Exercises for the course F7017T, Water turbines

Transcription

1 Exercses for the course F7017T, Water turbnes 1. Exercses on flud mechancs (6). Exercses on turbnes (8) 3. Exercses on sprals and draft tubes (3). Exercses smlartes and scale-up formula (13) 5. Exercses cavtaton (6) 6. Exercses turbne selecton (9) 7. Exercses runner desgn (to come) 8. Exercses on unsteadness (to come) Dr. Mchel Cervantes Dvson of Flud Mechancs Luleå Unversty of Technology Tel: +6 (0) E-mal: Last modfed by Mchel Cervantes - 1/19 -

2 1 - Exercses on flud mechancs Exercse 1-1: (Momentum prncple crcular et From Hydromekank, H. Gustavsson) A crcular et wth dameter d and flow rate Q ht a dsk normally. Determne the force on the dsc when t a) stands b) moves n the et drecton wth the velocty v c) determne the maxmal power you can transmt to the plate a) Q A Q F = ρ, b) F = ρ v A, c) 3 Q max = ρ 7 A Q d v Exercse 1-: (Momentum prncple crcular et From Hydromekank, H. Gustavsson) A flud flows out a ppe through a small crcular hole, see fgure. Determne the force on the end plate. 1 D F = ρq + π D d d D ρ, Q d Last modfed by Mchel Cervantes - /19 -

3 Exercse 1-3: (Angular momentum prncple sprnkler From Hydromekank, H. Gustavsson) A sprnkler rotates wth a constant angular velocty, see fgure. The flow rate s Q and each arm has an outlet area A. (a) Determne the torque T necessary to mantan the sprnkler at an angular velocty ω and determne the breakng power. For whch ω s t max? (b) If the sprnkler s torque free, what s the angular velocty? Q a) T = ρq r ω( r + b ) = ωt A Q ω max = 8A r r ( + b ) b) ω = Q r ( + b ) A r Exercse 1-: (Bernoull equaton tot tube) A tot tube s an nstrument allowng the measurement of a flud velocty such as water, see fgure below. The streamlnes at the pressure taps B and B have the same drecton as the ncomng flow n steady condtons. However, flows n water turbnes are hghly unsteady due to the movement of the runner blades, necessary to extract energy from the flud. Determne the flud velocty functon of the pressure at the dfferent taps and the flud densty for steady and unsteady condtons. U(t) A B ressure sensors ρ U = ( ) steady A B B 1, Uunsteady = A N ρ N = 1 B + B' Exercse 1-5: (Bernoull equaton Gbson method) Flow measurements n water turbnes are crucal for effcency measurements on full-scale machnes. A good accuracy s dffcult to obtan for low head machnes due to the shortness of the water passages. Luleå Unversty of Technology works on the development of the Gbson method for very low head. The method s based on the measurement of the dfferental pressure Δ n the penstock durng the closure of the gude vanes stuated at see level h, see fgure. However, gude vanes do not close completely; there s always some leakage, whch has to be determned n order to calculate the flow rate wth the Gbson method. h 1 above the gude vanes Assumng the penstock cross sectons at the pressure taps 1 and equal to A and much larger than the gude vanes openng area (a), determne the gude vanes leakage flow q takng advantage of the pressure taps 1 and. h 1 and h represent the pressure tape poston above the gude vanes. h above the gude vanes q a( h + h ) 1 g Last modfed by Mchel Cervantes - 3/19 -

4 Exercse 1-6: (Bernoull equaton flow measurement From Hydromekank, H. Gustavsson) The flow rate of a stream may be measured by placng an obstacle, see fgure below. Assumng a neglgble slop of the obstacle and water surface, a neglgble velocty upstream of the obstacle and a nearly constant velocty over the obstacle, show that d+h has a mnmum functon of the velocty for whch u = ( gq) 1/ 3, q d = g 1/ 3 and 1 q h = g 1/ 3. h Obstacle d Last modfed by Mchel Cervantes - /19 -

5 - Exercses on turbnes Exercse.1: elton turbne (et dameter From Hydromekank, H. Gustavsson) A ppe 300 m long wth a dameter of D p =15 cm and a frcton coeffcent λ=0.0 supples water from a reservor stuated 150 m above see level to a elton nozzle stuated 90 m above see level. Assumng the losses n the nozzle of the form 0.0 V /(g), determne the et dameter D, whch gves maxmal effect. Inlet losses from the reservor to the ppe are neglected. D 1/ 1+ ξ 5 = D λl, D =5 cm Exercse.: elton turbne (power, rotatonal speed, moment From Hydromekank, H. Gustavsson) A elton turbne wth a head H=670 m s consdered. The ppe between the reservor and the turbne s L=6 km long wth a dameter D p =1 m and a frcton coeffcent λ= The water et leavng the nozzle has a dameter D =18 cm and the runner dameter s D=R=1.5 m. The effcency of the turbne s η=85 %. Assumng the losses n the nozzle of the form 0.0 V /(g), perfect velocty condtons between the water et and the runner velocty, the water spreads at β=170 from the runner blades and neglectng the losses on the runner blades, determne: 1. the power of the turbne. the runner angular frequency 3. the torque actng on the runner 1 - = η( 1 cosβ) 1 gh - ω = R L D 1+ ξ + λ Dp D 3 T=/ω, T=386 knm πd gh 16 L D 1 + ξ + λ Dp D 1/ 3/, ω=36.5 rad/s, =1.1 MW Exercse.3: elton turbne (et dameter and hydraulc effcency From Hydromekank, H. Gustavsson) A elton turbne wth a head H=360 m and an effcency η of 85 % develops a power =500 kw. The runner s drven by two water ets at 00 rpm. The losses n the nozzle are 3 % and the frcton coeffcent of the blades s k=0.85. The water spreads at 170 from the runner blades. The velocty rato between the water et and the runner velocty s r = Rω / u = 0.6. Neglectng the losses n the ppe, determne: (a) the water et dameter (b) the hydraulc effcency of the turbne ϕ (a) A = where ηρgh ϕ gh ϕ (b) η ϕ ( 1 )( 1 cosβ) = 0.03, D =5 mm hydraulc = r r k, η hydraulc =88 % Last modfed by Mchel Cervantes - 5/19 -

6 Exercse.: Net head (From Flud Mechancs, Franzn and Fnnemore, 16.16) In the test of a Francs turbne, a pressure of 10 ka was measured at a pont A at the flange at the entrance to a spral turbne-case wth a dameter D s =600 mm. Neglectng the small velocty head n the talrace, fnd the net head on the turbne f the flow rate was Q=.5 m 3 /s and the flange was z A =3 m above the talrace. A Q 1 h = + z ρg πd + g A, h=1.1 m Exercse.5: Reacton turbne (runner dameter and power From Hydromekank, H. Gustavsson) A reacton turbne has ts gude vanes at an angle of 30 and the leadng edge runner blade angles makes an angle of 10 relatve to the tangent. The turbne blade heght at the nlet s ¼ of ther dameter. The water does not have any tangental velocty at the outlet of the runner. The head s of 15 m and the rotatonal speed of the runner s rotatons per seconds. The hydraulc effcency s of 88 % and the total effcency of 85 %. Determne the turbne runner dameter at the nlet and the power developed. ( ) ( 1) ( 1) ( β1) sn( α 1 ) ( ) gh sn β1 α1 D = ηhydraulc, D=0.51 m, ω cos α sn β = sn π ηρω 3 ghd 8 sn β α 1 1, =35. kw Exercse.6: ower (From Flud Mechancs, Franzn and Fnnemore, 16.17) A reacton turbne s suppled wth water through a 1500 mm dameter ppe (λ=0.011 mm) that s 50 m long. The water surface n the reservor s 7 m above the draft-tube nlet that s.1 m above the water level n the talrace. If the turbne effcency s 9% and the dscharge s 1 m 3 /s, what s the power output of the turbne n klowatts? By how much must the dscharge be ncreased to ncrease power producton by 500 kw assumng λ unchanged? Assume the velocty n the talrace can be neglected. 1 Q L = ηρgq ztw g πd D λ, =3.3 MW ( +Δ ) 1 Q Q L 3 +Δ = ηρg( Q+ΔQ) ztw λ, Δ Q = m / s g πd D Exercse.7: Francs turbne (gude vanes From Hydromekank, H. Gustavsson) A Francs turbne wth a flow rate Q= m 3 /s and a rotatonal speed N=600 rpm s consdered. The runner has an outer dameter D 1 =1. m, a blade angle leadng edge β=110 and a blade heght b 1 =0.1 m. Determne the angle α of the gude vanes for an attached flow. π DbN 1 1 α = cot ( β1) +, α=17. Q Exercse.8: Reacton turbne (effcency and blade angle From Hydromekank, H. Gustavsson) A reacton turbne has ts gude vanes postoned at an angle γ. The runner blades make an angle of 90 to the tangental drecton. The radal velocty trough the turbne s constant. Show that the maxmal hydraulc effcency s η h =1/(1+0.5 tan γ). Last modfed by Mchel Cervantes - 6/19 -

7 3 - Exercses on sprals and draft tubes Exercse 3.1: Spral nlet boundary condtons (Optonal!) a) The general form for the development of the mechancal energy (E) assumng ncompressble flow s r U u, v, w. Show that: obtaned by multplcaton of the Naver-Stokes equaton wth the velocty vector ( ) DE Dt 1 r r = + νu. U, where ρ t E + = ρ 1 U b) By takng the dvergence of the Naver-Stokes equaton and usng the defnton of the vortcty (ω) and dsspaton functon (φ), show that: 1 φ = ρω, where ν φ = μ U x U x U + x U x and ω = U x U x U x U x and thus DE Dt 1 + ρ t = ν E νω What does 1 ρ t and νω represent? r r U r c) Show that the convectve terms of the Naver-Stokes may be wrttenu. U = U ω. r E = dv U w. By applyng the dvergence operator to the precedng relaton, show that: ( ) d) Volume ntegrate E over a spral and show that: r r EdV = dv U ω d ( ) S What s the contrbuton of ν E to the varaton of the mechancal energy n the spral functon of the type of flow,.e. wth or wthout secondary flow? Exercse 3.: Draft tube (From Flud Mechancs, Franzn and Fnnemore, 16.18, modfed) A draft tube leadng from the dscharge sde of a turbne to the submerged dscharge n the talrace conssts of a ppe (λ = 0.05) of constant dameter 0.8 m and length 10.0 m. The flow rate s 9. m 3 /s. If ths draft tube was to be replaced by a dvergng tube 1.0 m long whose dameter ncrease lnearly from D 0 =0.8 m to D 1 =.5 m over the 1.0 m length and an dentcal surface roughness as the precedent draft tube, how much addtonal head would be developed by the replacement draft tube? Both draft tube wll be consdered straght wthout bend. a) Straght tube draft tube h frcton 1 Q = π L g D D λ h = =. m and h 1 Q = g πd dsch arge Last modfed by Mchel Cervantes - 7/19 -

8 b) Concal draft tube h frcton 8 λq L 1 ( ) 1 0 ( D0 1 ) = D and h π g D D h = = 0.93 m 1 Q = dsch arge g πd1 Exercse 3.3: Draft tube (From Flud Mechancs, Franzn and Fnnemore, 16.19) At ts upper end a draft tube has a dameter of.5 n where t ons the dscharge sde of the turbne at a pont 11.0ft above the surface of the water n the talrace. The dscharge end of the draft tube has a dameter of n and the velocty n the talrace s neglgble. The total head loss n the draft tube s 0.15V /g plus the submerged dscharge loss of V 3 /g, where subscrpts and 3 refer to the upper and lower ends of the draft tube, respectvely, (a) When the flow s 38.8 cfs, what s the pressure at the upper end of the draft tube? (b) Suppose the draft tube was of unform dameter; what then would be the pressure at the upper end of the tube? (c) How much head s saved by the dvergng tube? Assume the draft tube has a length of 18 ft a nd λ=0.00. (a) 1 Q Q = ρ gz πd πd3 (b) = a 1 Q = ρ 1.15 gz πd =.7 10 a (c) h = 1.6 m Last modfed by Mchel Cervantes - 8/19 -

9 - Exercses on smlartes and scale-up Exercse.1: Scale-up (From Flud Mechancs, Franzn and Fnnemore, 16.0) A model turbne, one-twenteth of prototype sze, has a maxmum hydraulc effcency of 86.%. Estmate the effcency of the prototype utlzng the Moody step-up formula. 1 η M D = 1 η DM 1 5, η = 9. % Exercse.: Dmensonless numbers (From Flud Mechancs, Franzn and Fnnemore, 16.1) A turbne runs at 150 rpm, dscharges 00 cfs and develops 1600 bhp under a net head of 81 ft. (a) What s ts effcency? (b) What would be the revolutons per mnute, Q, and brake horsepower of the same turbne under a net head of 16 ft for homologous condtons? (a) η =, η = 85.7 % ρgqh nd Q (b) n11 = =cst, n=1 rpm Q11 = = cst, Q=8 m 3 /s H D H = = cst, =55 bhp DH H 11 Exercse.3: Dmensonless numbers (From Flud Mechancs, Franzn and Fnnemore, 16.) If a turbne homologous to that of rob has a runner of twce the dameter, what would be the revolutons per mnute, Q, and brake horsepower under the same head of 81 ft? nd n11 = =cst, n=75 rpm H Q Q = =cst, Q=.6 m 3 /s D H 11 = = cst, =600 bhp DH H 11 Exercse.: Model test (From Flud Mechancs, Franzn and Fnnemore, 16.3) A.6 m dameter reacton turbne s to be operated at 00 rpm under a net head of 30m. A 1:10 model of ths turbne s bult and tested n the laboratory. If the model s operated at 600 rpm, under what net head should t be tested to smulate normal operatng condtons n the prototype? nd n11 = =cst, H=.7 m H Last modfed by Mchel Cervantes - 9/19 -

10 Exercse.5: Dmensonless numbers (From Flud Mechancs, Franzn and Fnnemore, 16.) A small Francs turbne (N s =30, D= ft) s tested and found to have an effcency of when operatng under optmum condtons. Approxmately what would be the maxmum effcency of a homologous runner (N s =30) wth a dameter of 6 ft. 1 η M D = 1 η DM 1 5, η = 91. % Exercse.6: Model test (From Flud Mechancs, Franzn and Fnnemore, 16.5) A 1-ft-dameter reacton turbne s to be operated at 100 rpm under a net head of 96ft. A 1:8 model of ths turbne s bult and tested n the laboratory. If the model s operated at 50 rpm, under what net head should t be tested to smulate normal operatng condtons? nd n11 = =cst, H M = 9.3 m H Exercse.7: Model to prototype (From Flud Mechancs, Franzn and Fnnemore, 16.6) A 1:8 model of a 1 ft dameter turbne s operated at 600 rpm under a net head of 5.0 ft. Under ths mode of operaton the bhp and Q of the model were observed to be 33 hp and 6 cfs, respectvely. From the above data compute (a) the specfc speed of the model and the value of φ (b) the effcency and shaft torque of the model (c) the effcency of the prototype (d) the flow rate and horsepower of the prototype f t s operated at 50 rpm under a net head of 00 ft n (a) NS =, N 5 S = 330 wth H(m), (bhp) and n(rpm) H (b) η u πn D 1 M M φ= =, φ = 0.79 (D M = 1/8 D = 1/8 ft) M gh gh M = ρ gq H M M T = ω, T = 3.9 knm, η = M 86 % (c) 1 η M D = 1 η DM 1 5, η = 90.8 % nd 50 1*8 (d)!!!!!!!!!!!!!! n 11 = = = and n11 H 00 M nmdm = = = H 5 M Last modfed by Mchel Cervantes - 10/19 -

11 Exercse.8: Dmensonless numbers (From Flud Mechancs, Franzn and Fnnemore, 16.7) Calculate the specfc speed of a elton turbne wth the followng characterstcs: statc head=18 ft, net head=00 ft, n=50 rpm, ptch dameter=16 n. Estmate the runner dameter wth the help of the fgure below, BG unts are used. u1 For elton turbne, φ=0.5, snce φ= we get gh φ H D =, D = 1. ft n Exercse.9.: Dmensonless numbers (From Flud Mechancs, Franzn and Fnnemore, 16.8) Fnd the specfc speed of a Francs turbne wth the followng characterstcs: = kw, H=87.6 m and n=150 rpm. Estmate the runner dameter. N S n =, N 5 S = 5.9 H φ=0.7, φ H D =, D = 1.10 ft n Exercse.10: Dmensonless numbers (From Flud Mechancs, Franzn and Fnnemore, 16.31) Fnd the specfc speed of a turbne that runs at a maxmum effcency of 90% at 300 rpm under a net head of 81 ft wth a flow rate of 50 cfs. Estmate the runner dameter. Last modfed by Mchel Cervantes - 11/19 -

12 Exercse.11: Dmensonless numbers (From Flud Mechancs, Franzn and Fnnemore, 16.3) A double-overhung mpulse turbne s consdered. Each wheel of the two-wheel unt develops 5,000 hp at 500 rpm under a head of 5330 ft. (a) What s the specfc speed of these wheels? (b) Estmate ther dameter and compare your answer wth ther actual dameter of ft. Exercse.1: Dmensonless numbers (From Flud Mechancs, Franzn and Fnnemore, 16.3) A Kaplan turbne at Rock Rver, Illnos develops 800 hp at 80 rpm under a head of 7 ft. (a) What s the specfc speed of ths turbne? (b) Estmate the runner dameter and compare your answer wth the actual dameter of 136 n. Exercse.13: Francs turbne (dmensonless numbers From Hydromekank, H. Gustavsson) A Francs prototype wll have a specfc speed n s =10 and develop a power of 30 MW at 180 rpm. A model of the Francs prototype wll be run wth Q=0.6 m3/s wth a head of.5 m. Assumng an effcency of 88 %, determne the model rotatonal speed, power and dmenson relatve to the prototype. N m =85 rpm, m =ρgq m H m η, D p =5.5 D m, H p =63.6 m Last modfed by Mchel Cervantes - 1/19 -

13 5 - Exercses on cavtaton Exercse 5.1: Cavtaton (From Flud Mechancs, Franzn and Fnnemore, 16.35) Consder the case of a Francs turbne havng a specfc speed of 0 that s set 10 ft above talwater elevaton. erform calculatons usng Fg and Eq. (16.) to fnd the maxmum permssble head under whch ths turbne should operate n order to be safe from cavtaton. Check your calculated result aganst the nformaton shown on Fg Do they agree? Usng Franzn and Fnnemore From fgure 16.17, σ = atm wv, From equaton 16.3, H Hs σ ρg ρg Usng Krvchenko: Recalculaton of Ns: N SKrvchenko 5 1 = N S 176. Franzn = Wth equaton 7.15: Wth equaton 7.13: 1.8 N S + 30 σ = = atm wv, H Hs, H 97.3 m σ ρg ρg Exercse 5.: Cavtaton (From Flud Mechancs, Franzn and Fnnemore, 16.36) Consder the case of a propeller turbne havng a specfc speed of 150 that s set 5 ft below talwater. erform calculatons usng Fg and Eq. (16.) to fnd the maxmum permssble head under whch ths turbne should operate n order to be safe from cavtaton. Check your calculated result aganst the nformaton shown n Fg Do they agree? Wth Krvchenko, N SKrvchenko 5 1 = N S Franzn = 0.308, σ = and H 17.8 m Last modfed by Mchel Cervantes - 13/19 -

14 Exercse 5.3: Cavtaton (From Flud Mechancs, Franzn and Fnnemore, 16.37) At ts maxmum effcency of 93% a turbne delvers 3000 hp to the shaft under a head of 7 ft when operatng at 300 rpm. Fnd the followng: (a) the flow rate through the turbne (b) the specfc speed of the turbne (c) the approxmate dameter of the turbne runner (d) the elevaton at whch the turbne should be set to be safe aganst cavtaton f t s nstalled at sea level. 3 (a) η =, Q = m / s ρgqh n (b) NS =, N 5 S = 78.3 wth H(ft), (bhp), n(rpm) H (c) φ=0.7, φ H D =, D = 3 ft n (d) Usng Krvchenko: Recalculaton of Ns: N SKrvchenko 5 1 = N S 35.9 Franzn = Wth equaton 7.15: Wth equaton 7.13: 1.8 N S + 30 σ = = H ρg atm wv, σ S ρg H, H S 5. m Exercse 5.: Cavtaton (From Flud Mechancs, Franzn and Fnnemore, 16.38) A propeller turbne operates at a maxmum effcency of 9% under a head of 30 ft at 50 rpm and develops a shaft power of 60 hp. Fnd (a) the flow rate through the turbne (b) the specfc speed of the turbne (c) the approxmate dameter of the turbne runner (d) how far above talwater elevaton the turbne can be set and stll be safe from cavtaton. Assume the turbne s at an elevaton of 100 ft. Last modfed by Mchel Cervantes - 1/19 -

15 Exercse 5.5: Cavtaton (From Flud Mechancs, Franzn and Fnnemore, 16.39) Repeat part (d) of rob for the case where the turbne s nstalled at elevaton 5000 ft. Exercse 5.6: Cavtaton (From Flud Mechancs, Franzn and Fnnemore, 16.0) A turbne whose specfc speed s 80 s to operate under a head of 50 ft at an elevaton where the atmospherc pressure s 1.8 psa. The water temperature s 50 F. (a) If ths turbne s set 6 ft above talwater, wll t be safe from cavtaton? (b) What s the hghest permssble elevaton of ths turbne wth respect to talwater when operatng under a head of 60 ft? Last modfed by Mchel Cervantes - 15/19 -

16 6 - Exercses on turbne selecton Exercse 6.1: Turbne selecton (From Flud Mechancs, Franzn and Fnnemore, 16.1) (a) A turbne s to be nstalled at a pont where the avalable head s 175 ft and the avalable flow wll average 1000 cfs. What type of turbne would you recommend? Specfy the operatng speed and the number of generator poles for 60-cycle electrcty f a turbne wth the hghest tolerable specfc speed to safeguard aganst cavtaton s selected. Assume a draft head of 10 ft and 90% turbne effcency. Approxmately what sze of turbne runner s requred? (b) For the same condtons, select a set of two dentcal turbnes to be operated n parallel. Specfy the speed and sze of the unts. (a) Safe from cavtaton: 1 atm wv, σ H s, σ 0.13 H ρg ρg Wth equaton 7.15: Fgure 5.16 n Krvchenko, 1.8 N S + 30 σ = 00000, NS > Francs turbne n11 75 rpm -> n 73 rpm and 3 and Q m / s D m Number of poles s =8 -> n=57 (see Krvchenko page 17) Exercse 6.: Turbne selecton (From Flud Mechancs, Franzn and Fnnemore, 16.1) What s the least number of dentcal turbnes that can be used at a powerhouse where the avalable head s 100ft and Q = 1650 cfs? Assume turbne effcency s 90% and speed of operaton s rpm. Specfy the sze and specfc speed of the unts. Exercse 6.3: Turbne selecton (From Flud Mechancs, Franzn and Fnnemore, 16.6) It s desred to develop 15,000 bhp under a head of 1000 ft. Make any necessary assumptons and estmate the dameter of the wheel requred and the rotatve speed. Exercse 6.: Turbne selecton (From Flud Mechancs, Franzn and Fnnemore, 16.7) A sngle hydraulc turbne s to be selected for a power ste wth a net head of 100 ft. The turbne s to produce 5,000 hp at maxmum effcency. What speed (rpm) and dameter should ths turbne have f (a) a Francs turbne s selected (b) a propeller turbne s selected? (c) What are the hghest "settngs" (above or below talwater) that should be recommended for each of these machnes for them to run cavtaton-free at ther ponts of maxmum effcency? Last modfed by Mchel Cervantes - 16/19 -

17 Exercse 6.5: Turbne selecton (From Flud Mechancs, Franzn and Fnnemore, 16.8) For 50-cycle electrcty how many poles would you recommend for a generator that s connected to a turbne operatng under a desgn head of 3000 ft wth a flow of 80 cfs? Assume turbne effcences as gven n Fg and be sure the turbne s free of cavtaton. Exercse 6.6: Turbne selecton (From Flud Mechancs, Franzn and Fnnemore, 16.9) Specfy the type, speed, and sze of a sngle turbne to be nstalled at a ste wth an effectve head of 8 m. a maxmum draft head of m, and a flow rate of 5 m 3 /s. How would your recommendaton change f the avalable flow was 50 m 3 /s? Exercse 6.7: Turbne selecton (From Flud Mechancs, Franzn and Fnnemore, 16.50) It s desred to develop 300,000 hp under a head of 9 ft and to operate at 60 rpm. (a) If turbnes wth a specfc speed of approxmately 150 are to be used, how many unts would be requred? (b) If Francs turbnes wth a specfc speed of 80 were to be used, how many unts would be requred? Exercse 6.8: Turbne selecton (From Flud Mechancs, Franzn and Fnnemore, 16.51) Select two, four, and sx dentcal turbnes for an nstallaton where h = 00 ft and total Q = 300 cfs. Develop 60-cycle electrcty usng ether 36- or 7-pole generators. Be sure your selecton s free of cavtaton. Assume the turbne effcency s 90%. Exercse 6.9: Turbne selecton (From Flud Mechancs, Franzn and Fnnemore, 16.5) A turbne s to be nstalled at a pont where the net avalable head s 35 m and the avalable flow wll average 3 m 3 /s. What type of turbne would you recommend? Specfy the operatng speed and number of generator poles for 60-cycle electrcty f a turbne wth the hghest tolerable specfc speed to safeguard aganst cavtaton s selected. Assume a draft head of 3 m and 90% turbne effcency. Approxmately what sze of turbne runner s requred? Last modfed by Mchel Cervantes - 17/19 -

18 7 - Exercses on runner desgn Last modfed by Mchel Cervantes - 18/19 -

19 8 - Exercses on unsteadness Exercse 8.1: Oscllatng plate (From Advanced Flud Mechancs, H. Gustavsson,.1) The space above an nfnte plate s flled wth a lqud. The plate oscllates n ts plane wth angular frequency ω. Use the velocty dstrbuton over one perod of the moton (π/w) per m, the followng quanttes: (a) the dsspaton ntegrated the y-drecton (b) the total knetc energy (c) the power needed to drve the plate Last modfed by Mchel Cervantes - 19/19 -