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HW7soln-1

# HW7soln-1 - 8.10 Water is the working ﬂuid in an ideal...

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Unformatted text preview: 8.10 Water is the working ﬂuid in an ideal Rankine cycle. Steam enters the turbine at 1400 lbﬂin.2 and 1000°F. The condenser pressure is 2 lbf/in.2 The net power output of the cycle is 1><109 Btu/h. Cooling water experiences a temperature increase from 60°F to 76°F, with negligible pressure drop, as it passes through the condenser. Determine for the cycle (a) the mass ﬂow rate of steam, in lb/h. (b) the rate of heat transfer, in Btu/h, to the working ﬂuid passing through the steam generator. (0) the thermal efﬁciency. (d) the mass ﬂow rate of cooling water, in lb/h. KNOWN: An ideal Rankine cycle with superheat operates with water as the working ﬂuid. The net power output of the cycle is given. FIND: Determine the mass ﬂow rate of steam, the rate of heat transfer to the working ﬂuid passing through the steam generator, the thermal efficiency, and the mass ﬂow rate of cooling water. SCHEMATIC AND GIVEN DATA: Q7“ p1 = 1400 tar/in? r, = 10000? 1 Generator _ W cycl- =1x10*Bm/h Cooling water p3 = p2 = 2 lbfl'in2 x3 = 0 (saturated liquid) Problem 8.10 (Continued) — Page 2 3’13 diagram p = 1400 Min2 ENGINEERING MODEL: 1. Each component is analyzed as a control volume at steady state. The control volumes are shown on the accompanying sketch by dashed lines. _ All processes of the working ﬂuid are internally reversible. . The turbine and pump operate adiabatically. . Kinetic and potential energy effects are negligible. . Condensate exits the condenser as saturated liquid. . There is no heat transfer between the outside of the condenser and the surroundings. ONU’I-bwk) ANALYSIS: First, ﬁx each of the principal states. State 1: p] = 14001bf/inz, T1 = 1000°F —> From Table A—4E: h] = 1493.5 Btu/1b and s; = 1.6094 Btu/(lb-°R) State 2: p2 = 2 lbf'lin.2, 32 = s. —> From Table A-3E: x2 = (1.6094 — 0.1750)/1.7448 = 0.3221 and 112 = ha + x22;ng = 94.02 + (0.3221)(1022. 1) = 934.29 Btu/1b State 3: p3 =p2 = 2 lbf/in.2, sat liq. —> From Table A-3E: kg = kg = 94.02 Btu/1b and v3 = v8 = 0.01623 £13111: State 4: 124 Z hat“ WOW—PB) 144 in2 ﬁZ 3 in = 94.02 Btu/lb + 0.01623[ﬁ—](1400 — lb in2 lBtu 778 ft - lbf ’= 98.22 Btuflb Problem 8.10 (Continued) — Page 3 (a) The mass ﬂow rate of steam is found as follows. Mass and energy rate balances for control volumes enclosing the turbine and pump give W1: 551011—112) and WP =n'1(h4 45) The net power of the cycle is chcle =Wt _Wp whl)i(h4 _h3)] Solving for n'z m = chcle [(hl _ hZ )— (h4 _ I13 Inserting values 1x109 93”— 1493.5_“- —934.29 JEJ—[gszztu— 94.02 ii) lb 1b lb 1b (13) The rate of heat transfer to the working ﬂuid passing through the steam generator can be determined by applying mass and energy balances to a control volume around the steam generator to give Q‘m = r7301] — h4)=(1.80><1061b/h)(1493.5 Btu/1b — 93.22 Btu/lb) = 2.51><109 Btu/h (c) The thermal efficiency is W 77 = Q?“ = (1x109 Btu/h)/(2.51><109 Btufh) = 0.3984 (39.84%) (d) The mass ﬂow rate of cooling water through the condenser is determined by applying steady state mass and energy rate balances to a control volume enclosing the condenser. "'12 =m3 Em and ma:mbEn-1cw and 0=m(h2"h3)+mcw(ha _hb) Solvmg for mCW = ".1012 “’13) mew hb _ ha Problem 8.10 (Continued) — Page 4 For the cooling water, h it M T). Consequently, from Table A-2E h, = 28,08 Btu/lb hh : 44.09 Btu/1b Substituting values [1.80 ><105lw11t-)~1934.29E:—;u —94.02 5%] = “WWW—ﬂ“— : 9.45 ><107 lb/h 44.09_i’—28.03—u 1b 1b FRU®LEM 8.11 KNOOJM‘. A Vapcw' pow pLauA- warms ad- ﬁmotp eraJre W'f'H/J WW LIB-Ho; wor'ﬁl'rg M.Da\$mme low/own a} (WM 'Lpa si-aies M‘fkeoddﬂ- Ewe: Dakarmine ﬁeﬁmHmrmaJ eLKLECEeMﬂ , amt Clo) ~Hme rode: Er? W ﬁvamséiev‘ (km AMA QM. e= u: ‘ Steam generator Qm Stale p TC'C) h (klfkg) l 6 MR: 500 3422.2 2 10 kPa — -- ' '16333 gm 3 10 kPa Sal. 191.33 4 7.5 MPa 199.4 (. _ Condenser s 7 MPa_ - 4o. ,"-167,.5_7_.< i; 7 6 5 MP3 " 550 ‘ 3345.3' Wp —>~\ﬁ, EQGINEERNG— MODE] 1605.344 COM—rdwmme DWVMES M54 3 ’62) The mvbine W UL 0W ad/thaad—icau ,(3) [(142445 +6 {(116 aged: cmmnegleL—gif. 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HW7soln-1 - 8.10 Water is the working ﬂuid in an ideal...

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