CAER urbomachinery Chapter / urbomachinery 800 / 0 8 8 rad /s, u r 8 8 0 0 m /s, u r 8 8 0 0 8 m /s, rbv, but V u since, n n 0 0 0 0 0 0 m / s V V 0 0 m /s, rb 0 0 0 Vn u 0 8 6 77 m /s, tan tan 0 n t V t 0 ( 90 under ideal conditions) r V rv t t 000 0 0( 0 6 77 0) 6 N m W 88 6 980 W, t / 980 /( 980 0 0 ) 7 m ft gal / sec 0 67 ft / sec, 000 09 rad /sec, 7 8 gal 0 0 67 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 6 0 8 0 67 7 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
Chapter / urbomachinery 6 Compute loss in suction pipe: h f L K L ga 0 0 0 0 0 9 0 8 8 m 0 9 8 0 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 0 0 0 8 m 979 8 N N 970 00 0 8 0 6 m / s, from Fig 9, m and W 9 kw 00 7 6 m, 970 00 W W 9 7 kw 970 0 / 600 C 0 00 06 0 ( in m /h) g 98 C 0 00 6 0 ( in m) abulate C and C using selected values of and from Fig 6: (m /h) C 0 (m) C 0 0 0 6 0 0 00 06 0 9 0 6 00 7 9 0 6 0 00 8 08 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
Chapter / urbomachinery 800 0 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 70 78 rad /s, 0 0 09 78 / 7 ft, 0 08 78 7 7 8 ft, 0 0 78 7 NS 7 ft, W 0 00 9 78 7 6 0 ft - lb /sec, or W 6 0 / 0 horsepower 6 600 6 8 rad /s, 7 / 60 0 78 m / s, 0 ( g ) 6 8 0 78 ( 9 8 9 ) / / 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
Chapter / urbomachinery 0 Assume a pump speed N = 000 rpm, or 000 09 rad /s 0 W /( ) 00 0 /( 880 0 66) m, f 09 0 66 ( 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 0 067 C W g and C Combining and solving for and, / C g / C and C 0 66 / 08 9 8 / 0 067 0 m, 066 08 0 8 rad/s, 880 900 kg/m, g 98 or N 8 0 / 67 rpm W C 0 07 900 8 0 0 W, or kw W Radial flow: from Fig, at best, : C 0 07, C 0 06, C 0 W 0 66 / 0 06 9 8 / 0 0 878 m, 066 006 0878 9 rad/s, or 9 0 N 6 rpm W 0 007 900 9 0 878 6 0 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
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 6 00 9 96 m, 0 W W N 7 00 06 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
Chapter / urbomachinery 6 Compute system demand: f L K V g 00 0 00 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 0 0008 ln 0 7 ln 0 7 0 07, z f L ga 0 07 80 60 ( / ) 60 0 89 00 From Fig 6, at best, ft / sec, and ft 9 8 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
Chapter / urbomachinery Assume three pumps in series, so that 6 ft hen the demand head is 60 0 89 6 ft ence three pumps in series are appropriate he required power is W or W 0 / 0 06 hp / 6 086 6/ 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 9 6 67 m 9 8 (b) NS = 67 m, N = 00 rpm, N = 000 rpm, / = NS NS N N 67 000 8 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 0 7 60 v a -09 09 f ln 7Re ln 7 (0 ) 00 fl V 00 00 z 0 m g 00 98 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
Chapter / urbomachinery (a) Choose a radial-flow pump Use Fig to select the size and speed: C 0, C 0 06, 0 7, 0 0 0 0089 m, C C g 0 0089 C 0 06 0 090 0 0 0089 0 090 m 0 06 9 8 0 (b) Available net positive suction head: (c) NS p p a g v 0 90 rad /s, or N 90 680 rpm 0 0 86 0 z 9 9 8 9 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 7 8 7 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( 8 7 9 ) 80 7 N m 7 W 6 80 7 0 8 W, or 7 MW Under ideal conditions, and W W f, hence W / 7 0 8 /( 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
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 / / 0 0 99 0 76 rpm 0 Write energy eqn from upper reservoir (loc ) to surge tank (loc ) and solve for : ga f L z z ( ) / 9 8 ( / ) 0 8 0 0 000 / ( 60 68 ) 0 0 m / s Apply energy eqn from loc to lower reservoir (loc ) and determine : z z f L K v ga 0 0 00 0 0 68 9 0 8 m 9 8 0 8 W 980 0 0 0 9 89 0 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
Chapter / urbomachinery 00 / 0 0 9 rad /s, and from Fig at best efficiency ( = 08), 0, cv = 09 V cv g 0 9 9 80 6 m /s, 6 W 0 78 m /s 980 0 08 his is the discharge from all of the jets etermine the wheel radius r : r g 0 9 80 0 9 0 97 m, ence, the diameter of the wheel is r 0 97 9 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 7,00 0 6 ft 6 60 08 Write energy eqn from upper reservoir (loc ) to lake (loc ): z f L K z, ga 00 0 000,60 0 6 660, 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
Chapter / urbomachinery which reduces to 8 6 7 99 0 89 0 6 0 Solving, 8 ft W 7, 000 0 76 6,000 kw, 6 008 0 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 09 09 0 898 m and W 6 0 0 0 m / s 980 89 8 0 8 Write energy eqn from reservoir to turbine outlet: f L K ga, 0 0 000 0 89 8 9 8 ( / ), 9 67 06 which reduces to 0 Solving = m (b) Compute jet velocity: V cv g 0 98 9 8 89 8 7 9 m /s he flow through one nozzle is /, and the jet area is j / ence j / V / 79 0 06 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
Chapter / urbomachinery 8 ( 9 8 7) W 000 0 / 0 / 99 0 6 W (one unit) otal power developed is 9 0 6 W ence, required number of units is 9/ 99 8 Use two turbines 0 (a) fl z z ga 000 0 9 89 8 m, 098 (0780 ) W 980 0 8 08 6 0 W, or 6 kw (b) Compute the specific speed of the turbine: N 00 6 rad/s, 0 0 W 6 / 6 6 0 /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 7 680 rpm ; W 980 0 8 0 9 6 0 0 0 0 0 0 0 0 9 m, or approximately 00 m ; 0 9 8 8 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 0 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