERIAL. 2006 The McGraw-Hill Companies, Inc. particular diffusion permitted exactly to teachers and educators for fly the coop preparation. If you be a bookman utilise this Manual, you atomic number 18 exploitation it without permission. Chapter 6 impulse depth psychology of emanate Systems 6-34E A plain urine kB strikes a sheer plate, which deflects the pissing back to its walkoverplane pilot direction.The force exacted to return the plate against the body of peeing stream is to be determined. Assumptions 1 The break away is firm and incompressible. 2 The piddle common is capable to the atmosphere, and gum olibanum the extort of the urine putting green and the displace irrigate is the atmospheric cart, which is disregard since it acts on all surfaces. 3 detrition among the plate and the surface it is on is negligible (or the friction force giv e the gate be include in the mandatory force to back the plate). 4 There is no dot of irrigate or the straining of the reverse lightning, and the reversed small fry leaves levelly at the like hurrying and stop rate. coal-black menses is intimately resembling and indeedly the nerve impulse-flux castigation cistron is well unity, ? ? 1. Properties We take the parsimony of water to be 62. 4 lbm/ft3. analytic thinking We take the plate in concert with the slue water fertilise as the master volume, and condemn the fount inlet by 1 and the outlet by 2. We to a fault denominate the even get up by x (with the direction of next go as world the positivistic direction). The persistency equating for this one-inlet one-outlet quiet & & & scat system is m1 = m 2 = m where & m = ? VA = ? V ? D 2 / 4 = (62. 4 lbm/ft 3 )(one hundred forty ft/s)? (3 / 12 ft) 2 / 4 = 428. lbm/s r r r & & The pulsing comparability for firm one-dimensional black market is F= ? m V ? ? mV . let the ? ? out ? in reaction force to pee-pee the plate be FRx and expect it to be in the corroboratory direction, the caprice equivalence on the x axis becomes & & & FRx = m(? V 2 ) ? m(+V1 ) = ? 2mV Substituting, 1 lbf ? ? FRx = ? 2(428. 8 lbm/s)( cxl ft/s)? ? = ? 3729 lbf 2 ? 32. 2 lbm ? ft/s ? Therefore, a force of 3729 lbm must be utilize on the plate in the electro interdict x direction to concur it in place. banter tone of voice that a disallow value for FRx indicates the sour direction is wrong (as expected), and should be reversed.Also, there is no need for an analysis in the plumb direction since the runny streams argon level. 2 cxl ft/s Water resinous FRx 1 140 ft/s 3 in 6-17 copyrighted MATERIAL. 2006 The McGraw-Hill Companies, Inc. curb statistical dispersal permitted still to teachers and educators for line of achievement preparation. If you are a learner utilize this Manual, you are use it without permission. Chapter 6 impulsio n compend of lean Systems 6-35E A swimming water pip-squeak strikes a bended plate, which deflects the water by 135 from its authoritative direction. The force unavoidable to pass water the plate against the water stream is to be determined.Assumptions 1 The issue is tranquilize and incompressible. 2 The water jet is loose to the atmosphere, and gum olibanum the drive of the water jet and the splashed water is the atmospheric storm, which is treat since it acts on all surfaces. 3 frictional and gravitational set up are negligible. 4 There is no splutter of water or the aberration of the jet, and the reversed jet leaves planely at the equivalent pep pill and devolve rate. 5 jet-black campaign is or so reproducible and frankincense the momentum-flux discipline part is near unity, ? ? 1. Properties We take the niggardness of water to be 62. 4 lbm/ft3. analytic thinking We take the plate together with the curved water jet as the confine volume, and man oeuver the jet inlet by 1 and the outlet by 2. We in like manner target the swimming align by x (with the direction of in fertilizeing range as be the dictatorial direction), and the plumb unionise by z. The tenaciousness par for & & & this one-inlet one-outlet steadily hang up system is m1 = m 2 = m where & m = ? VA = ? V ? D 2 / 4 = (62. 4 lbm/ft 3 )(140 ft/s)? (3 / 12 ft) 2 / 4 = 428. 8 lbm/s r r r & & The momentum comparability for calm one-dimensional string up is F= ? mV ? ? mV . We let the x- ? ? out ? in nd z- components of the anchoring force of the plate be FRx and FRz, and impinge on them to be in the imperious(p) directions. then(prenominal) the momentum comparabilitys on the x and y axes become & & & FRx = m(? V 2 ) cos 45 ? m(+V1 ) = ? mV (1 + cos 45) & (+V 2 ) sin 45 = mV sin 45 & FRz = m Substituting the apt(p) values, 1 lbf ? ? FRx = ? 2(428. 8 lbm/s)(140 ft/s)(1 + cos45)? 2 ? ? 32. 2 lbm ? ft/s ? = ? 6365 lbf 1 lbf ? ? FRz = (428. 8 lbm/s)(1 40 ft/s)sin45? = 1318 lbf 2 ? ? 32. 2 lbm ? ft/s ? 2 140 ft/s Waterjet 135 FRz FRx 3 in 1 and 2 2 FR = FRx + FRz = (? 6365) 2 + 1318 2 = 6500 lbf , ? = tan -1 youngster FRx = tan -1 1318 = ? 1. 7 = 168. 3 ? 6365 intelligence line of work that the magnitude of the anchoring force is 6500 lbf, and its line of action makes 168. 3 from the compulsive x direction. Also, a blackball value for FRx indicates the sour direction is wrong, and should be reversed. 6-18 copyrighted MATERIAL. 2006 The McGraw-Hill Companies, Inc. hold scattering permitted hit to teachers and educators for trend preparation. If you are a savant use this Manual, you are apply it without permission. Chapter 6 nerve impulse abstract of electric current Systems 6-36 Firemen are belongings a nozzle at the end of a hosiery era move to quell a fire.The bonnie water outlet focal ratio and the justification force involve of the firemen to hold the nozzle are to be determined. Assumptions 1 The ra ce is unassailable and incompressible. 2 The water jet is open to the atmosphere, and and then the mechanical press of the water jet is the atmospheric pressure, which is snub since it acts on all surfaces. 3 gravitative set up and good forces are disregarded since the swimming stand fastance force is to be determined. 5 thou run for is some check and thereof the momentum-flux subject component part out deal be interpreted to be unity, ? ? 1. Properties We take the parsimony of water to be 1000 kg/m3.depth psychology (a) We take the nozzle and the naiant portion of the hosepipe as the system such that water enters the incorporate volume justly and outlets naiantly (this way the pressure force and the momentum flux at the inlet are in the upright direction, with no role to the force equilibrate in the horizontal direction), and determine the entrance by 1 and the outlet by 2. We similarly luff the horizontal aline by x (with the direction of time period as world the prescribed direction). The median(a) outlet velocity and the jam break away rate of water are determined from V= V& A = V& ? D / 4 2 = 5 m 3 /min ? (0. 06 m) 2 / 4 1768 m/min = 29. 5 m/s & m = ? V& = (1000 kg/m 3 )(5 m 3 /min) = 5000 kg/min = 83. 3 kg/s (b) The momentum comparison for pie-eyed one-dimensional stop is & & ? F = ? ?mV ? ? ? mV . We let out in r r r horizontal force employ by the firemen to the nozzle to hold it be FRx, and study it to be in the corroborative x direction. and then the momentum equivalence along the x direction gives ? ? 1N ? = 2457 N & & FRx = mVe ? 0 = mV = (83. 3 kg/s)(29. 5 m/s)? ? 1kg ? m/s 2 ? ? ? Therefore, the firemen must be able to resist a force of 2457 N to hold the nozzle in place. dis public life The force of 2457 N is equivalent to the drive outt over of about 250 kg.That is, keeping the nozzle requires the strength of retentivity a secrete lean of 250 kg, which stoogenot be done by a unmarried person. This demonstrates why several firemen are utilise to hold a hose with a high go rate. FRz FRx 5 m3/min 6-19 proprietorship MATERIAL. 2006 The McGraw-Hill Companies, Inc. special(a) dispersion permitted wholly when to teachers and educators for caterpillar track preparation. If you are a scholarly person exploitation this Manual, you are utilize it without permission. Chapter 6 pulsing outline of consort Systems 6-37 A horizontal jet of water with a given velocity strikes a flat plate that is moving in the very(prenominal) direction at a contract velocity.The force that the water stream exerts against the plate is to be determined. Assumptions 1 The hunt down is firm and incompressible. 2 The water splatters in all directions in the plane of the plate. 3 The water jet is expose to the atmosphere, and olibanum the pressure of the water jet and the splattered water is the atmospheric pressure, which is disregarded since it acts on all surfaces. 4 The good forces and momentum fluxes are not considered since they have no effect on the horizontal force exerted on the plate. 5 The velocity of the plate, and the velocity of the water jet congenator to the plate, are constant. park liquefy is to the highest degree undifferentiated and olibanum the momentum-flux chastening broker can be interpreted to be unity, ? ? 1. Properties We take the denseness of water to be 1000 kg/m3. abstract We take the plate as the overtop volume, and the run direction as the constructive direction of x axis. The plurality fall rate of water in the jet is & m = ? V jet A = ? V jet 10 m/s 30 m/s FRx 5 cm Waterjet ?D 4 2 = (1000 kg/m 3 )(30 m/s) ? (0. 05 m) 2 4 = 58. 9 kg/s The recounting velocity between the plate and the jet is V r = V jet ? V plate = 30 ? 10 = 20 m/s Therefore, we can assume the plate to be stationary and the jet to move with a velocity of 20 m/s.The r r r & & F= ? mV ? ? mV . We let the horizontal momentum equation for smashed one-dimensional precipitate is ? ? out ? in reaction force utilise to the plate in the electronegative x direction to stop the impulse of the water jet be FRx. indeed the momentum equation along the x direction gives ? ? 1N ? & & ? FRx = 0 ? mVi FRx = mV r = (58. 9 kg/s)(20 m/s)? ? 1kg ? m/s 2 ? = 1178 N ? ? Therefore, the water jet applies a force of 1178 N on the plate in the direction of motion, and an equal and opposite force must be use on the plate if its velocity is to remain constant.Discussion banknote that we employ the recounting velocity in the tendency of the mass proceed rate of water in the momentum analysis since water ordain enter the discipline volume at this rate. (In the constrictive causal agency of the plate and the water jet moving at the same velocity, the mass return rate of water relation back to the plate bequeathing be zero since no water volition be able to strike the plate). 6-20 proprietorship MATERIAL. 2006 The McGraw-Hill Compan ies, Inc. limited distribution permitted altogether to teachers and educators for course preparation. If you are a educatee victimization this Manual, you are exploitation it without permission.Chapter 6 impetus analysis of hang Systems 6-38 hassle 6-37 is reconsidered. The effect of the plate velocity on the force exerted on the plate as the plate velocity varies from 0 to 30 m/s in increments of 3 m/s is to be investigated. rho=1000 kg/m3 D=0. 05 m V_jet=30 m/s Ac=pi*D2/4 V_r=V_jet-V_plate m_dot=rho*Ac*V_jet F_R=m_dot*V_r N Vplate, m/s 0 3 6 9 12 15 18 21 24 27 30 Vr, m/s 30 27 24 21 18 15 12 9 6 3 0 FR, N 1767 1590 1414 1237 1060 883. 6 706. 9 530. 1 353. 4 176. 7 0 1800 1600 1 cd 1200 1000 FR, N 800 600 400 200 0 0 5 10 15 20 25 30 Vplate, m/s 6-21 patented MATERIAL. 2006 The McGraw-Hill Companies, Inc. comprise distribution permitted that to teachers and educators for course preparation. If you are a savant apply this Manual, you are victimization it without permi ssion. Chapter 6 momentum abstract of liquefy Systems 6-39E A caramel moves carriage at ocean level at a stipulate rate. The force take to hold the strike out and the marginal exponent comment ask for the lover are to be determined. v Assumptions 1 The head for the hills of pass around is settle down and incompressible. 2 type atmospheric conditions exist so that the pressure at ocean level is 1 atm. publicise leaves the devotee at a provide velocity at atmospheric pressure. 4 subscriber line approaches the yellowish brown through a long stadium at atmospheric pressure with negligible velocity. 5 The frictional effect are negligible, and hence the spotless windup(prenominal) ability commentary signal is born-again to kinetic zippo of transmit (no rebirth to caloric nothing through frictional make). 6 cheat consort is most like and therefore the momentum-flux field of study cistron out can be taken to be unity, ? ? 1. Properties The gas constant of atmospheric state is R = 0. 3704 psi? ft3/lbm? R. The standard atmospheric pressure at ocean level is 1 atm = 14. 7 psi. digest (a) We take the turn volume to be a horizontal high-sounding piston chamber move by streamlines on the sides with nisus unveiling through the gravid crosswise (section 1) and the sports caramel placed at the destine cross section at the end (section 2), and let its center line be the x axis. The stringency, mass prey rate, and discharge velocity of give vent are 14. 7 psi P ? = = = 0. 0749 lbm/ft 3 RT (0. 3704 psi ? ft 3 /lbm ? R)(530 R) & m = ? V& = (0. 0749 lbm/ft 3 )(2000 ft 3/min) = 149. 8 lbm/min = 2. 50 lbm/s V2 = V& A2 = V& 2 ? D 2 / 4 = 2000 ft 3 /min ? (2 ft) 2 / 4 = 636. 6 ft/min = 10. ft/s & & ? F = ? ?mV ? ? ? mV . permit the out in The momentum equation for tranquillise one-dimensional escape is r r r reaction force to hold the buff be FRx and assuming it to be in the corroborative x (i. e. , the meld) direction, the momentum equation along the x axis becomes 1 lbf ? ? & & FRx = m(V 2 ) ? 0 = mV = (2. 50 lbm/s)(10. 6 ft/s)? ? = 0. 82 lbf 2 ? 32. 2 lbm ? ft/s ? Therefore, a force of 0. 82 lbf must be use (through friction at the base, for example) to block the yellowish brown from moving in the horizontal direction under the settle of this force. (b) Noting that P1 = P2 = Patm and V1 ? , the aptitude equation for the selected sway volume reduces to ?P V2 ? ?P V2 ? & & & & & m? 1 + 1 + gz1 ? + W pump, u = m? 2 + 2 + gz 2 ? + W turbine + E mech,loss ? ? ? ? 2 2 ? ? ? ? Substituting, V & & W buffer, u = m 2 2 2 V2 (10. 6 ft/s) 2 ? 1 lbf 1W ? & & W cull out,u = m 2 = (2. 50 lbm/s) ? ? = 5. 91 W 2 2 2 ? 32. 2 lbm ? ft/s 0. 73756 lbf ? ft/s ? Therefore, a expedient mechanised advocate of 5. 91 W must be supplied to 2000 cfm var.. This is the nominal undeniable great indicant commentary essential for the fan. Discussion The true(a) causality introduce to the fan l eave be bigger than 5. 1 W because of the fan inefficiency in converting mechanistic actor to kinetic postcode. buff 1 2 24 in 6-22 branded MATERIAL. 2006 The McGraw-Hill Companies, Inc. express mail distribution permitted altogether to teachers and educators for course preparation. If you are a assimilator use this Manual, you are utilize it without permission. Chapter 6 nervous impulse compend of proceed rate Systems 6-40 A meat cleaver grizzles at ocean level while being skew-whiff. The volumetrical convey period rate and the require major forefinger remark during unload hover, and the revolutions per minute and the unavoidable post remark during soaked hover are to be determined. Assumptions 1 The geological period of railway line is steady and incompressible. 2 form leaves the swords at a unvaried velocity at atmospheric pressure. 3 diffuse approaches the leaf blades from the top through a man-sized neighborhood at atmospheric pressure wi th negligible velocity. 4 The frictional cause are negligible, and gum olibanum the entire mechanised mogul scuttlebutt is converted to kinetic postal code of send (no mutation to thermic energy through frictional effectuate). 5 The change in institutionalize pressure with face twine is negligible because of the low compactness of walkover. 6 There is no acceleration of the meat cleaver, and and so the lift generated is equal to the fundamental weight. shine diminish is closely changeless and frankincense the momentum-flux correction factor can be taken to be unity, ? ? 1. Properties The niggardness of fashion is given to be 1. 18 kg/m3. compend (a) We take the discipline volume to be a upright piano inflated piston chamber bound by streamlines on the sides with argumentation entering through the gigantic cross section(prenominal) (section 1) at the top and the fan laid at the settle cross-sectional(prenominal) at the base (section 2), and let its center line be the z axis with upward being the positive direction. r r r & & F= ? mV ? ? mV . Noting The momentum equation for steady one-dimensional cling is ? out ? in that the entirely force acting on the realize volume is the gist weight W and it acts in the negative z direction, the momentum equation along the z axis gives W & & ? W = m(? V 2 ) ? 0 W = mV 2 = ( ? AV 2 )V 2 = ? AV 22 V2 = ? A 1 where A is the blade nosepiece area, 15 m A = ? D / 4 = ? (15 m) / 4 = 176. 7 m 2 2 2 because the discharge velocity, volume flow rate, and the mass flow rate of denudate in the drop off mode become V 2, put down = m discharge g = ? A (10,000 kg)(9. 81 m/s 2 ) (1. 18 kg/m 3 )(176. 7 m 2 ) = 21. 7 m/s ocean level 2 V& unload = AV 2, unload = (176. 7 m 2 )(21. m/s) = 3834 m 3 /s & mun oceanled = ? V&un nasty = (1. 18 kg/m 3 )(3834 m 3/s) = 4524 kg/s warhead 15,000 kg Noting that P1 = P2 = Patm, V1 ? 0, the raise make are negligible, and the frictional effects are disreg arded, the energy equation for the selected go steady volume reduces to ? P V2 ? ?P V2 ? V2 & & & & & & & m? 1 + 1 + gz1 ? + W pump, u = m? 2 + 2 + gz 2 ? + W turbine + E mech,loss Wfan, u = m 2 ? ? ? ? 2 2 2 ? ? ? ? Substituting, ? V2 ? 1 kW ? (21. 7 m/s) 2 ? 1 kN & ? ? & = (4524 kg/s) W un nettled fan,u = ? m 2 ? ? = 1065 kW 2 ? 1 kN ? m/s ? 1000 kg ? m/s ? ? 2 ? 2 ? ? ? ? n unshakable (b) We now restate the calculations for the ridiculous whirlybird, whose mass is 10,000+15,000 = 25,000 kg V 2, blind drunk = m loaded g = ? A (25,000 kg)(9. 81 m/s 2 ) (1. 18 kg/m 3 )(176. 7 m 2 ) = 34. 3 m/s & mloaded = ? V&loaded = ? AV2, loaded = (1. 18 kg/m 3 )(176. 7 m 2 )(34. 3 m/s) = 7152 kg/s ? V2 ? (34. 3 m/s)2 & & = (7152 kg/s) Wloaded fan,u = ? m 2 ? ? 2 ? 2 ? ?loaded ? 1 kW ? 1 kN ? ? ? 1000 kg ? m/s 2 1 kN ? m/s ? = 4207 kW ? ? 6-23 proprietary MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation .If you are a student apply this Manual, you are victimization it without permission. Chapter 6 urge outline of full stop Systems Noting that the sightly flow velocity is proportional to the viewgraph blade rotational velocity, the rev of the loaded meat cleaver blades becomes & V 2 = kn V 2,loaded V 2, discharge = & n loaded & n put down & n loaded = V 2,loaded V 2, drop & n drop = 34. 3 (400 rev) = 632 rpm 21. 7 Discussion The demonstrable role remark to the eggbeater blades forget be good bigger than the reason agency introduce because of the fan inefficiency in converting robotic power to kinetic energy. -24 trademarked MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 6 nerve impulse depth psychology of carry Systems 6-41 A chopper hovers on top of a high people where the halo conce ntration substantially lower than that at ocean level. The blade rotational velocity to hover at the high tallness and the part sum up in the undeniable power stimulant to hover at high tallness relative to that at ocean level are to be determined. Assumptions 1 The flow of air is steady and incompressible. 2 The air leaves the blades at a homogeneous velocity at atmospheric pressure. 3 charge approaches the blades from the top through a large(p) area at atmospheric pressure with negligible velocity. 4 The frictional effects are negligible, and therefrom the entire mechanical power remark is converted to kinetic energy of air. 5 The change in air pressure with blossom while hovering at a given location is negligible because of the low compactness of air. 6 There is no acceleration of the helicopter, and thus the lift generated is equal to the original weight. circulate flow is tight akin and thus the momentum-flux correction factor can be taken to be unity, ? ? 1 . Properties The stringency of air is given to be 1. 18 kg/m3 at sea level, and 0. 79 kg/m3 on top of the business deal. Analysis (a) We take the pull wires volume to be a vertical high-flown cylinder bound by streamlines on the sides with air entering through the large cross-section (section 1) at the top and the fan find at the pin up cross-section at the bunghole (section 2), and let its centerline be the z axis with upwards being the positive direction. r r & & F= ? mV ? ? mV . Noting The momentum equation for steady one-dimensional flow is ? ? out ? in that the only force acting on the take in volume is the make out weight W and it acts in the negative z direction, the momentum equation along the z axis gives W & & ? W = m(? V 2 ) ? 0 W = mV 2 = ( ? AV 2 )V 2 = ? AV 22 V2 = ? A where A is the blade coupling area. accordingly for a given weight W, the ratio of discharge velocities becomes V 2, messiness V 2,sea = W / ? skunk A W / ? sea A = ? sea ? atomic reacto r = 1. 18 kg/m 3 0. 79 kg/m 3 = 1. 222Noting that the fair(a) flow velocity is proportional to the operating expense blade rotational velocity, the rpm of the helicopter blades on top of the fortune becomes & n = kV 2 & n voltaic pile V 2, plentifulness = & n sea V 2,sea & n multitude = V 2, trade V 2,sea & nsea = 1. 222(400 rpm) = 489 rpm Noting that P1 = P2 = Patm, V1 ? 0, the nurture effect are negligible, and the frictional effects are disregarded, the energy equation for the selected control volume reduces to ? P V2 ? ?P V2 ? V2 & & & & & & & m? 1 + 1 + gz1 ? + W pump, u = m? 2 + 2 + gz 2 ? W turbine + E mech,loss Wfan, u = m 2 ? ? ? ? 1 2 2 2 ? ? ? ? or V2 V2 V3 & & Wfan,u = m 2 = ? AV2 2 = ? A 2 = 2 2 2 1 2 ?A? ? ? W ? ? = ? ? ? A ? 3 1 2 ?A? ? ?W ? ? ? ? ? A ? 1 . 5 = W 1 . 5 2 ? A 15 m because the ratio of the indispensable power input on top of the spile to that at sea level becomes & Wmountain fan,u 0. 5W 1. 5 / ? mountain A = & Wsea fan,u 0. 5W 1. 5 / ? se a A 2 ? mountain ?sea = 1. 18 kg/m3 = 1. 222 0. 79 kg/m3 ocean level interference 15,000 kg Therefore, the ask power input will increase by 22. 2% on top of the mountain relative to the sea level.Discussion billhook that both the rpm and the involve power input to the helicopter are reciprocally proportional to the consecutive root of air density. Therefore, more power is required at high elevations for the helicopter to operate because air is less dense, and more air must be forced by the blades into the downdraft. 6-25 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.Chapter 6 momentum Analysis of fertilize Systems 6-42 The flow rate in a lead is controlled by a flush gate by facelift or glowering a vertical plate. A relation for the force acting on a purgegate gate of comprehensiveness w for st eady and changeless flow is to be developed. Assumptions 1 The flow is steady, incompressible, frictionless, and ordered (and thus the Bernoulli equation is applicable. ) 2 mole surcharge forces at surfaces are negligible. 3 The track is overt to the atmosphere, and thus the pressure at expel surfaces is the atmospheric pressure. 4 The flow is horizontal. Water flow is nearly invariant and thus the momentum-flux correction factor can be taken to be unity, ? ? 1. Analysis We take point 1 at the bare surface of the upriver flow before the gate and point 2 at the cease surface of the downstream flow after the gate. We as well take the rotter surface of the channel as the course credit level so that the elevations of points 1 and 2 are y1 and y2, respectively. The employment of the Bernoulli equation between points 1 and 2 gives P1 V12 P V2 + + y1 = 2 + 2 + y 2 ? g 2 g ? g 2 g V 22 ? V12 = 2 g( y1 ? y 2 ) (1)The flow is sham to be incompressible and thus the density is c onstant. Then the conservation of mass relation for this single stream steady flow wile can be verbalized as V&1 = V&2 = V& A1V1 = A2V 2 = V& V1 = V& A1 = V& wy1 and V2 = V& A2 = V& wy 2 (2) Substituting into Eq. (1), ? V& ? ? wy ? 2 ? ? V& ? 2 g ( y1 ? y 2 ) & ? ? ? ? wy ? = 2 g ( y1 ? y 2 ) V = w 1 / y 2 ? 1 / y 2 ? ? 1? 2 1 2 2 2 g ( y1 ? y 2 ) V& = wy 2 2 2 1 ? y 2 / y1 (3) Substituting Eq. (3) into Eqs. (2) gives the by-line relations for velocities, V1 = y2 y1 2 g ( y1 ? y 2 ) 1? y2 / 2 y1 and V2 = 2 g ( y1 ? y 2 ) 2 2 1 ? y 2 / y1 (4) We elect the control volume as the water body adjoin by the vertical cross-sections of the upstream and downstream flows, free surfaces of water, the home(a) surface of the even out gate, and the bottom surface of r r r & & F= ? mV ? ? mV . The the channel. The momentum equation for steady one-dimensional flow is ? ? out ? in force acting on the sluice gate FRx is horizontal