ENGINE SHAFTS RPM CPRATIO INLET-TEMP EXH-TEMP AIRFLOW POWER HEATRATE LHV% ISOWOR
ID: 3230139 • Letter: E
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ENGINE SHAFTS RPM CPRATIO INLET-TEMP EXH-TEMP AIRFLOW POWER HEATRATE LHV% ISOWORK Traditional 1 27245 9.2 1134 602 7 1630 14622 24.6 232.86 Traditional 1 14000 12.2 950 446 15 2726 13196 27.3 181.73 Traditional 1 17384 14.8 1149 537 20 5247 11948 30.1 262.35 Traditional 1 11085 11.8 1024 478 27 6726 11289 31.9 249.11 Traditional 1 14045 13.2 1149 553 29 7726 11964 30.1 266.41 Traditional 1 6211 15.7 1172 517 176 52600 10526 34.2 298.86 Traditional 1 6210 17.4 1177 510 193 57500 10387 34.7 397.93 Traditional 1 3600 13.5 1146 503 315 89600 10592 34 284.44 Traditional 1 3000 15.1 1146 524 375 113700 10460 34.4 303.2 Traditional 1 3000 15 1171 525 514 164300 10086 35.7 319.65 Traditional 1 18000 12.7 1038 525 11 2000 14628 24.9 181.82 Traditional 1 11140 9.1 1038 523 25 5223 13396 26.9 208.92 Traditional 1 16630 15 1232 571 19 5500 11726 30.7 289.47 Traditional 2 7900 15.6 1077 482 47 11700 11252 32 248.94 Traditional 1 5100 10 963 485 123 26555 12449 28.9 215.89 Traditional 1 5160 12.3 1135 542 144 42170 11030 32.6 292.85 Traditional 1 3600 12.6 1113 534 295 86650 10787 33.4 293.73 Traditional 1 3000 12.3 1124 541 410 124700 10603 34 304.15 Traditional 1 3000 14.2 1204 553 515 172985 10144 35.5 335.89 Traditional 1 14000 15.9 1177 521 27 6930 11674 30.8 256.67 Traditional 1 3660 14.6 1135 526 56 14838 11510 31.3 264.96 Traditional 1 5400 15.3 1149 514 172 49500 10946 32.9 287.79 Traditional 1 3600 14.2 1141 526 362 109370 10508 34.3 302.13 Traditional 1 3600 11 1149 544 354 108719 10604 33.9 307.12 Traditional 1 3600 14.2 1177 525 378 120500 10270 35.1 318.78 Traditional 1 3000 14.2 1116 511 448 132220 10529 34.2 295.13 Traditional 1 3000 11.1 1149 537 500 157010 10360 34.7 314.02 Traditional 1 22516 6.6 899 512 7 1210 14796 24.3 172.86 Traditional 1 14950 9.7 916 444 19 3515 12913 27.9 185 Traditional 1 14950 10.7 1054 517 19 4600 12270 29.3 242.11 Traditional 1 14950 12 1093 513 22 5500 11842 30.4 250 Traditional 1 14950 15 1121 490 27 7520 10656 33.8 278.52 Traditional 2 8568 16.2 1066 464 39 9286 11360 31.7 238.1 Traditional 2 8568 17.6 1104 487 42 10685 11136 32.3 254.4 Traditional 1 11220 15.8 1121 493 49 13500 10814 33.3 275.51 Traditional 1 4473 8.9 960 517 158 32776 13523 26.6 207.44 Traditional 1 3600 12.4 1079 515 311 81600 11289 31.9 262.38 Traditional 1 3000 12.5 1041 490 400 100500 11183 32.2 251.25 Traditional 2 10400 15 1057 479 26 6844 10951 32.9 263.23 Advanced 1 6600 20 1288 546 120 43000 9722 37 358.33 Advanced 1 5100 14.8 1288 590 204 70905 10481 34.3 347.57 Advanced 1 3600 15.5 1327 599 448 174000 9812 36.7 388.39 Advanced 1 3600 18.5 1371 626 445 186600 9669 37.2 419.33 Advanced 1 3000 14.6 1327 599 648 259670 9643 37.3 400.73 Advanced 1 3000 23.2 1427 566 685 282000 9115 39.5 411.68 Advanced 1 3000 23.2 1427 621 685 331000 9115 39.5 483.21 Advanced 1 7280 14.3 1271 556 49 13680 11588 31.1 282.86 Advanced 1 7280 14.6 1271 556 88 27010 10888 33.1 306.93 Advanced 1 3600 16 1343 607 453 185400 9738 37 409.27 Advanced 1 3600 20 1427 596 567 254000 9295 38.7 447.97 Advanced 1 3000 17 1343 586 651 270300 9421 38.2 415.21 Advanced 1 3000 21 1427 587 737 334000 9105 39.5 453.19 Advanced 1 5400 16.1 1288 531 188 62300 10233 35.2 331.38 Advanced 1 5400 16.2 1310 589 187 68000 10186 35.3 363.64 Advanced 1 3600 16 1288 551 425 153600 9918 36.3 361.41 Advanced 1 3600 16.9 1343 577 440 182000 9209 39.1 413.64 Advanced 1 3600 15 1349 590 450 186500 9532 37.8 414.44 Advanced 1 3000 14 1260 585 510 189000 9933 36.2 370.59 Advanced 1 3600 19.2 1427 594 550 253000 9152 39.3 460 Advanced 1 3000 17 1316 584 642 265540 9295 38.7 413.61 Aeroderiv 2 33000 6.9 888 513 3 486 16243 22.2 162 Aeroderiv 2 30000 8.5 1004 561 4 806 14628 24.6 202 Aeroderiv 2 18910 14 1066 532 8 1845 12766 28.2 230.63 Aeroderiv 3 3600 35 1288 448 152 57930 8714 41.3 341.64 Aeroderiv 3 3600 20 1160 456 84 25600 9469 38 304.76 Aeroderiv 2 16000 10.6 1232 560 14 3815 11948 30.1 272.5 Aeroderiv 1 14600 13.4 1077 536 20 4942 12414 29 247.1 2. Cooling methods for gas turbines. In the Journal of Engineering for Gas Turbines and Power researchers studied gas turbines augmented with high-pressure inlet fogging. They classified turbines into three categories: traditional, advanced, and aeroderiva tive. Results from the experiment are contained in the spreadsheet "GASTURBINE" (posted on Canvas). Use the "Heatrate" column, along with the engine category (col- umn A to answer the questions below. (a) Use a hypothesis test to determine if the data contains sufficient evidence to detect a difference between the mean heat rates of traditional augmented gas turbines and aeroderivative augmented gas turbines. (b) Use a hypothesis test to determine if the data contains sufficient evidence to detect a difference between the mean heat rates of advanced augmented gas turbines and aeroderivative augmented gas turbines.Explanation / Answer
H0 = There is no significant difference between mean heat rates of traditional augmented gas turbines and aeroderivative gas turbines. That is µ1 = µ2
H1 = There is significant difference between mean heat rates of traditional augmented gas turbines and aeroderivative gas turbines. That is µ1 µ2
Assuming unequal variance, the t statistic is given by:
t = ( x1 – x2 )/(s12 /n1+ s22/n2)
Means:
x1 = 11544.07692
x2 = 12311.71429
Sample variance:
s12 = 1636565.336
s22= 7032314.238
t = ( 11544.07692-12311.71429 )/(1636565.336/39+ 7032314.238/7)
t = -0.750360538
t critical value:
t* = [t1* s12 /n1+t2* s22/n2] /[ s12 /n1+ s22/n2]
where t1 and t2 are the table values of t at a prefixed level of significance with (n1 -1) and (n2-1) d.f respectively.
t(0.05/2,38) = 2.024
t(0.05/2,7)=2.37
t* = 2.364624
since tcal = -0.75036 > ttab = -2.365, we do not reject the null hypothesis. Hence we conclude that there is no significant difference between mean heat rates of traditional augmented gas turbines and aeroderivative gas turbines. That is µ1 = µ2.
H0 = There is no significant difference between mean heat rates of advanced augmented gas turbines and aeroderivative gas turbines. That is µ3 = µ2
H1 = There is significant difference between mean heat rates of advanced augmented gas turbines and aeroderivative gas turbines. That is µ3 µ2
Assuming unequal variance, the t statistic is given by:
t = ( x3 – x2 )/(s32 /n3+ s22/n2)
Means:
x3 = 9764.285714
x2 = 12311.71429
Sample variance:
s32 = 407690.9143
s22= 7032314.238
t = (9764.285714-12311.71429 )/( 407690.9143/21+ 7032314.238/7)
t = -2.517361807
t critical value:
t* = [t1* s12 /n1+t2* s22/n2] /[ s12 /n1+ s22/n2]
where t1 and t2 are the table values of t at a prefixed level of significance with (n1 -1) and (n2-1) d.f respectively.
t(0.05/2,21) = 2.08
t(0.05/2,7)=2.37
t* = 2.446911846
since tcal = -2.5174 < ttab = -2.4469, we reject the null hypothesis. Hence we conclude that there is significant difference between mean heat rates of advanced augmented gas turbines and aeroderivative gas turbines. That is µ3 µ2.
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