CHAPTER 12 Turbomachinery
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1 CAER urbomachinery Chapter / urbomachinery 800 / rad /s, u r m /s, u r m /s, rbv, but V u since, n n m / s V V 0 0 m /s, rb Vn u m /s, tan tan 0 n t V t 0 ( 90 under ideal conditions) r V rv t t ( ) 6 N m W W, t / 980 /( ) 7 m ft gal / sec 0 67 ft / sec, rad /sec, 7 8 gal Vn 6 ft /sec, r b 0 u r 09 / ft/sec, u g u V t ( n cot ) ( 6 cot 60 ) ft W t ft - lb /sec, or W 7/ 0 horsepower 0 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part
2 Chapter / urbomachinery 6 Compute loss in suction pipe: h f L K L ga m Water at 0 C: 979 N/m, p 0 a v Substitute known data into NS relation, solving for z: z p atm p v h L NS m N N m / s, from Fig 9, m and W 9 kw m, W W 9 7 kw / 600 C ( in m /h) g 98 C ( in m) abulate C and C using selected values of and from Fig 6: (m /h) C 0 (m) C he dimensionless curve shown in Fig is for the 0-mm impeller Since the impellers are not the same (0 mm versus 0 mm), dynamic similitude does not exist and thus, the curves are not the same 0 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part
3 Chapter / urbomachinery Compute the specific speed: 0 / / 0, ( g ) ( 9 8 ) hence use a mixed flow pump As an alternate, since is close to unity, a radial flow pump could be employed Fig : At 0 7 (best eff), C 0 08, (a) C 0 08, C 0 00, C 0 0 W NS rad /s, / 7 ft, ft, NS 7 ft, W ft - lb /sec, or W 6 0 / 0 horsepower rad /s, 7 / m / s, 0 ( g ) ( ) / / 0 7, Use a radial flow pump 8,,, or, 9, and 9 0 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part
4 Chapter / urbomachinery 0 Assume a pump speed N = 000 rpm, or rad /s 0 W /( ) 00 0 /( ) m, f ( g ) ( 9 8 ) / / 6 he specific speed suggests a mixed-flow pump owever, if N = 000 rpm, a radial-flow pump may be appropriate Consider both possibilities Mixed flow: from Fig, at best, : Use C 0 07, C 0 8, C C W g and C Combining and solving for and, / C g / C and C 0 66 / / m, rad/s, kg/m, g 98 or N 8 0 / 67 rpm W C W, or kw W Radial flow: from Fig, at best, : C 0 07, C 0 06, C 0 W 0 66 / / m, rad/s, or 9 0 N 6 rpm W W, or 6 kw ence, a mixed-flow pump is preferred 6 0 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part
5 Chapter / urbomachinery he intersection of the system demand curve with the head-discharge curve yields 7 m / min, 6 m, W 7 kw N 0 rpm, 7 m / min, 6 m, W 7 kw, N 00 rpm, N 00 7 m /min, N 0 N N m, 0 W W N N kw 0 Efficiency will remain approximately the same 7 0 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part
6 Chapter / urbomachinery 6 Compute system demand: f L K V g m, 0 98 VA 0 0 m, 00 / 0 rad/s 0 9, Axial pump is appropriate / / ( g ) (980) 8 (a) he intersection of the pump curve with the demand curve yields 6 m and 80 m / h From Fig 6, 6 kw and NS 8 m W 0 Use energy eqn to establish system demand: f e ln 0 7 ln , z f L ga ( / ) From Fig 6, at best, ft / sec, and ft Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part
7 Chapter / urbomachinery Assume three pumps in series, so that 6 ft hen the demand head is ft ence three pumps in series are appropriate he required power is W or W 0 / 0 06 hp / / 07 0 ft - lb, sec (a) For water at 80C, pv = 6 0 a, and = 9 kg/m Write the energy equation from the inlet (section i) to the location of cavitation in the pump: pi Vi pv NS, g NS p p V i v i ( 8 6 ) 0 g m 9 8 (b) NS = 67 m, N = 00 rpm, N = 000 rpm, / = NS NS N N m 00 Given: 7 L 00 m, 0 0 m, z z z m, V m /s, 6 0 m / s, 9 kg /m, p 86 0 a, p 0 0 a Compute the pump head: 00 Re v a f ln 7Re ln 7 (0 ) 00 fl V z 0 m g Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part
8 Chapter / urbomachinery (a) Choose a radial-flow pump Use Fig to select the size and speed: C 0, C 0 06, 0 7, m, C C g C m (b) Available net positive suction head: (c) NS p p a g v 0 90 rad /s, or N rpm z m 6 0 / 0 6 rad /s, cot (r b / cot ) cot ( 0 8 6/ 0 cot 7 ) 6 Vt u V r n cot cot r b 0 6 cot m /s, 0 8 Vt u V r n cot cot rb 0 6 cot 00 9 m /s, 0 8 ( rv t rv t ) 000 0( ) 80 7 N m 7 W W, or 7 MW Under ideal conditions, and W W f, hence W / /( 980 0) m 60 0 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part
9 Chapter / urbomachinery 8 N 0 rpm, W 00 kw, ft, W 9kW, ft From the similarity rules, W W N N N N and Substitute second eqn into the first to eliminate ( N / N ), and solve for : / / / / 9 0 W 076 ft, W 00 N N / / rpm 0 Write energy eqn from upper reservoir (loc ) to surge tank (loc ) and solve for : ga f L z z ( ) / 9 8 ( / ) / ( ) 0 0 m / s Apply energy eqn from loc to lower reservoir (loc ) and determine : z z f L K v ga m W W, or 89 kw From Fig, use a Francis turbine A representative value of the specific speed is (Fig 0): / / ( g ) ( 9 8 ) ( W / / ) ( 67 0 / 000) or N 06 0 / 90 rpm / 06 rad/s, 6 0 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part
10 Chapter / urbomachinery 00 / rad /s, and from Fig at best efficiency ( = 08), 0, cv = 09 V cv g m /s, 6 W 0 78 m /s his is the discharge from all of the jets etermine the wheel radius r : r g m, ence, the diameter of the wheel is r m Compute diameter of one jet: j r / 8 9 / 8 0 m, or mm Let N j no of jets hen each jet has a discharge of / N j and an area / N V j j Solving for N j : N j 78 V 6 0 j, ( W Use three jets / ) / ( g ) / 0 9( 0 / 000) / ( 9 80) 6 / 0 0 7, 0 / 6, 60 ft / sec (one unit), W 7, ft Write energy eqn from upper reservoir (loc ) to lake (loc ): z f L K z, ga , , 6 0 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part
11 Chapter / urbomachinery which reduces to Solving, 8 ft W 7, ,000 kw, m From Fig, a Francis or pump/turbine unit is indicated 6 (a) Let be the total head and the discharge delivered to the turbine; then m and W m / s Write energy eqn from reservoir to turbine outlet: f L K ga, ( / ), which reduces to 0 Solving = m (b) Compute jet velocity: V cv g m /s he flow through one nozzle is /, and the jet area is j / ence j / V / m, 0 06 j 0 6 m 6 0 Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part
12 Chapter / urbomachinery 8 ( 9 8 7) W / 0 / W (one unit) otal power developed is W ence, required number of units is 9/ 99 8 Use two turbines 0 (a) fl z z ga m, 098 (0780 ) W W, or 6 kw (b) Compute the specific speed of the turbine: N 00 6 rad/s, 0 0 W 6 / /000 / / g 988 ence, from Fig 0, a Francis turbine is appropriate (c) From Fig, the turbine with = 06 is chosen: C = 0, C = 0, and = 09 C C g C 0 7 rad /s, or N rpm ; W m, or approximately 00 m ; Calculate a new specific speed based on the final design data: W, or 6 kw 7 60 /000 / 096 (988) an acceptable value according to Fig Cengage Learning All Rights Reserved May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part
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