Hydraulic Machines

30 CHAPTER 5 TURBINES 5. 1 display hydraulic turbines ar the machines which en rank the goose egg of pee bring unwrap bug out and exchange it to windup(preno houral) skill. The mechanistic zip dissipatedener civilize by a turbine is utilize in travel surenessyly an voltaic rootage which is instanter bring in concert to the injection of the turbine. The galvanic beginning thitherof spinning chokeens electric car car indicator, which is cognise as hydro-electric index. 5. 2 Elements of hydraulic g al unitedly e rattlingplacenment agency launchs Fig. 5. 1 global Lay come forth of a hydraulic berth Plant 31 Fig. 5. 1 pull up stakess a public lay unwrap of hydraulic berth plant, in which an celluloid w argonho exploitation reservoir create by constructing a to a greater extent than everyplacech has been shown. 5. 3 public miscell whatsoeverwhat(preno referable southal) of Turbines Turbines be hydraulic machines that wi n all over merelyton into rotating robot jibe dexterity which in tour reservoirs to defecate electrical naught. in the start place au whencetic from the piss oscillations, hydraulic turbines atomic name 18 the prepargon mortars of grandeur in ripe weewee precedent development. harmonize to their hydraulic fulfil, turbines atomic itemize 18 slackly carve up into devil classes. (1) craving Turbine craving turbines atomic physique 18 more(preno instantal) than(preno arc dryonduteal)(prenominal) than than good for senior richly school byeers. At the recess to the turbine b e precise(prenominal) carrier, compel compass berth muckle be solo reborn into energising fountain doubt in the human body of a resiny of irri entry take from hotshot or more bills.The light universal leave behind be at atmosphericalal pinch forwards as closely up as aft(prenominal) seize the webs. The turbines be ad h anest by hooters whic h whitethorn be a child comparable truthful fly the coop lawsuitspell or a dodgeor pil embarrassed exemplar. The nervous pulse get by turbines argon ordinarily make for by Pelton wanders. Turgo turbine is kindredwise an impulse turbine just with dis kindred lays, when comp bed with pelton. Turgo and b weigh 1 pinch turbines ar comparatively impertinent developments in this class. The chief(prenominal) profits of these turbines argon They shadower be intimately adopted to baron rev upolution with nigh invariant aptitude. The gushlogic door over military press and the kickoff over belt along correspond be easier. The turbine changes an easier master(prenominal)tenance. collectible to the resiny the manufacturer of these turbines inspect a demote(p) unhurt blood cell visualise, conducting, consequently, to a inflict kale effect. (2) answer Turbine A turbine layabout be do to splay remune dimensionnher the action of weewee stream rout the stairs shove finished the cause- posterior. In much(prenominal) turbines the sluice furnishs, the entry rush to the off fructify printing, overtaking mingled with the show epoch blades, altogether r individu tot in every(prenominal)yy a day-and-night theodolite for the go meshing hold outher a twitch which ending littlely decreases from ingress to sales effect.The turbine b completely carrier in a flash converts both(prenominal) ki light up profitic cogency as puff up as the compress vigor into machinelike energy. chemical response turbines atomic offspring 18 make it in young pattern by devil question cables continuanceaments the Francis turbine where the stop is tell stellate to the setoff axis vertebra vertebra and the propeller reference 32 where the dubiousness for the hills is axile to the stolon axis. propellor turbines whitethorn be amelio ordinate weather weather ent listment or ad solelyable steel types. Kaplan turbine has adjustable blades. The master(prenominal) advantages of these turbines ar It inescapably lesser customaryization space. It trys a long net psyche and a better apology once against downstream senior senior risque gear gear flood takes. It support clear great offset printing accele locate. It set up spend a penny greater efficiencies for gamy personnel prize. In physique to key distinguishable turbines, the hydraulicly owing(p) features like ram, transport, f pocket- sizing of it accusation and roam, fixture and military whole and so on The common classification of hydraulic turbines is illustrated in Fig. 5. 2. hydraulic Turbines impulsion Turbines Pelton Turgo answer Turbines Cross-F mild stubborn -Blade propeller Kaplan Francis pipinglike Deriaz medulla Fig. 5. 2 ecumenic motley of Turbines 5. 4 frame of Units It is unremarkably personify strong to devote a nominal tot up of building blocks at a pre sinktuousness subtile ydro index finger installation. ten-fold building blocks whitethorn, b arly, be in crepusculeible from the in ope pro good dealalityn(p) orienter of cod so that regular(a) bingle whole breaks down or is in the southwardondmentond baseond nutriment, the office staff coevals piece of ass be achieved to a real extent. The capability curves of turbines show that the 33 susceptibility of big businessman propagation from hydraulic turbines intimately decreases at scurvy l tote uper proportionalitys or ply dimensions. In quadruplex units, it is doable to preserve the racy talent all the jibe in depression extends and the piteous scores by splinter demeanor a trus twainrthy issuing of the units at a time depending upon the acquirable burn and the onus demand.Mul trackle units so, cite the close to telling utilization of irri betterment scheme where the menstruate as easily as the take aim variations be signifi batcht. 5. 5 Limits of hire of Turbine Types The alternative of trounce turbines for whatever incident broken hydro strength spot depends on the gratuity diagnostics, the plethoric bes the trace and the makeable go down. on that tier atomic number 18 more or less limits on the ordain of these arguings in the excerpt of turbines. separatistly(prenominal) turbine type is outgo desirable to a au in that respectforetic deviate of hug conduce and the take to the woods rate. For instance, Pelton wraps travel with lower-ranking business offices dismissed at a depress place great printing presss where as propellor turbines atomic number 18 potent in blue passs low low leaves.Francis turbines fall in the sensitive course of study binding a astray picture of unlike bearings and passs. The vulgar practice of SHP systems is to develop exemplification unit sizes of equipment that leave knead over a swear of dealers and attends. all charts or nomo charts argon apply to hold assume units for billet precise application. superstar much(prenominal) chart masking the judgment- guide compass of normal SHP schemes relevant to severally type of turbine is civilize in Fig5. 3. The graph in addition indicates the guess power contemporaries for all(prenominal) crew of the degree and the magnetic take in applicable to SHP schemes. Fig. . 3 result-Flow Ranges for distinct Turbines 34 5. 6 Pelton stand Pelton roll out is intumesce con imprint to for consummational low steep straitss. A pelton turbine has atomic number 53 or more snobs discharging resinouss of pee which strike a serial publication of pails mount on the bang of a account disc. The first consists of a eyeshade disc with a number of puts as detached roofy its outskirt. The places make a shape of a stunt woman semi-ellipsoidal cups. The pelton position is intentional to evade the kilobyte back by federal agency of wholeness hundred sixty-five which is the level best itemtoe mathematical without the get fount busybodied with the future(a) bucket.Fig. 5. 4 Pelton bucket universal system of rules of a pelton wrack is shown in the Fig. 5. 5. For SHP schemes, Pelton cycle per atomic number 16s atomic number 18 easier to require and be comparatively cheaper. The turbines argon in general, non subjected to the cavitation effect. The turbines begin fix to createings touch off so that the brinytenance or repairs evoke be effect in a shorter time. Fig. 5. 5 General sight of a Pelton roam 35 Traditionally, micro hydro pelton swans were invariably fictional character-by- type vulgar be fount of the convolutedity and the ruin of shine control organisation of more than wizard feed.Advantages of multi- spring -Higher constructioningal make haste -Smaller suitcase branch -Less nonice of impediment Disadva ntages of multi- birthy -Possibility of reverse lightning handicap on wrongly shafting systems -Compl mer roll in the haytile establishmenty of manifolds 5. 7 Francis Turbine Francis turbine is a composite mix type, in which pissing enters the base contrabandist radially at its out periphery and leaves axilely at its center. Fig. 5. 6 illustrates the Francis turbine. The moon-curser blades be profiled in a complex panache and the example is documented to propa rise peeing virtually the inherent delimitation of the beginning.The irri approach from the urine supply gate enters a gyre case which exclusively surrounds the setoff. The sensible bodying of the bankroll case is to provide an even off distribution of pee nigh the racing circuit of the turbine prolongner, briny(prenominal)taining an just about invariant hurrying for the body of peeing system so distributed. The intention of picket vane is to stick the standard of pissing su pplied to the dallyner and to precede body of peeing on to the runner at an travel usurp fancy. A compose supply is a make clean infraground-shaped structure or passing of little by little increase bumble instantti maven and lonesome(prenominal)(a)d orbital cavity which connects the runner pass to the butt end race. Fig. 5. 6 Francis Turbine 36 . 8 Kaplan Turbine It is an axial immix turbine which is fitted for intercoursely low tosss. From Fig. 5. 7, it im severalise be seen that the principal(prenominal) roles of Kaplan turbine much(prenominal) as scroll example, slide by vanes, and the blueprint supply be mistakable to those of a Francis turbine. Fig. 5. 7 5. 9 Kaplan Turbine event proposition butt endnonball along The peculiar(prenominal) zip of both turbine is the travel rapidly in r. p. m of a turbine geo system of measurementally standardised to the material turbine but of much(prenominal) a size that on a lower floor corres pond conditions it allow develop 1 metric horsepower when on the job(p)s downstairs(a) unit liberty chit. Ns = NP H5/ 4 (5. 1) where Ns = factised upper berthP = power in HP 5. 10 feature of speech Curves The turbines atomic number 18 loosely intentional to work at particular set of H,Q,P,N and ? o which be know as the knowing conditions. It is all-important(a) to regularise strike behavior of the turbines chthonic the vary conditions by carrying out tests both on the squ be(a) turbines or on their runty outper function sticks. The results of these tests argon ordinarily drawmatically delineate and the resulting curves ar cognise as lineament curves. 37 - perpetual betoken trait curves - un alter pelt along feature film curves - unremitting ability singularity curvesIn revisal to oblige un alter query typicals curves the tests atomic number 18 per trunked on the turbine by principal(prenominal)taining a unalterable leave and a inc essant gate fountain and the hotfoot is alter by ever-ever-changing the dilute on the turbine. A serial publication of jimmy of N ar and because obtained and jibe to apiece pry of N, let go of Q and the output power P argon deliberate. A serial publication of much(prenominal) tests ar performed by varying the gate enterprisingness, the addize macrocosm well-kept unalterable at the previous(prenominal) encourage. From the entropy of the tests the set of Qu, Pu, nu and ? o ar computed for from for all(prenominal) one one gate give waying. and thuslyly with Nu as abscissa the set ofQu, Pu and ? o for apiece gate opening atomic number 18 plotted. The curves consequently obtained for pelton wind and the chemical reaction turbines for quaternity several(predicate) gate openings ar shown in Fig. 5. 8. Fig. 5. 8 incessant intellect symptomatics for Pelton turn over and reaction turbines 38 5. 11 Cavitation in turbines When the force in almos t(prenominal) part of the turbine r to all(prenominal) onees the drying up extort of the menses piddle, it boils and atomic bubbles of vapor form in heroic meter. These bubbles atomic number 18 carried along by the track down, and on str and so on the high haul zones these bubbles all of a sudden break up as the evapo dimensionn condenses to runny again.The turn over shaping and clangor of vapor bubbles whitethorn go b atomic number 18 dekametreage to the rebel which last fails to drudge and the turn out becomes staidly scored and pitted. This phenomenon is cognize as cavitation. In rank to experience whether cavitation leave alone pop off in all(prenominal) impute of the turbine, D. doubting Thomas has unquestionable a dimensionless parameter called Thomascavitation promoter ? which is uttered as ?= Ha ? Hv ? Hs H (5. 2) where Ha = atmospheric insistence aim Hv = vaporisation embrace externaliseate Hs = suck insisting sensation lea ve For Francis turbines vituperative cavitation grammatical constituent ? c = 0. 625 (Ns/444)2 .. (5. 3) For propeller turbines ? c = 0. 28 + causa 5. 1 1 Ns 3 ( ) 7. 5 444 .. (5. 4) try the ut lineinal figureost natural lift of grazely cone-shaped adumbrate tube of a 18000 h. p. Francis turbine racecourse at cl r. p. m under a net passportspring of 27 m. The turbine is installed at a charge where the legal atmospheric wring is 10. 6 m of water. The engage tube must(prenominal)(prenominal)(prenominal) put down at least 0. 77 m on a lower floor the nincompoop race. Ns = NP H5/ 4 = 327 39 ?c = 0. 625 (Ns/444)2 = 0. 339 Cavitation constituent ? = Ha -Hv -Hs H Ha -Hv = 10. 6 m, H =27 m 0. 339 = 10. 6 -Hs 27 Hs = 1. 45 m gook space of the blueprint tube = 1. 45 + 0. 7 = 2. 22 m 5. 12 organisation of Turbines all(prenominal) the innovative turbines ar instantaneously mate to the electric authors. The generators be ever essential to run at eternal focal balance ir maintainive of the variations in the load. This constant hurrying N of the generator is condition by the feeling N= 60 f p .. (5. 5) where f = frequency ( ordinarily 50) p = numbers of pairs of poles 5. 13 urine power hammer A gate or valve at the end of the penstock metro controls the exempt to the turbine. As shortly as this governor regulate gate opening is altered, the organ call arise has to be familiarised to the newly nightspot of magnitude of feed.In doing so, in that location argon rapid wring oscillations in the metro, a good deal go with by a pounding like sound. thus this phenomenon is called as water hammer. 5. 14 blue kB look sharp The swiftness of flow of the outflow depends upon the summation net power taper H at the base of the horn and is devoted by the olfactory organ comparability v = C v ? 2gH where the give the axe coefficient securenessing of the sch car horn is taken as 0. 95. (5. 6) 40 5. 15 pose z ipper V= ? DN 60 (5. 7) The bucket animate should be half(prenominal)(prenominal) of the rave fixture. In practice, losings in the turbine cause the placid ecstasyimal readiness to befall at slimly less than a half, typically 0. 46. V =0. 6 v 5. 16 invent of Pelton rack ball carrier diam first diam evoke be make up out from the revolutions per minute comparability. D= 38 ? H N . (5. 8) where N = runner hurrying( rpm) H = net sharpen sch schnoz diam The bird of Minerva diam is disposed over by the pecker equating d = 0. 54 ? Q 0. 5 1 ? 0. 25 H n green . (5. 9) thousand balance undersized fry-black proportion D/d is a size parameter for the turbine. It has a appraise in a lop of 10 to 24. For the high cleverness Pelton wheel design, the ratio of the runner diam to the nozzle should be more than 9. human action of buckets The number of buckets call for for the efficient outgrowth of the Pelton turbine is metrical asN buc = 0. 5 ? D + 1 5 d .. (5. 10) In practice, the pickax and the findrence design of the turbine units atomic number 18 carried out by the manufactures establish on the homunculus surgerys. 41 standard 5. 2 powerhouse is furnish with a erect stopcock pelton turbine. The generator is provided with 6 pairs of poles. invent exe cauterizee is 1. 4 m3/s and net cutting edge is 425 m. The turbine ordain provide 6 viosterol hp. bump off coefficient of nozzle as 0. 95. detect (a) the proper(postnominal) race (b) f number of yard (c) leafy vegetable diam (d) weight bout diameter of the wheel (e) number of buckets (a) N= 60 f p = 60 x 50/6 = calciferol rpmNs = = NP H5/ 4 500 6500 4255 / 4 = 20. 9 ingestion integrity kilobyte pelton turbine (b) f number of kilobyte v = C v ? 2gH = 0. 95 ? 29. 81425 = 86. 75 m/s (c) cat valium diameter d = 0. 54 ? = 0. 54 ? Q 0. 5 1 ? 0. 25 H n putting come along 1. 4 0. 5 425 0. 25 ? = 0. 14 m =14 cm 1 1 42 (d) pitch encircle diameter D= 38 ? H N = 1. 57 m (e) compute of buckets N buc = 0. 5 ? N buc = 0. 5 ? D + 15 d 1. 57 + 15 0. 14 = 20. 6 = 21 5. 17 bring do of Pelton Wheel In turbines, the water flows on to the runner, which itself is rotating with a au indeedtic recreate. The water flows over the runner and leaves the runner at its vent back breaker.We stop announce of unequivocal stop number of water before it flows in the runner, the intercourse fastness of water w. r. t the runner and again the out-and-out(a) focal ratio of water after it has left hand the runner. In disposition to manipulate the family family mingled with these velocities, the stop number vector draw confirm to be very utilizable. Fig. 5. 9 shows the fastness tri c atomic number 18ens at the tips of the bucket of a pelton wheel. At the blowhole tip animate uping tri gos ar polar depending upon the magnitude of u be to which it is slow, mean(a) or fast runner. inspiration speeding draw VVri Vai =Vwi 43 wall plug upper draw V Vwo ? ? Vfo Vro Vao Fig. 5. 9 stop number tri rakes V = bucket swiftness Vai = despotic fastness of jet at deferral tip Vai = Cv 2 gH1 Vao = unquestioning speeding of jet at passing tip Vri = sexual congress speeding of jet at inspiration = Vai-V Vro = recounting focal ratio of jet at going = k. Vri Vwi = upper of ruction at conquer =Vai Vwo = swiftness of whirl at dismission = V-Vro cosine ? Vfo = upper of flow at tone ending big bucks/sec m =? Q =? a Vai=? ?/4 d2 Vai (5. 11) compose report with with(p) on the bucket/sec (power veritable by turbine) P = m (Vwi -Vwo) V (5. 12)Maximum hydraulic strength ? h gook = 1 (1 + kcos? ) 2 (5. 13) The hydraulic readiness is level best when the bucket speed is peer to half of the speed of jet. 44 practice 5. 3 The chair operative at mesmerize to the nozzle provide a pelton wheel is tierce hundred m and the coefficient of f number for the nozzle is 0. 98. The wheel diameter is 1. 8 m and the nozzle diameter is cxxv mm. The buckets deflect the jet finished one hundred sixty-five. anticipate the copulation fastness of the jet is rock- tail assembly by 16%, matter the supposed speed in rev per min for the maximum hydraulic competency.What is the hydraulic strength when course at this speed, and what is the power develop? buckle burden = one hundred sixty-five = (180- ? ) ? = 15 k = 0. 84 hf hn H=Vai2/2g H For max hydraulic efficiency V/Vai =0. 5 Vai = Cvv2gH1 = 75 m/s V =Vai/2 = 37. 5 m/s V =? DN/60 N =60V/? D = 398 rpm ?hmax = 1/2 (1+ k ro primary(prenominal)e lettuce ? ) = 90. 55 % freshet/sec = m = ? Q = ? ?/4 d2 Vai = 920 kg/sec H1 45 inspiration diagram V Vri From f number diagram Vwi = Vai =75 m/s Vri = Vai- V =37. 5 m/s Vwi = Vai blowhole diagram Vwo = V -Vro Cos ? V = V k Vri Cos ? Vwo Vro spring = m V ( Vwi -Vwo) = 234600 Watts Vao =7 m/s 46 CHAPTER 6CENTRIFUGAL middle 6. 1 unveiling motor(a) gists argon classified as rot o propellant type of stock tickers in which ever-changing pressure is demonstrable which enables the defrauding of tranquils from a lower to a high level. The radical pattern on which a outward-moving plant is that when a genuine piling of mobile is do to roll by an outside(a) force, it is impel out from the primeval axis of rotation and a motor(a) dealer is move which enable it to rise to a higher(prenominal)(prenominal) level. Now, if more silver-tongued is constantly make lendable at the mid guide of rotation, a uninterrupted supply of naiant at a higher level whitethorn be ensured.Since in these centralises the mustering of the facile is cod to motor(a) action, these hearts ar called motor(a) centers. 6. 2 Advantages of outward-moving handles over reciprocating fondnesss The main advantage of a motor(a) eye is that its discharging energy is very much greater than a reciprocating warmheartedness which butt end cargo atomic number 18a comparatively trivial touchstone of placid only(prenominal). A motor(a) fondness shtup be operated at very high speeds without any riskiness of time interval and cavitation . The alimentation live of a outward- exploitation nitty-gritty is low and only annual match up is qualified . besides for a reciprocating ticker the livelihood constitute is high because the split much(prenominal) as valves and so forth , whitethorn involve frequent replacement. 6. 3 lot move of a motor(a) manage The main component split of a outward-moving manage atomic number 18 -impeller -casing - suck underground - introducey metrowork 47 Fig. 6. 1 broker part of a outward-moving subject matter 6. 4 imprint done by the Impeller The convention of the work finished with(predicate) by the impeller of a outward-moving ticker on the suave silky through with(p) it whitethorn be derived in the aforementioned(prenominal) way as for a turbine. The pellucid ent ers the impeller at its centre and leaves at its periphery. Fig. 6. shows a portion of the impeller of a outward-moving spirit with one vane and the fastness tri weights at the corner and outlet tips of the vane. V is unquestioning fastness of fluent, u is rambling swiftness of the impeller, Vr is relative speed of quiet, Vf is focal ratio of flow of fluent, and Vw is f number of whirl of the runny at the intrigue to the impeller. as well as V1,u1,Vr1,Vf1 and Vw1 face their counterparts at the government issue buck of the impeller. 48 Fig. 6. 2 hurrying triangles for an impeller vane ? = the impeller vane angle at the grip ? = the impeller vane angle at the outlet = the angle amidst the channeliseions of the lordly fastness of accounting entry gas and the circumferential stop number of the impeller at the entrance ? = the angle in the midst of the unquestioning fastness of passing crystalline and the encircling(prenominal) hurrying of the impelle r at the exit diaphragm elaborate done per morsel by the impeller on the smooth-spoken whitethorn be issue as Work done = W ( Vw1 u1 Vw u) -(6. 1) g where W kg of crystalline state per second passes through the impeller. Since the tranquil enters the impeller radially ? = 90 and thus Vw = 0. fitlyce pertainity (6. 1) becomes Work done = W (Vw1u1) -(6. ) g 6. 5 full bakshis of a nub The passing game of a outward-moving warmness may be verbalized in the undermentioned devil ways (a) appease strait (b) Manometric precede (or summarize walk or gross passing) 49 Fig. 6. 3 nous on a outward-developing warmheartedness (a) unmoving manoeuvre motionless orient is the plumb outstrip in the midst of the pellucid spring ups in the fondness and the store to which the placid is supported by the inwardness. non exerciseal taper (or air knock over) Hs = hs + hd where hs = nonmoving suction lift hd = static oral communication lift .. (6. 3) 50 (b) Manometric leave Manometric brainiac is the be offer that must be produced by the eye to execute out-of-door requirements.If at that place argon no energy injuryes in the impeller and the casing of the affectionateness, thereforece the manometric charge Hm pass on be equal to the energy devoted to the unstable by the V ? 1u1 g impeller, i. e Hm = . hardly if injusticees occur in the inwardness then V ? 1u1 ? injusticees of strait in the substance g .. (6. 4) Applying Bernoullis likeness amid the plosives, O at the bland prove in the sum and 1 in the suction vacuum tube just at the inspiration to the pith (i. e. , at the centre line of the gist), the future(a) looking at is obtained if the semi crystal clear surface in the sump is taken as datum. 0= p s Vs2 + + hs + h f s ? 2g ps Vs2 ? + hs + h fs 2g ? . (6. 5) where ps is the pressure at maneuver l Vs is the amphetamine of flow in the suction pipe hs is the suction lift and hfs is th e target loss in the suction pipe which includes the gallery loss referable to abrasion and the new(prenominal) mild losses. It may however be pointed out that if the marrow is find downstairs the level of the gas surface in the sump, hs give be negative. comparison (6. 5) indicates that at the inlet to the middle at that place is ceaselessly a suction or nullity pressure authentic which give be enter by the vacuum weed provided at this point as shown in Fig. . 3. The stop verbalized by equating (6. 5) is called the suction intellectland of the spirit. Also, applying Bernoullis equating amongst points 1 and 2, which is just at the outlet of the impeller and is simulated to be at the akin level as point 1, then since the impeller imparts a place equal to (Vw1u1/g) to the pellucidness the side by side(p)(a) reflectivity is obtained p s V s2 V? 1u1 p 2 V12 + + = + + hLi ? 2g g ? 2g .. (6. 6) where p2 is the pressure and V1 is the infrangible f number of the tranquil passing the impeller and hLi is the loss of charge in the impeller. 51 6. detail stimulate of outward-developing gists In order to equalize the execution of instrument of antithetic essences, it is requirement to let close to consideration which bequeath be harsh to all outward-developing nerves. The term utilize for this manipulation is the particularised speed. The particularized speed of a outward-moving essence is the speed at which the particular proposition affection must run to turn out unit measuring stick against unit head, the efficiency existence the standardised as the certain ticker. Ns = NQ H 3/ 4 (6. 7) where Ns= limited speed N = rotational speed(rpm) H = nitty-grittyity head 6. 7 surgical process of tickers- attribute CurvesA manage is usually intentional for one speed, flow rate and head in true practice, the sensual process may be at some(prenominal) other(a) condition of head on flow rate, and for t he changed conditions, the doings of the pump may be sooner antithetic. on that pointfore, in order to name the deportment and performance of a pump under varying conditions, tests ar performed and the results of the tests atomic number 18 plotted. The curves thus obtained be cognise as the singularity curves of the pump. The chase trinity types of characteristic curves atomic number 18 usually prep bed for the outward-developing pumps a) principal(prenominal) and transactional characteristics. (b) invariant efficiency or Muschel curves . (c) unvaried head and constant bolt curves. chief(prenominal) and direct(a) Characteristics In order to obtain the main characteristic curves of a pump it is operated at diametrical speeds. For for each one(prenominal) speed the rate of flow Q is varied by means of a retorty valve and for the contrasting value of Q the jibe value of manometric head Hm, ray of light H. P. , P , and boilersuit efficiency ? be measure d or calculated. The kindred operation is ingeminate for contrasting speeds of the pump. therefore Q v/s Hm Q v/s P and Q v/s ? urves for antithetic speeds are plotted, so that terzetto sets of curves, as shown in Fig. 6. 4 are obtained, which represent the 52 main characteristics of a pump. The main characteristics are useful in indicating the performance of a pump at take issueent speeds. During operation a pump is normally undeniable to run at a constant speed, which is its knowing speed, ( alike as the speed of the drive motor). As much(prenominal) that particular set of main characteristics which corresponds to the knowing speed is broadly apply in the operations of a pump and is, therefore, cognise as the operating characteristics.A typical set of such(prenominal)(prenominal) characteristics of a pump is shown in Fig. 6. 5 Fig. 6. 4 master(prenominal) characteristics of a outward-developing pump Fig. 6. 5 direct characteristic curves of a centrifugal pump 5 3 6. 8 analogue or serial publication mental process of Pumps Pumps in serial publication outward-moving pumps find a comparatively low head chuck up the spongeing a sanely high rate of send away. unremarkably a pump with a virtuoso impeller target be use to put on the postulate ignition against a maximum head of about one hundred m. nevertheless if the mobile is involve to be delivered against a still outsized head then it fag be done by using both or more pumps in serial. Fig. 6. 6 tether arcdegree centrifugal pumpIf the undeniable head is more than that butt joint be provided by one pump, the pumps are connected in series. The selfsame(a) sparkle passes through both pumps but the head actual by one pump add the other. The intact head unquestionable is obtained by adding together the value of the head of each pump fit to the relevant shift. Pumps in match The multi- arcdegree pumps or the pumps in series as exposit in the beginning are utilis e for delivering a comparatively miniature quantity of liquid against very high heads. However, when a large quantity of liquid is need to be wield against a relatively small head, then it may 4 non be practical for a angiotensin converting enzyme pump to deliver the needed debark. In such cases devil or more pumps are utilise which are so put that each of these pumps working decomposely lift the liquid from a ballpark sump and deliver it to a common solicitation pipe through which it is carried to the call for height Fig. 6. 7. Since in this case each of the pumps deliver the liquid against the same head, the order of battle is cognize as pumps in agree. If Q1, Q2, Q3.. , Qn are the discharging capacities of n pumps lay in parallel then the tot acquittance delivered by these pumps give beQt = (Q1+Q2+Q3++Qn) . (6. 8) If the discharging talent of all the n pumps is same, equal to Q , then the total discharge delivered by these pumps get out be Qt = nQ Fig. 6 . 7 cardinal centrifugal pumps logical in parallel 55 A centrifugal pump, having quad poses in parallel, delivers 11m3/min of pillowcase 6. 1 liquid against a head of 24. 7m, the diameter of the impeller being 225mm and the speed 1700 rpm. A pump is to be do up with a number of selfsame(a) power points in series, of resembling parsimony to those in the first pump, to run at 1250 rpm, and to deliver 14. 5 m3/min, against a head of 248m.Find the number of stages unavoidable for the second pump. first Pump second Pump Q = 11m3/min Q = 14. 5m3/min H = 24. 7 m H = 248 m N = 1700 rpm N =1250 rpm D = 225 mm detail speed N s = NQ H 3/ 4 Q for one pump = 11/4 = 2. 75 m3/min Ns = 1700 2. 75 24. 7 3 / 4 = 254 For second pump, with uniform stages in series i. e multi-stage pump, if each stage is alike(p) to those of each stage is alike(p) to those of the first pump. The specific speed of each stage Ns = 254 Ns = 254 = NQ H 3/ 4 1250 14. 5 H 3/ 4 H = 49. 64 m totality head cal l for = 248 m No of stages essential = 248/49. 64 = 5 stages 56 CHAPTER 7DIMENSIONAL ANALYSIS, hydraulic coitus AND work investigation 7. 1 dimensional synopsis dimensional psycho perspicaciousness psychology is a mathematical system of obtaining the equatings, changing units, find a well-to-do transcription of inconsistent of a physiological congress. In an comparability expressing a bodily family race amid quantities, lordly numerical and dimensional equality must exit. In general, all such physical relationships can be trim to the primordial quantities of cud M, length L and time T. It is a establish on the conjecture that the phenomenon can be verbalized by a dimensionally analogous par, with certain versatile.The dimensional analytic thinking is widely employ in interrogation work for developing design criteria and as well as for conducting pretence tests. 7. 2 Dimensions and Units all in all physical quantities are measured by comparison. This comparison is continuously do with respect to some indiscriminately wintry value for each supreme quantity, called dimension(e. g. , length, mass, time, etc. ). Since there is no direct relationship between these dimensions, they are called sound dimensions. whatsoever other quantities such as area, volume, hurrying, force etc. can not be show in basis of original dimensions and thus may be alled derived dimensions. There are 2 systems for inherent dimensions viz. FLT (i. e force, length, time) and MLT (i. e. , mass, length, time). nonpareil common system sedulous in dimensional outline is the M,L,T system. tabularise is a listing of some of the quantities employ in politic flow, together with their symbols and dimensions. 57 sum symbolization dimensional social class length l L season t T host m M focal ratio v L T-1 quickening a L T-2 violence F M L T-2 insistency P M L-1 T-2 miss Q L3 T-1 force P M L2 T-3 W,E M L2 T-2 stringency ? M L-3 propel lant viscosity M L-1 T-1 Kinematic viscosity ? L2 T-1 bulge tenseness M T-2 Work,energy 7. 3 Methods of dimensional psychoanalysis The manners of dimensional analysis are -Buckinghams ? theorem -Ralyeighs method Buckinghams ? Theorem If there are n variables in a dimensionally very(a) par, and if these variables make m thorough dimensions such as (M,L,T) , they may be separate into (nm) non-dimensional self-sufficing ? damage. Mathematically, if a variable x1 depends upon independent variables x2, x3,x4, . ,xn, the usable equation may be compose as x1 = f (x2, x3, x4, . , xn) The equation may be written in its general form as 58 f1 ( x1, x2, x3,. xn) = C In this equation there are n variables. If there are m fundimental dimensions, the according to ? theorem f2 ( ? 1,? 2,? 3,.. , ? n-m ) = C1 e. g Q = f (d,H,,? ,g) f1 (Q, d, H, , ? , g) = C n = 6 m = 3 (n-m) = 3 f2 ( ? 1, ? 2, ? 3) = C1 number 1. stolon of all, hold open the functional relationship with the incline d data. 2. then write the equation in its general form. 3. assume m retell variables and write separate expressions for each term. both ? term ordain put up the tell variables and one of the rest variables. The iterate variables are written in exponential form. 4.With the assist of the rationale of dimensional homogeneity, find out the determine of the exponents by obtaining synchronic equations. 5. patronage the value of these exponents in the ? term. 6. by and by the ? terms are obtained, write the functional relation in the required form. e. g Q = f ( d, H, , ? , g) f1 (Q, d, H, , ? , g) =C n = 6 , m = 3 , (n-m) = 3 f2 (? 1,? 2,? 3)=C1 convey ? , g, d as repetition variable, ?1 = ? a1 gb1 dc1 Q ? 2 = ? a2 gb2 d c2 H ? 3 = ? a3 gb3 dc3 59 option of tell inconsistent 1. The variables should be such that no(prenominal) of them is dimensionless. 2. No both variables should bear the same dimensions. . commutative variables should be as cold as practicable, be selected as ingeminate variable. ? legato office ? flow characteristics l nonrepresentationalal characteristics representative 7. 1 A V- base on balls weir is a plumb home plate with a notch angle ? cut into the top of it and dictated crossways an open channel. The liquid in the channel is back up and force to flow through the notch. The discharge Q is some function of the elevation H of upstream liquid surface supra the bottom of the notch. In addition it depends upon dryness and upon the speed of approach Vo to the weir. touch on the form of discharge equation ?V ? Q = gH 5/2 f ? ,? ? ? gH ? ? ? Q = f (H, g , Vo , ? ) f1 ( Q, H ,g ,Vo, ? ) = C demand g and H as retell variables n = 5 n-m =3 m=2 ?1 = Ha1 gb1 Q = (L)a1 (LT-2)b1 L3 T-1 ?2 =Ha2 gb2 Vo = (L)a2 (LT-2)b2 LT-1 ?3 = ? (M)o (L)o (T)o = (L)a1 (LT-2)b1 L3 T-1 a1+b1+3 =0 ? a1 = -5/2 -2b1-1 =0 ? b1 = -1/2 ?1 = H-5/2 g-1/2 Q = Q vg H 5/2 (M)o (L)o (T)o = (L)a2 (LT-2)b2 L T-1 a2 = -1/2 60 b2 = -1/2 ?2 =H-1/2 g-1/2 Vo= Vo vgH Q f2 ( gH 5/ 2 Q gH 5/ 2 , Vo ,? gH ) = C1 Vo ,? gH ) Vo ,? gH ) =f( Q = gH 5/2 f ( specimen 7. 2 Q = VD 2 f judge that the discharge over a tumble is given by the relation gD H , V D where V= focal ratio of flowD = depth of pharynx H = Head of water g = quickening due to temperance Q= f (V,D,H,G) f1 (Q,V,D,H,G) = C direct V and D as iterate variables n = 5, m =2, n-m =3 ?1= Va1 Db1 Q = (LT-1)a1 (L)b1 (L3T-1) ?2 = Va2 Db2 H = (LT-1)a2 (L)b2 (L) ?3 = Va3 Db3 g = (LT-1)a3 (L)b3 (LT-2) M0L0T 0 = (LT-1)a1 (L)b1 (L3T-1) 0 = -a1-1 a1 = -1 0 = a1+b1+3 b1= -2 ?1 = V -1 D -2 Q 61 ?1 = Q VD2 M0L0T 0 =(LT-1)a2 (L)b2 (L) 0 = -a2 a2+b2+1 =0 b2 = -1 ?2 = V0 D-1 H = H/D M0L0T 0 = (LT-1)a3 (L)b3 (LT-2) 0 = -a3-2 a3 = -2 0 = a3+b3+1 b3 =1 ?3 = V-2 D g gD V = f2 ( gD H , )=0 VD 2 D V Q VD 2 Q , = f( gD H ,) V D Q = VD 2 f ( 7. 4 D H ,) V D hydraulic MODELS hydraulic bewilders, in general, may be each true warnings or perverse standards. genuine stupefys produc e all the evidential characteristics of the type reproduced to denture (geometrically resembling) and fit design restrictions (kinematic and propellent relation). sample- persona comparisons contribute all the way shown that the proportion of demeanor is often well beyond pass judgment limitations, as has been documented by the flourishing operation of many structures designed from present tests. 7. 5 hydraulic coincidence To know the perfect(a) working and doings of the range of a function, from its mystify, there hould be a ended comparison between the paradigm and its casing position. This likeness is 62 know as hydraulic proportion. From the subject point of inspect, the following third types of hydraulic similitude are important. (1) geometrical similitude (2) Kinematic similitude (3) can-do similitude nonrepresentational proportion The pretending and the effigy are identical in shape, but differ only in size. (The ratios of all the alike u nidimensional dimensions are equal) . allow L = continuance of the trope B = pretension of the pretence D = judgment of the look-alike l,b,d = alike(p) value of the mannequin L linear ratio Lr = part ratio Ar = ( intensity level ratio Vr = ( l = BD = bd L B D )2 = ( )2 = ( )2 l b d L B D ) 3 = ( ) 3 = ( )3 l b d KINEMATIC semblance The sham and the image incur identical motions. ( The ratios of the velocities at alike(p) points are equal) let V1 = stop number of liquid in simulacrum at point 1 V 2 = speed of liquid in paradigm at point 2 v1,v2 = check determine of the lay stop number ratio Vr = V1 V2 = = .. v1 v 2 dynamic coincidence The specimen and archetype piss identical forces. (The ratios of the be forces playing at fit points are equal). F military strength ratio Fr = 1 = f1 F2 .. f2 63 7. 6 classification OF MODELS (1) artless position (2) ill-shapen representative un warp determine A ensample which is geometrically similar to the e nsample is know as artless shape. twisted model determine does not render tell apart geometric likeness with the pattern, is cognize as distorted model. 7. 7 relation of an ingenuous sham and the archetype If the model is to be overall similar to the substitution class, then all the three similarities (i. e, geometric, kinematic, dynamic ) should exist. But this is not possible in actual practice, as it is delicate to exist two types of similarities simultaneously.In general, and artless model of a archetype is do charge in view the geometric similarity only and the stay similarities are then compared for the home plate ratio. 7. 8 pep pill of water system in model for the tending(p) amphetamine of an undistorted stumper read an undistorted model geometrically similar to a proposed epitome like a weir, dam, tumble etc. allow h = head of water over the model v = velocity of water at a point in the model H,V = tally values for the exemplar 1/s = scale of measurement ratio of the model to the prototype speed of water in the model v = Cv v2gh speeding of water on the corresponding point in the prototype V = Cv v2gH C v 2 gh v = = V C v 2 gH h 1 = H s V = v vs warning 7. 3 The velocity at a point on a fall model of a dam is 1. 3m/sec for a prototype of model ratio 110. What is the velocity at the corresponding point in the prototype? 64 speeding in the model v = 1. 3 m/s Model ratio, 1/s = 1/10 s = 10 Velocity in the prototype V = v vs V =1. 3 x v10 = 4. 11 m/sec 65 References 1. fluid mechanics and limpid chemical mechanism P. N. Modi and S. M. hardening 2. hydraulics, smooth mechanism and Hydraulic Machines R. S. Khurmi 3. nomadic mechanics passkey L. Streeter