Tablas de Flujo Compresible (Version 1)

TABLAS DE FLUJO COMPRESIBLE

Ingrese el número de Mach M

FLUJO ISENTRÓPICO

Tabla A.1

Funciones para flujo isentrópico unidimensional para un gas perfecto[ Calor específico y peso molecular constantes ]

k = 1.67

0 0 1 1 1 0 0

0.01 0.011554 56.234506 0.9998601 0.99995 0.9999665 43.280734 56.2298107 0.01292199 77.3939498 0.0218191

0 #DIV/0! 1 1 1 #DIV/0! #DIV/0! 0 #DIV/0! 0

0.26 0.2970649 2.2614064 0.910745 0.9671294 0.9778555 1.8316664 2.13864099 0.32133166 3.27535799 0.5285036

0 #DIV/0! 1 1 1 #DIV/0! #DIV/0! 0 #DIV/0! 0

4.32 1.8535246 6.7448603 0.0002556 0.0519689 0.1378948 1.1965186 0.04833527 0.10773558 2.13959641 0.0201937

0 #DIV/0! 1 1 1 #DIV/0! #DIV/0! 0 #DIV/0! 0

3.2 1.7565849 3.4110304 0.0020003 0.1084326 0.2257133 1.1629357 0.08348385 0.21303283 2.07954387 0.0675329

0 #DIV/0! 1 1 1 #DIV/0! #DIV/0! 0 #DIV/0! 0

A P wf If

ONDA DE CHOQUE NORMAL

Choque normal unidimensional de un gas perfecto( Calor específico y peso molecular constantes )

k = 1.26

1.00 1.00000 1.00000 1.00000 1.00000 1.0000000 1.8081161

1.01 0.99012 1.02241 1.01775 1.00458 0.9999987 1.8284661

1.02 0.98048 1.04505 1.03559 1.00914 0.9999899 1.8491887

1.03 0.97107 1.06791 1.05352 1.01366 0.9999664 1.8702769

1.04 0.96188 1.09099 1.07154 1.01815 0.9999217 1.8917242

1.05 0.95290 1.11429 1.08965 1.02261 0.9998497 1.9135245

1.06 0.94412 1.13782 1.10785 1.02705 0.9997447 1.9356720

1.07 0.93555 1.16157 1.12613 1.03147 0.9996016 1.9581614

1.08 0.92717 1.18554 1.14449 1.03587 0.9994154 1.9809876

1.09 0.91897 1.20974 1.16293 1.04025 0.9991816 2.0041461

1.10 0.91096 1.23416 1.18146 1.04461 0.9988961 2.0276322

1.11 0.90312 1.25880 1.20006 1.04895 0.9985551 2.0514420

1.12 0.89544 1.28367 1.21873 1.05328 0.9981550 2.0755713

1.13 0.88793 1.30876 1.23748 1.05760 0.9976925 2.1000167

1.14 0.88058 1.33407 1.25630 1.09027 0.9971647 2.1247745

FLUJO FANNO

Tabla A.1

k = 1.4

0 0 1 1 1 0 0

0.01 0.0109543 57.873843 0.99993 0.99995 0.99998 45.64948 57.8697917 0.01183145 84.5264124 0.017279

0.02 0.021908 28.94213 0.9997201 0.9998 0.99992 22.83364 28.9340278 0.02365864 42.2796859 0.0345517

0.03 0.0328604 19.300542 0.9993703 0.9995501 0.99982 15.232315 19.2883876 0.03547732 28.2047667 0.051812

0.04 0.0438108 14.481486 0.9988808 0.9992004 0.9996801 11.434618 14.4652783 0.04728323 21.1727976 0.0690537

0.05 0.0547586 11.59144 0.998252 0.9987511 0.9995002 9.1583705 11.5711816 0.05907215 16.9580069 0.0862705

0.06 0.0657031 9.66591 0.9974841 0.9982023 0.9992805 7.6428474 9.64159138 0.07083983 14.1518035 0.1034564

0.07 0.0766436 8.29153 0.9965775 0.9975542 0.999021 6.5620227 8.26314782 0.08258209 12.150505 0.1206051

0.08 0.0875796 7.26161 0.9955329 0.9968072 0.9987216 5.7528834 7.22917111 0.09429472 10.6522702 0.1377105

0.09 0.0985103 6.46134 0.9943506 0.9959615 0.9983826 5.1248666 6.42483914 0.10597357 9.48940896 0.1547666

0.1 0.1094351 5.82183 0.9930314 0.9950174 0.998004 4.6236343 5.78125867 0.1176145 8.56130711 0.1717673

0.11 0.1203534 5.29923 0.9915759 0.9939755 0.9975858 4.2146078 5.25458855 0.12921339 7.80393719 0.1887067

0.12 0.1312645 4.86432 0.989985 0.9928361 0.9971283 3.8747344 4.81560138 0.14076619 7.17461402 0.2055787

0.13 0.1421678 4.49686 0.9882594 0.9915997 0.9966314 3.5880546 4.44406282 0.15226884 6.64378612 0.2223775

0.14 0.1530626 4.18240 0.9864001 0.9902668 0.9960953 3.3431685 4.12551977 0.16371736 6.19034513 0.2390972

0.15 0.1639483 3.9103428 0.9844082 0.988838 0.9955202 3.1317161 3.84937332 0.17510778 5.79881141 0.2557321

0.16 0.1748242 3.6727386 0.9822845 0.9873138 0.9949061 2.9474274 3.60767429 0.18643621 5.45757509 0.2722764

0.17 0.1856898 3.463509 0.9800303 0.9856949 0.9942532 2.7855076 3.39434391 0.19769876 5.15775789 0.2887245

0.18 0.1965443 3.2779265 0.9776468 0.9839819 0.9935617 2.6422273 3.20465426 0.20889165 4.89245433 0.3050709

0.19 0.2073873 3.1122587 0.9751351 0.9821756 0.9928318 2.5146422 3.03487278 0.2200111 4.65621262 0.3213101

0.2 0.2182179 2.963520 0.9724967 0.9802767 0.9920635 2.4003968 2.88201343 0.23105343 4.4446712 0.3374366

0.21 0.2290356 2.8292936 0.9697328 0.9782859 0.9912571 2.2975841 2.74365895 0.24201499 4.25429915 0.3534451

0.22 0.2398399 2.7076021 0.966845 0.9762041 0.9904128 2.204644 2.61783159 0.2528922 4.08220746 0.3693305

0.23 0.25063 2.5968121 0.9638347 0.9740321 0.9895308 2.1202874 2.50289757 0.26368156 3.92600944 0.3850875

0.24 0.2614054 2.4955625 0.9607034 0.9717707 0.9886112 2.0434402 2.3974954 0.27437961 3.78371609 0.4007113

0.25 0.2721655 2.402710 0.9574528 0.969421 0.9876543 1.9732001 2.30048146 0.28498298 3.65365657 0.4161967

0.26 0.2829097 2.3172873 0.9540846 0.9669838 0.9866604 1.9088033 2.21088805 0.29548837 3.53441699 0.4315391

0.27 0.2936373 2.2384706 0.9506003 0.9644601 0.9856295 1.8495995 2.12789086 0.30589254 3.42479286 0.4467336

0.28 0.3043478 2.1655536 0.9470019 0.9618509 0.9845621 1.7950311 2.05078334 0.31619234 3.32375166 0.4617757

0.29 0.3150406 2.0979276 0.9432911 0.9591572 0.9834582 1.7446171 1.97895639 0.32638469 3.23040324 0.4766609

0.3 0.3257152 2.0350653 0.9394697 0.9563802 0.9823183 1.6979411 1.91188215 0.33646658 3.14397605 0.4913847

0.31 0.3363708 1.9765071 0.9355397 0.9535208 0.9811424 1.65464 1.84910086 0.34643511 3.06379803 0.505943

0.32 0.3470071 1.9218513 0.931503 0.9505802 0.979931 1.6143963 1.79021023 0.35628743 2.98928105 0.5203316

0.33 0.3576233 1.8707447 0.9273616 0.9475595 0.9786843 1.5769307 1.73485676 0.3660208 2.91990824 0.5345465

0.34 0.368219 1.8228758 0.9231175 0.94446 0.9774025 1.5419969 1.68272853 0.37563254 2.85522345 0.5485837

0.35 0.3787936 1.7779687 0.9187728 0.9412827 0.9760859 1.5093767 1.63354926 0.38512009 2.79482262 0.5624396

0.36 0.3893466 1.7357783 0.9143296 0.938029 0.9747349 1.4788761 1.5870734 0.39448094 2.73834652 0.5761104

0.37 0.3998773 1.696086 0.9097899 0.9347 0.9733497 1.4503221 1.54308193 0.40371271 2.68547471 0.5895928

0.38 0.4103854 1.6586962 0.9051561 0.931297 0.9719306 1.4235597 1.50137888 0.41281307 2.63592043 0.6028832

A P wf If

0.39 0.4208701 1.6234335 0.9004301 0.9278212 0.9704781 1.39845 1.46178841 0.42177981 2.58942629 0.6159784

0.379 0.4093356 1.6623367 0.9056236 0.9316406 0.9720741 1.4261594 1.50545136 0.41190901 2.64073412 0.6015629Tabla A.1

k = 1.4

0.40 0.4313311 1.59014 0.8956144 0.924274 0.9689922 1.3748679 1.42415226 0.4306108 2.5457606 0.6288754

0.41 0.4417678 1.5586734 0.890711 0.9206567 0.9674735 1.3527003 1.38832759 0.439304 2.5047142 0.6415712

0.42 0.4521796 1.5289048 0.8857224 0.9169707 0.9659223 1.3318451 1.35418519 0.44785748 2.46609784 0.654063

0.43 0.4625662 1.5007175 0.8806507 0.9132171 0.9643388 1.3122095 1.32160787 0.45626939 2.42973982 0.6663479

0.44 0.4729269 1.4740054 0.8754982 0.9093975 0.9627234 1.2937092 1.29048909 0.46453796 2.39548401 0.6784236

0.45 0.4832614 1.4486718 0.8702674 0.9055132 0.9610764 1.2762675 1.2607318 0.47266155 2.36318814 0.6902875

0.46 0.4935691 1.4246285 0.8649605 0.9015656 0.9593983 1.259814 1.23224736 0.48063859 2.33272226 0.7019374

0.47 0.5038495 1.401795 0.8595798 0.897556 0.9576893 1.2442846 1.2049547 0.4884676 2.30396745 0.7133711

0.48 0.5141021 1.3800973 0.8541278 0.893486 0.9559498 1.2296205 1.1787795 0.49614722 2.27681466 0.7245866

0.49 0.5243266 1.3594677 0.8486068 0.8893569 0.9541803 1.2157674 1.15365352 0.50367615 2.25116373 0.735582

0.50 0.5345225 1.3398438 0.8430192 0.8851701 0.952381 1.2026756 1.12951397 0.51105322 2.22692247 0.7463557

0.51 0.5446892 1.3211681 0.8373673 0.8809272 0.9505523 1.1902992 1.10630299 0.51827732 2.20400589 0.756906

0.52 0.5548265 1.3033878 0.8316536 0.8766295 0.9486946 1.1785959 1.08396718 0.52534747 2.18233554 0.7672314

0.53 0.5649338 1.2864538 0.8258805 0.8722785 0.9468083 1.1675264 1.06245715 0.53226274 2.16183882 0.7773306

0.54 0.5750106 1.2703211 0.8200503 0.8678756 0.9448938 1.1570544 1.04172719 0.53902234 2.14244853 0.7872025

0.55 0.5850567 1.2549476 0.8141654 0.8634224 0.9429514 1.1471463 1.02173492 0.54562554 2.12410229 0.796846

0.56 0.5950716 1.2402944 0.8082282 0.8589203 0.9409816 1.1377708 1.00244097 0.5520717 2.1067422 0.8062602

0.57 0.6050549 1.2263255 0.8022411 0.8543707 0.9389848 1.1288988 0.98380875 0.55836028 2.09031436 0.8154442

0.58 0.6150061 1.2130072 0.7962065 0.8497752 0.9369612 1.1205031 0.96580418 0.56449084 2.0747686 0.8243974

0.59 0.624925 1.2003083 0.7901266 0.8451352 0.9349115 1.1125585 0.94839552 0.570463 2.06005811 0.8331193

0.60 0.6348111 1.1881995 0.784004 0.8404522 0.9328358 1.1050415 0.93155311 0.5762765 2.0461392 0.8416095

0.61 0.644664 1.1766537 0.7778408 0.8357277 0.9307347 1.0979298 0.91524926 0.58193114 2.03297102 0.8498677

0.62 0.6544834 1.1656455 0.7716394 0.8309631 0.9286086 1.091203 0.89945806 0.58742682 2.02051533 0.8578937

0.63 0.664269 1.1551511 0.7654022 0.8261598 0.9264578 1.0848416 0.88415525 0.59276352 2.00873633 0.8656876

0.64 0.6740204 1.1451483 0.7591314 0.8213195 0.9242828 1.0788275 0.86931808 0.59794129 1.99760042 0.8732493

0.65 0.6837372 1.1356162 0.7528294 0.8164434 0.9220839 1.0731437 0.85492522 0.60296028 1.98707606 0.8805792

0.66 0.6934191 1.1265352 0.7464983 0.8115332 0.9198617 1.0677742 0.8409566 0.60782071 1.97713361 0.8876775

0.67 0.7030659 1.1178871 0.7401404 0.8065902 0.9176164 1.0627039 0.82739338 0.61252289 1.96774518 0.8945447

0.68 0.7126771 1.1096546 0.7337579 0.8016158 0.9153486 1.0579186 0.81421782 0.61706718 1.95888454 0.9011813

0.69 0.7222525 1.1018216 0.727353 0.7966115 0.9130586 1.0534049 0.80141319 0.62145403 1.95052693 0.907588

0.70 0.7317917 1.0943727 0.7209279 0.7915788 0.9107468 1.0491504 0.78896375 0.62568398 1.94264902 0.9137655

0.71 0.7412946 1.0872936 0.7144847 0.786519 0.9084137 1.045143 0.77685463 0.62975762 1.93522877 0.9197148

0.72 0.7507607 1.0805709 0.7080255 0.7814336 0.9060597 1.0413715 0.76507177 0.63367562 1.92824537 0.9254367

0.73 0.7601899 1.0741918 0.7015524 0.7763239 0.9036852 1.0378254 0.75360192 0.6374387 1.92167915 0.9309324

0.74 0.7695818 1.0681443 0.6950676 0.7711914 0.9012906 1.0344944 0.7424325 0.64104768 1.91551146 0.9362031

0.75 0.7789362 1.0624171 0.6885729 0.7660374 0.8988764 1.0313692 0.73155164 0.64450341 1.90972467 0.9412499

0.76 0.7882528 1.0569994 0.6820705 0.7608632 0.8964429 1.0284407 0.72094808 0.64780684 1.90430208 0.9460743

A P wf If

0.77 0.7975315 1.0518812 0.6755622 0.7556703 0.8939906 1.0257002 0.71061114 0.65095894 1.89922781 0.9506777

0.78 0.8067719 1.0470528 0.66905 0.75046 0.8915199 1.0231398 0.7005307 0.65396076 1.89448683 0.9550617

0.79 0.8159738 1.0425053 0.6625359 0.7452336 0.8890311 1.0207517 0.69069714 0.65681342 1.89006484 0.9592278

Tabla A.1

k = 1.4

0.80 0.825137 1.03823 0.6560216 0.7399924 0.8865248 1.0185285 0.68110132 0.65951808 1.88594828 0.96317770.81 0.8342613 1.0342189 0.6495091 0.7347377 0.8840013 1.0164633 0.67173458 0.66207595 1.88212422 0.96691330.82 0.8433465 1.0304643 0.6430001 0.7294708 0.8814611 1.0145494 0.66258864 0.6644883 1.87858039 0.97043640.83 0.8523924 1.0269589 0.6364964 0.7241929 0.8789045 1.0127805 0.65365565 0.66675645 1.87530509 0.97374880.84 0.8613988 1.0236958 0.6299998 0.7189053 0.876332 1.0111506 0.64492813 0.66888176 1.87228718 0.9768527

0.85 0.8703655 1.0206685 0.6235118 0.7136093 0.873744 1.0096541 0.63639893 0.67086565 1.86951604 0.979750.86 0.8792923 1.0178709 0.6170343 0.708306 0.8711408 1.0082853 0.62806125 0.67270956 1.86698154 0.98244290.87 0.8881791 1.0152969 0.6105688 0.7029967 0.868523 1.0070391 0.61990861 0.67441501 1.86467404 0.98493360.88 0.8970257 1.012941 0.6041169 0.6976825 0.8658908 1.0059105 0.61193481 0.67598352 1.86258429 0.98722430.89 0.9058319 1.0107981 0.5976802 0.6923646 0.8632448 1.0048947 0.60413394 0.67741668 1.86070351 0.9893173

0.90 0.9145976 1.0088629 0.5912601 0.6870442 0.8605852 1.0039873 0.59650033 0.67871609 1.85902326 0.9912150.91 0.9233227 1.0071307 0.5848581 0.6817223 0.8579125 1.0031838 0.58902859 0.6798834 1.85753551 0.99291980.92 0.932007 1.0055971 0.5784758 0.6764002 0.8552271 1.0024802 0.58171354 0.6809203 1.85623255 0.99443410.93 0.9406505 1.0042576 0.5721144 0.6710787 0.8525295 1.0018723 0.57455024 0.68182849 1.85510703 0.99576040.94 0.9492528 1.0031083 0.5657754 0.6657592 0.8498198 1.0013565 0.56753394 0.68260972 1.8541519 0.9969014

0.95 0.9578141 1.0021452 0.55946 0.6604425 0.8470987 1.000929 0.56066011 0.68326575 1.8533604 0.99785940.96 0.9663341 1.0013646 0.5531696 0.6551298 0.8443664 1.0005864 0.5539244 0.68379837 1.85272607 0.99863730.97 0.9748128 1.000763 0.5469053 0.649822 0.8416233 1.0003254 0.54732263 0.6842094 1.85224271 0.99923760.98 0.9832501 1.0003371 0.5406685 0.6445201 0.8388699 1.0001427 0.54085081 0.68450069 1.85190437 0.9996630.99 0.9916458 1.0000838 0.5344603 0.6392252 0.8361064 1.0000352 0.53450509 0.68467408 1.85170536 0.9999162

1.00 1 1 0.5282818 0.6339381 0.8333333 1 0.52828179 0.68473146 1.8516402 11.01 1.0083125 1.0000829 0.5221341 0.6286599 0.830551 1.0000343 0.52217736 0.68467471 1.85170364 0.99991711.02 1.0165832 1.0003297 0.5160183 0.6233913 0.8277598 1.0001353 0.5161884 0.68450576 1.85189065 0.99967041.03 1.0248122 1.000738 0.5099353 0.6181334 0.82496 1.0003004 0.51031165 0.68422652 1.85219638 0.99926261.04 1.0329993 1.0013052 0.5038863 0.612887 0.8221521 1.0005271 0.50454394 0.68383892 1.85261617 0.9986965

1.05 1.0411446 1.0020291 0.4978721 0.6076529 0.8193363 1.000813 0.49888227 0.68334491 1.85314556 0.99797511.06 1.0492478 1.0029074 0.4918936 0.6024319 0.8165132 1.0011558 0.49332371 0.68274645 1.85378024 0.9971011.07 1.0573092 1.0039381 0.4859517 0.597225 0.8136829 1.0015532 0.48786547 0.6820455 1.85451609 0.99607741.08 1.0653285 1.0051192 0.4800474 0.5920328 0.8108459 1.002003 0.48250483 0.68124403 1.85534912 0.99490691.09 1.0733058 1.0064489 0.4741813 0.5868562 0.8080025 1.0025034 0.47723919 0.680344 1.85627552 0.9935924

1.10 1.081241 1.0079253 0.4683542 0.5816959 0.805153 1.0030521 0.47206606 0.6793474 1.85729158 0.9921371.11 1.0891342 1.0095469 0.4625669 0.5765527 0.8022978 1.0036473 0.46698301 0.6782562 1.85839378 0.99054341.12 1.0969853 1.0113121 0.4568201 0.5714272 0.7994372 1.0042873 0.4619877 0.67707237 1.85957869 0.98881451.13 1.1047944 1.0132193 0.4511145 0.5663201 0.7965716 1.0049701 0.45707789 0.67579791 1.86084303 0.98695321.14 1.1125614 1.0152671 0.4454507 0.5612322 0.7937012 1.0056941 0.45225141 0.67443478 1.86218362 0.9849625

A P wf If

1.15 1.1202864 1.0174543 0.4398292 0.5561641 0.7908264 1.0064576 0.44750615 0.67298496 1.86359742 0.98284511.16 1.1279693 1.0197796 0.4342508 0.5511163 0.7879476 1.0072591 0.44284009 0.67145041 1.86508148 0.9806041.17 1.1356102 1.0222419 0.4287158 0.5460896 0.7850649 1.008097 0.43825127 0.6698331 1.86663297 0.9782421.18 1.1432091 1.02484 0.4232249 0.5410846 0.7821788 1.0089699 0.43373781 0.66813498 1.86824914 0.97576211.19 1.150766 1.0275729 0.4177785 0.5361017 0.7792896 1.0098762 0.42929788 0.66635801 1.86992737 0.9731669

Tabla A.1

k = 1.4

1.20 1.158281 1.0304398 0.412377 0.5311416 0.7763975 1.0108147 0.4249297 0.66450412 1.8716651 0.97045951.21 1.1657541 1.0334395 0.407021 0.5262048 0.7735029 1.011784 0.42063157 0.66257524 1.87345988 0.96764251.22 1.1731854 1.0365715 0.4017107 0.5212919 0.770606 1.0127828 0.41640183 0.6605733 1.87530934 0.96471881.23 1.1805749 1.0398348 0.3964465 0.5164033 0.7677072 1.0138099 0.41223888 0.6585002 1.8772112 0.96169121.24 1.1879226 1.0432289 0.3912288 0.5115395 0.7648067 1.0148641 0.40814117 0.65635785 1.87916324 0.9585624

1.25 1.1952286 1.0467529 0.3860579 0.506701 0.7619048 1.0159443 0.4041072 0.65414812 1.88116334 0.95533531.26 1.202493 1.0504064 0.380934 0.5018882 0.7590018 1.0170493 0.40013552 0.65187288 1.88320944 0.95201251.27 1.2097158 1.0541888 0.3758575 0.4971016 0.7560979 1.0181781 0.39622472 0.64953399 1.88529955 0.94859671.28 1.2168972 1.0580996 0.3708285 0.4923415 0.7531935 1.0193296 0.39237343 0.6471333 1.88743175 0.94509071.29 1.2240371 1.0621383 0.3658472 0.4876085 0.7502889 1.0205029 0.38858032 0.64467262 1.8896042 0.941497

1.30 1.2311357 1.0663045 0.3609139 0.4829028 0.7473842 1.0216969 0.38484412 0.64215376 1.89181509 0.93781841.31 1.238193 1.070598 0.3560287 0.4782248 0.7444797 1.0229108 0.38116357 0.63957851 1.8940627 0.93405741.32 1.2452091 1.0750183 0.3511917 0.473575 0.7415757 1.0241435 0.37753748 0.63694865 1.89634536 0.93021671.33 1.2521842 1.0795653 0.346403 0.4689535 0.7386725 1.0253944 0.37396467 0.63426592 1.89866144 0.92629881.34 1.2591183 1.0842386 0.3416628 0.4643607 0.7357702 1.0266624 0.370444 0.63153207 1.9010094 0.9223062

1.35 1.2660114 1.0890382 0.3369711 0.459797 0.7328692 1.0279469 0.36697436 0.6287488 1.90338772 0.91824141.36 1.2728638 1.0939639 0.3323279 0.4552626 0.7299696 1.0292469 0.36355469 0.62591781 1.90579494 0.9141071.37 1.2796754 1.0990155 0.3277333 0.4507578 0.7270718 1.0305618 0.36018394 0.62304078 1.90822965 0.90990531.38 1.2864465 1.104193 0.3231872 0.4462828 0.7241759 1.0318908 0.3568611 0.62011935 1.91069048 0.90563881.39 1.2931771 1.1094964 0.3186898 0.4418379 0.7212822 1.0332332 0.35358518 0.61715517 1.91317613 0.9013098

1.40 1.2998674 1.1149257 0.3142409 0.4374233 0.7183908 1.0345883 0.35035523 0.61414985 1.91568531 0.89692071.41 1.3065174 1.1204809 0.3098405 0.4330392 0.7155021 1.0359555 0.34717032 0.61110496 1.91821679 0.89247391.42 1.3131272 1.1261621 0.3054885 0.4286859 0.7126162 1.037334 0.34402955 0.60802209 1.92076938 0.88797161.43 1.3196971 1.1319695 0.3011848 0.4243634 0.7097333 1.0387234 0.34093203 0.60490277 1.92334193 0.88341611.44 1.326227 1.137903 0.2969294 0.420072 0.7068537 1.0401229 0.33787692 0.60174852 1.92593331 0.8788095

1.45 1.3327172 1.143963 0.2927222 0.4158119 0.7039775 1.041532 0.33486337 0.59856085 1.92854246 0.87415421.46 1.3391678 1.1501496 0.288563 0.4115831 0.7011049 1.0429501 0.33189058 0.59534123 1.93116833 0.86945211.47 1.3455789 1.156463 0.2844516 0.4073859 0.6982363 1.0443767 0.32895775 0.59209111 1.93380992 0.86470561.48 1.3519506 1.1629035 0.2803879 0.4032203 0.6953716 1.0458113 0.32606413 0.58881192 1.93646623 0.85991661.49 1.3582831 1.1694714 0.2763718 0.3990864 0.6925112 1.0472533 0.32320896 0.58550507 1.93913634 0.8550872

1.50 1.3645765 1.1761671 0.2724031 0.3949844 0.6896552 1.0487023 0.32039151 0.58217194 1.94181932 0.85021941.51 1.3708309 1.1829907 0.2684815 0.3909144 0.6868038 1.0501577 0.31761108 0.57881389 1.94451431 0.84531521.52 1.3770466 1.1899428 0.2646068 0.3868763 0.6839571 1.0516192 0.31486697 0.57543225 1.94722043 0.8403765

A P wf If

1.53 1.3832236 1.1970237 0.2607789 0.3828704 0.6811154 1.0530863 0.31215851 0.57202833 1.94993686 0.83540541.54 1.3893622 1.2042338 0.2569975 0.3788965 0.6782788 1.0545584 0.30948504 0.56860342 1.95266282 0.8304035

1.55 1.3954623 1.2115736 0.2532623 0.3749548 0.6754475 1.0560354 0.30684592 0.56515878 1.95539751 0.82537291.56 1.4015243 1.2190435 0.2495731 0.3710454 0.6726216 1.0575166 0.30424053 0.56169566 1.9581402 0.82031521.57 1.4075482 1.2266441 0.2459297 0.3671682 0.6698013 1.0590017 0.30166826 0.55821525 1.96089017 0.81523241.58 1.4135343 1.2343759 0.2423318 0.3633232 0.6669868 1.0604904 0.29912851 0.55471877 1.9636467 0.8101261.59 1.4194826 1.2422393 0.238779 0.3595105 0.6641782 1.0619823 0.2966207 0.55120737 1.96640914 0.8049979

Tabla A.1

k = 1.4

1.6 1.4253933 1.250235 0.2352712 0.35573 0.6613757 1.063477 0.29414426 0.5476822 1.96917681 0.79984961.61 1.4312666 1.2583636 0.2318079 0.3519818 0.6585793 1.0649742 0.29169866 0.54414438 1.9719491 0.79468291.62 1.4371027 1.2666256 0.228389 0.3482658 0.6557893 1.0664736 0.28928333 0.540595 1.97472538 0.78949931.63 1.4429017 1.2750217 0.225014 0.344582 0.6530058 1.0679748 0.28689777 0.53703515 1.97750507 0.78430041.64 1.4486638 1.2835525 0.2216827 0.3409303 0.6502289 1.0694775 0.28454145 0.53346586 1.9802876 0.7790877

1.65 1.4543891 1.2922188 0.2183948 0.3373108 0.6474587 1.0709815 0.28221387 0.52988817 1.98307241 0.77386281.66 1.4600778 1.3010212 0.2151499 0.3337233 0.6446954 1.0724864 0.27991455 0.52630308 1.98585897 0.7686271.67 1.4657302 1.3099604 0.2119476 0.3301678 0.6419392 1.073992 0.277643 0.52271158 1.98864676 0.76338191.68 1.4713463 1.3190371 0.2087877 0.3266442 0.63919 1.075498 0.27539875 0.51911461 1.99143528 0.75812881.69 1.4769263 1.3282522 0.2056698 0.3231525 0.6364481 1.0770041 0.27318136 0.51551312 1.99422405 0.7528691

1.7 1.4824704 1.3376064 0.2025935 0.3196925 0.6337136 1.0785101 0.27099036 0.51190803 1.99701261 0.74760411.71 1.4879789 1.3471004 0.1995585 0.3162643 0.6309865 1.0800157 0.26882533 0.50830022 1.9998005 0.74233511.72 1.4934517 1.3567352 0.1965644 0.3128676 0.628267 1.0815207 0.26668583 0.50469057 2.0025873 0.73706351.73 1.4988892 1.3665115 0.1936108 0.3095024 0.6255552 1.083025 0.26457145 0.50107992 2.00537257 0.73179041.74 1.5042915 1.3764301 0.1906975 0.3061686 0.6228512 1.0845281 0.26248177 0.4974691 2.00815591 0.7265171

1.75 1.5096588 1.386492 0.1878239 0.3028661 0.620155 1.0860301 0.26041641 0.49385891 2.01093694 0.72124471.76 1.5149913 1.3966981 0.1849898 0.2995948 0.6174669 1.0875305 0.25837497 0.49025015 2.01371527 0.71597431.77 1.5202891 1.4070492 0.1821948 0.2963544 0.6147869 1.0890294 0.25635706 0.48664358 2.01649054 0.71070721.78 1.5255524 1.4175462 0.1794385 0.293145 0.612115 1.0905263 0.25436231 0.48303994 2.01926239 0.70544441.79 1.5307814 1.4281902 0.1767204 0.2899664 0.6094514 1.0920213 0.25239036 0.47943996 2.02203049 0.7001868

1.8 1.5359763 1.4389821 0.1740403 0.2868184 0.6067961 1.093514 0.25044084 0.47584433 2.02479451 0.69493571.81 1.5411373 1.4499227 0.1713977 0.2837009 0.6041493 1.0950044 0.24851341 0.47225375 2.02755413 0.68969191.82 1.5462645 1.4610133 0.1687922 0.2806137 0.601511 1.0964922 0.24660772 0.46866888 2.03030904 0.68445651.83 1.5513582 1.4722547 0.1662236 0.2775568 0.5988813 1.0979773 0.24472343 0.46509037 2.03305896 0.67923031.84 1.5564185 1.4836479 0.1636913 0.2745299 0.5962603 1.0994596 0.24286021 0.46151883 2.03580359 0.6740144

1.85 1.5614455 1.4951941 0.161195 0.2715329 0.593648 1.1009389 0.24101775 0.45795489 2.03854267 0.66880951.86 1.5664396 1.5068943 0.1587342 0.2685656 0.5910445 1.102415 0.23919572 0.45439913 2.04127593 0.66361661.87 1.5714008 1.5187496 0.1563087 0.2656279 0.5884499 1.1038879 0.23739382 0.45085212 2.04400312 0.65843641.88 1.5763294 1.530761 0.153918 0.2627196 0.5858643 1.1053573 0.23561174 0.44731442 2.04672399 0.65326991.89 1.5812255 1.5429297 0.1515618 0.2598406 0.5832876 1.1068232 0.23384918 0.44378656 2.04943831 0.6481177

1.9 1.5860894 1.5552568 0.1492396 0.2569905 0.5807201 1.1082854 0.23210585 0.44026907 2.05214585 0.6429806

A P wf If

1.91 1.5909211 1.5677434 0.146951 0.2541694 0.5781617 1.1097439 0.23038147 0.43676245 2.0548464 0.63785951.92 1.5957209 1.5803908 0.1446957 0.2513769 0.5756125 1.1111985 0.22867576 0.43326717 2.05753974 0.63275491.93 1.600489 1.5932001 0.1424733 0.248613 0.5730725 1.112649 0.22698843 0.42978373 2.06022568 0.62766761.94 1.6052256 1.6061724 0.1402833 0.2458774 0.5705418 1.1140955 0.22531923 0.42631255 2.06290402 0.6225982

1.95 1.6099308 1.619309 0.1381255 0.24317 0.5680204 1.1155378 0.22366789 0.4228541 2.06557457 0.61754731.96 1.6146049 1.6326112 0.1359994 0.2404905 0.5655085 1.1169757 0.22203414 0.41940877 2.06823717 0.61251571.97 1.619248 1.6460801 0.1339046 0.2378387 0.563006 1.1184093 0.22041774 0.415977 2.07089163 0.60750391.98 1.6238602 1.659717 0.1318408 0.2352146 0.560513 1.1198384 0.21881844 0.41255916 2.07353779 0.60251241.98 1.624779 1.6624647 0.1314317 0.234693 0.5600155 1.1201237 0.2185006 0.4118773 2.07406601 0.6015165

Tabla A.1

k = 1.4

2.00 1.6329932 1.6875 0.1278045 0.2300481 0.5555556 1.1226828 0.21567014 0.40576679 2.0788046 0.59259262.01 1.6375142 1.7016487 0.1258313 0.2275055 0.5530912 1.124098 0.21412067 0.40239297 2.08142496 0.58766542.02 1.6420051 1.7159705 0.1238875 0.2249897 0.5506365 1.1255083 0.21258734 0.39903451 2.08403643 0.58276062.03 1.6464662 1.7304669 0.1219728 0.2225004 0.5481915 1.1269138 0.21106994 0.39569174 2.08663888 0.57787872.04 1.6508976 1.7451391 0.1200868 0.2200375 0.5457562 1.1283143 0.20956822 0.39236496 2.08923218 0.5730202

2.05 1.6552995 1.7599886 0.1182292 0.2176008 0.5433306 1.1297099 0.20808199 0.38905447 2.09181622 0.56818552.06 1.659672 1.7750168 0.1163995 0.21519 0.5409148 1.1311004 0.20661102 0.38576056 2.09439089 0.5633752.07 1.6640155 1.7902249 0.1145974 0.2128051 0.5385088 1.1324857 0.20515509 0.38248348 2.09695606 0.5585892.08 1.6683299 1.8056145 0.1128225 0.2104456 0.5361125 1.1338659 0.20371402 0.37922351 2.09951164 0.55382812.09 1.6726156 1.8211869 0.1110746 0.2081116 0.5337262 1.1352408 0.20228758 0.37598088 2.10205752 0.5490925

2.10 1.6768728 1.8369436 0.1093532 0.2058026 0.5313496 1.1366105 0.20087559 0.37275584 2.10459362 0.54438252.11 1.6811015 1.8528861 0.1076579 0.2035187 0.528983 1.1379748 0.19947784 0.3695486 2.10711985 0.53969862.12 1.685302 1.8690158 0.1059885 0.2012594 0.5266262 1.1393337 0.19809415 0.36635938 2.10963611 0.5350412.13 1.6894744 1.8853341 0.1043445 0.1990247 0.5242794 1.1406872 0.19672432 0.36318838 2.11214233 0.530412.14 1.693619 1.9018427 0.1027257 0.1968143 0.5219425 1.1420353 0.19536817 0.36003579 2.11463843 0.5258058

2.15 1.6977359 1.918543 0.1011317 0.194628 0.5196155 1.1433778 0.19402551 0.35690179 2.11712434 0.52122892.16 1.7018253 1.9354366 0.0995621 0.1924655 0.5172985 1.1447148 0.19269618 0.35378656 2.11959999 0.51667932.17 1.7058873 1.952525 0.0980167 0.1903268 0.5149914 1.1460463 0.19137998 0.35069024 2.12206533 0.51215732.18 1.7099223 1.9698097 0.096495 0.1882115 0.5126943 1.1473721 0.19007676 0.347613 2.12452027 0.50766332.19 1.7139302 1.9872924 0.0949968 0.1861195 0.5104072 1.1486923 0.18878633 0.34455497 2.12696479 0.5031972

2.20 1.7179114 2.0049745 0.0935217 0.1840506 0.5081301 1.1500068 0.18750853 0.34151628 2.12939881 0.49875942.21 1.7218659 2.0228579 0.0920693 0.1820045 0.505863 1.1513156 0.1862432 0.33849707 2.13182229 0.49435012.22 1.725794 2.0409439 0.0906395 0.1799811 0.5036058 1.1526187 0.18499017 0.33549744 2.13423518 0.48996942.23 1.7296959 2.0592344 0.0892318 0.1779801 0.5013587 1.1539161 0.18374929 0.3325175 2.13663744 0.48561742.24 1.7335717 2.0777309 0.087846 0.1760013 0.4991215 1.1552077 0.1825204 0.32955734 2.13902904 0.4812943

2.25 1.7374215 2.096435 0.0864817 0.1740445 0.4968944 1.1564935 0.18130334 0.32661706 2.14140993 0.47700022.26 1.7412456 2.1153486 0.0851387 0.1721095 0.4946773 1.1577736 0.18009796 0.32369674 2.14378009 0.47273532.27 1.7450442 2.1344733 0.0838165 0.1701962 0.4924701 1.1590478 0.17890412 0.32079646 2.14613948 0.46849972.28 1.7488173 2.1538107 0.082515 0.1683042 0.490273 1.1603162 0.17772167 0.31791627 2.14848807 0.46429342.29 1.7525653 2.1733626 0.0812338 0.1664334 0.4880858 1.1615787 0.17655047 0.31505624 2.15082585 0.4601165

A P wf If

2.30 1.7562882 2.1931308 0.0799726 0.1645836 0.4859086 1.1628354 0.17539037 0.31221642 2.15315278 0.45596922.31 1.7599862 2.213117 0.0787311 0.1627546 0.4837414 1.1640862 0.17424123 0.30939686 2.15546885 0.45185142.32 1.7636595 2.233323 0.0775091 0.1609462 0.4815842 1.1653312 0.17310292 0.3065976 2.15777404 0.44776332.33 1.7673082 2.2537505 0.0763063 0.1591581 0.4794369 1.1665702 0.17197531 0.30381866 2.16006834 0.44370482.34 1.7709326 2.2744014 0.0751223 0.1573902 0.4772996 1.1678034 0.17085825 0.30106008 2.16235174 0.4396761

2.35 1.7745328 2.2952774 0.0739569 0.1556423 0.4751722 1.1690307 0.16975162 0.29832187 2.16462422 0.43567722.36 1.7781089 2.3163805 0.0728098 0.1539142 0.4730548 1.1702521 0.1686553 0.29560405 2.16688578 0.4317082.37 1.7816611 2.3377124 0.0716808 0.1522056 0.4709473 1.1714675 0.16756915 0.29290663 2.16913641 0.42776862.38 1.7851897 2.359275 0.0705696 0.1505164 0.4688496 1.1726771 0.16649304 0.2902296 2.1713761 0.4238592.39 1.7886947 2.3810702 0.0694758 0.1488464 0.4667619 1.1738808 0.16542687 0.28757298 2.17360487 0.4199792

Tabla A.1

k = 1.4

2.4 1.7921763 2.4030999 0.0683994 0.1471954 0.464684 1.1750786 0.1643705 0.28493674 2.1758227 0.41612922.41 1.7956347 2.4253659 0.0673399 0.1455632 0.462616 1.1762704 0.16332383 0.28232089 2.1780296 0.41230892.42 1.79907 2.4478702 0.0662971 0.1439496 0.4605578 1.1774564 0.16228672 0.27972539 2.18022558 0.40851842.43 1.8024825 2.4706148 0.0652708 0.1423544 0.4585095 1.1786365 0.16125907 0.27715023 2.18241063 0.40475762.44 1.8058722 2.4936015 0.0642608 0.1407774 0.4564709 1.1798106 0.16024076 0.27459538 2.18458477 0.4010264

2.45 1.8092393 2.5168324 0.0632667 0.1392184 0.4544422 1.1809789 0.15923169 0.27206081 2.18674801 0.39732482.46 1.812584 2.5403094 0.0622884 0.1376772 0.4524232 1.1821413 0.15823173 0.26954648 2.18890035 0.39365282.47 1.8159065 2.5640345 0.0613255 0.1361537 0.4504139 1.1832978 0.15724079 0.26705236 2.19104182 0.39001042.48 1.8192068 2.5880098 0.060378 0.1346477 0.4484144 1.1844485 0.15625875 0.26457839 2.19317241 0.38639732.49 1.8224853 2.6122372 0.0594454 0.1331589 0.4464246 1.1855933 0.15528552 0.26212454 2.19529216 0.3828136

2.5 1.8257419 2.6367188 0.0585277 0.1316872 0.4444444 1.1867322 0.15432099 0.25969074 2.19740106 0.37925932.51 1.8289768 2.6614566 0.0576245 0.1302325 0.442474 1.1878653 0.15336505 0.25727696 2.19949915 0.37573412.52 1.8321903 2.6864528 0.0567356 0.1287944 0.4405131 1.1889926 0.15241761 0.25488312 2.20158644 0.37223812.53 1.8353825 2.7117093 0.0558609 0.1273729 0.4385619 1.190114 0.15147856 0.25250916 2.20366295 0.36877112.54 1.8385534 2.7372284 0.0550001 0.1259678 0.4366202 1.1912297 0.15054782 0.25015503 2.20572871 0.365333

2.55 1.8417034 2.7630121 0.054153 0.1245789 0.4346881 1.1923395 0.14962528 0.24782065 2.20778373 0.36192392.56 1.8448324 2.7890626 0.0533193 0.123206 0.4327655 1.1934435 0.14871084 0.24550595 2.20982804 0.35854342.57 1.8479408 2.815382 0.0524989 0.1218489 0.4308525 1.1945418 0.14780443 0.24321085 2.21186167 0.35519162.58 1.8510285 2.8419725 0.0516915 0.1205075 0.4289489 1.1956344 0.14690593 0.24093529 2.21388464 0.35186832.59 1.8540958 2.8688362 0.050897 0.1191815 0.4270548 1.1967211 0.14601527 0.23867917 2.21589697 0.3485734

2.6 1.8571429 2.8959754 0.0501152 0.1178709 0.4251701 1.1978022 0.14513236 0.23644243 2.2178987 0.34530682.61 1.8601697 2.9233922 0.0493458 0.1165755 0.4232948 1.1988775 0.1442571 0.23422497 2.21988986 0.34206842.62 1.8631766 2.9510889 0.0485886 0.115295 0.4214288 1.1999472 0.14338941 0.23202671 2.22187046 0.3388582.63 1.8661637 2.9790678 0.0478436 0.1140294 0.4195722 1.2010112 0.14252921 0.22984756 2.22384056 0.33567552.64 1.869131 3.007331 0.0471103 0.1127784 0.4177249 1.2020695 0.1416764 0.22768742 2.22580017 0.3325208

2.65 1.8720787 3.0358809 0.0463888 0.1115419 0.4158869 1.2031221 0.14083091 0.22554622 2.22774933 0.32939372.66 1.875007 3.0647198 0.0456788 0.1103197 0.4140581 1.2041692 0.13999266 0.22342384 2.22968807 0.32629412.67 1.8779161 3.0938499 0.0449801 0.1091117 0.4122385 1.2052106 0.13916156 0.2213202 2.23161643 0.3232219

A P wf If

2.68 1.880806 3.1232735 0.0442925 0.1079177 0.4104282 1.2062465 0.13833754 0.21923519 2.23353443 0.32017692.69 1.8836768 3.1529931 0.0436159 0.1067376 0.4086269 1.2072767 0.13752051 0.21716871 2.23544212 0.317159

2.7 1.8865288 3.183011 0.04295 0.1055712 0.4068348 1.2083014 0.1367104 0.21512067 2.23733953 0.31416792.71 1.8893621 3.2133294 0.0422948 0.1044183 0.4050518 1.2093206 0.13590714 0.21309096 2.2392267 0.31120372.72 1.8921768 3.2439509 0.04165 0.1032787 0.4032778 1.2103343 0.13511064 0.21107947 2.24110367 0.30826612.73 1.894973 3.2748778 0.0410155 0.1021524 0.4015129 1.2113425 0.13432083 0.20908611 2.24297046 0.30535492.74 1.8977509 3.3061126 0.0403911 0.1010392 0.3997569 1.2123452 0.13353764 0.20711075 2.24482712 0.30247

2.75 1.9005105 3.3376576 0.0397767 0.099939 0.39801 1.2133425 0.13276101 0.2051533 2.24667369 0.29961132.76 1.9032522 3.3695153 0.0391721 0.0988515 0.3962719 1.2143343 0.13199084 0.20321364 2.24851021 0.29677862.77 1.9059758 3.4016882 0.038577 0.0977766 0.3945427 1.2153207 0.13122709 0.20129166 2.25033672 0.29397172.78 1.9086817 3.4341788 0.0379915 0.0967143 0.3928224 1.2163018 0.13046967 0.19938725 2.25215325 0.29119042.79 1.9113699 3.4669895 0.0374153 0.0956642 0.3911108 1.2172774 0.12971852 0.1975003 2.25395985 0.2884347

Tabla A.1

k = 1.4

2.8 1.9140406 3.5001229 0.0368483 0.0946264 0.3894081 1.2182478 0.12897357 0.19563069 2.25575656 0.28570432.81 1.9166938 3.5335814 0.0362903 0.0936007 0.3877141 1.2192128 0.12823476 0.19377831 2.25754341 0.2829992.82 1.9193298 3.5673678 0.0357412 0.0925869 0.3860288 1.2201725 0.12750201 0.19194305 2.25932046 0.28031872.83 1.9219486 3.6014844 0.0352008 0.0915848 0.3843523 1.2211269 0.12677527 0.19012479 2.26108774 0.27766332.84 1.9245504 3.6359339 0.0346691 0.0905945 0.3826843 1.2220761 0.12605447 0.1883234 2.2628453 0.2750325

2.85 1.9271352 3.6707189 0.0341458 0.0896156 0.381025 1.2230201 0.12533954 0.18653879 2.26459317 0.27242622.86 1.9297033 3.705842 0.0336308 0.0886481 0.3793742 1.2239588 0.12463044 0.18477082 2.2663314 0.26984422.87 1.9322547 3.7413059 0.033124 0.0876919 0.3777319 1.2248924 0.12392708 0.18301937 2.26806004 0.26728642.88 1.9347896 3.7771131 0.0326253 0.0867467 0.3760982 1.2258208 0.12322942 0.18128434 2.26977912 0.26475252.89 1.937308 3.8132663 0.0321345 0.0858126 0.3744729 1.2267441 0.12253739 0.1795656 2.2714887 0.2622424

2.9 1.9398102 3.8497682 0.0316515 0.0848893 0.3728561 1.2276623 0.12185094 0.17786303 2.27318881 0.25975592.91 1.9422961 3.8866216 0.0311762 0.0839768 0.3712476 1.2285753 0.12117 0.17617652 2.2748795 0.25729292.92 1.944766 3.923829 0.0307084 0.0830748 0.3696475 1.2294834 0.12049452 0.17450594 2.27656081 0.25485312.93 1.94722 3.9613933 0.0302481 0.0821834 0.3680557 1.2303863 0.11982444 0.17285117 2.27823279 0.25243642.94 1.9496581 3.9993172 0.029795 0.0813023 0.3664722 1.2312843 0.11915971 0.17121209 2.27989548 0.2500427

2.95 1.9520806 4.0376035 0.0293492 0.0804314 0.3648969 1.2321772 0.11850027 0.16958858 2.28154893 0.24767172.96 1.9544874 4.0762549 0.0289104 0.0795706 0.3633298 1.2330652 0.11784607 0.16798053 2.28319318 0.24532322.97 1.9568787 4.1152742 0.0284786 0.0787198 0.3617709 1.2339483 0.11719704 0.16638781 2.28482827 0.24299722.98 1.9592547 4.1546642 0.0280536 0.0778789 0.3602202 1.2348264 0.11655315 0.1648103 2.28645426 0.24069332.99 1.9616154 4.1944278 0.0276353 0.0770478 0.3586775 1.2356997 0.11591433 0.16324788 2.28807119 0.2384115

3.00 1.963961 4.2345679 0.0272237 0.0762263 0.3571429 1.236568 0.11528054 0.16170043 2.2896791 0.23615163.10 1.9866081 4.6573106 0.0234487 0.0685172 0.3422313 1.2449893 0.109208 0.14702293 2.30527231 0.21471623.20 2.0078586 5.1209575 0.0202278 0.0616542 0.328084 1.2529508 0.10358546 0.13371161 2.32001409 0.1952763.30 2.0278117 5.6286468 0.0174768 0.0555412 0.3146633 1.2604771 0.09837061 0.12165117 2.33394998 0.17766263.40 2.0465595 6.1836988 0.0151246 0.0500927 0.3019324 1.2675922 0.09352596 0.1107317 2.34712471 0.1617155

3.50 2.0641874 6.7896205 0.0131109 0.0452327 0.2898551 1.2743198 0.08901817 0.10084974 2.3595817 0.1472836

A P wf If

3.60 2.0807742 7.450111 0.0113847 0.040894 0.2783964 1.2806823 0.08481753 0.09190889 2.3713628 0.13422623.70 2.096393 8.1690665 0.0099029 0.037017 0.2675227 1.2867014 0.08089746 0.08382004 2.38250803 0.1224133.80 2.1111111 8.9505853 0.008629 0.0335494 0.2572016 1.2923977 0.07723418 0.07650131 2.39305546 0.11172453.90 2.1249909 9.7989735 0.007532 0.0304445 0.2474023 1.2977906 0.07380631 0.06987788 2.4030412 0.1020515

4.00 2.1380899 10.71875 0.0065861 0.0276616 0.2380952 1.3028986 0.07059462 0.06388165 2.41249934 0.09329454.10 2.1504614 11.714652 0.005769 0.0251644 0.2292526 1.3077389 0.06758177 0.05845086 2.42146199 0.08536324.20 2.1621544 12.79164 0.0050621 0.022921 0.2208481 1.312328 0.06475209 0.05352961 2.42995934 0.07817614.30 2.1732144 13.954904 0.0044494 0.0209034 0.2128565 1.3166811 0.06209138 0.04906744 2.43801972 0.07165944.40 2.1836833 15.209867 0.0039176 0.0190867 0.2052545 1.3208126 0.05958678 0.0450189 2.4456697 0.0657468

4.50 2.1936001 16.562195 0.0034553 0.017449 0.1980198 1.3247358 0.05722662 0.04134304 2.45293412 0.06037854.60 2.2030005 18.017795 0.0030526 0.0159709 0.1911315 1.3284634 0.05500024 0.03800307 2.45983626 0.05550074.70 2.2119178 19.582828 0.0027012 0.0146353 0.18457 1.3320071 0.05289796 0.03496591 2.46639785 0.05106514.80 2.2203828 21.26371 0.0023943 0.013427 0.1783167 1.3353778 0.05091093 0.03220188 2.47263922 0.0470285

Tabla A.1

k = 1.4

4.9 2.2284241 23.067119 0.0021256 0.0123326 0.1723544 1.3385858 0.04903106 0.02968431 2.47857936 0.04335185 2.236068 25 0.00189 0.0113402 0.1666667 1.3416408 0.04725096 0.02738926 2.48423601 0.046 2.2952762 53.179784 0.0006334 0.0051936 0.1219512 1.3654768 0.03368202 0.01287578 2.52837172 0.01880417 2.3333333 104.14286 0.0002416 0.0026088 0.0925926 1.3809524 0.02515628 0.00657492 2.55702694 0.00960228 2.3590713 190.10938 0.0001024 0.0014135 0.0724638 1.3914835 0.01947273 0.00360178 2.57652671 0.00526019 2.3772174 327.1893 4.739E-05 0.000815 0.0581395 1.3989387 0.01550421 0.00209277 2.59033106 0.0030563

10 2.3904572 535.9375 2.356E-05 0.0004948 0.047619 1.4043936 0.01262835 0.00127763 2.60043168 0.0018659

0 0 0 0 1.4289 0 0 2.6458 0

k = 1.4

0.79 0.815974 1.042505 0.662536 0.745234 0.889031 1.020752 0.690697 0.656813 1.890065 0.959228

A P wf If

Tabla A.1

[ b ] k = 1

A Pwf If

Tabla A.1

[ b ] k = 1

A Pwf If

Tabla A.1

[ c ] k = 1.1

A Pwf If

Tabla A.1

[ c ] k = 1.1

A Pwf If

Tabla A.1

[ d ] k = 1.2

A Pwf If

Tabla A.1

[ d ] k = 1.2

A Pwf If

Tabla A.1

[ e ] k = 1.3

A Pwf If

Tabla A.1

[ e ] k = 1.3

A Pwf If

Tabla A.1

[ f ] k = 1.67

A Pwf If

Tabla A.1

[ f ] k = 1.67

A Pwf If

724.4992

Tabla 2

Choque normal unidimen sional de un gas perdecto( Calor específico y peso molecular constantes )

k = 1.4

1.00 1.00000 1.00000 1.00000 1.00000 1.0000000 1.89292921.01 0.99013 1.02345 1.01669 1.00664 0.9999987 1.91521441.02 0.98052 1.04713 1.03344 1.01325 0.9999900 1.93789661.03 0.97115 1.07105 1.05024 1.01981 0.9999670 1.96096831.04 0.96203 1.09520 1.06709 1.02634 0.9999233 1.9844225

1.05 0.95313 1.11958 1.08398 1.03284 0.9998530 2.00825291.06 0.94445 1.14420 1.10092 1.03931 0.9997507 2.03245321.07 0.93598 1.16905 1.11790 1.04575 0.9996115 2.05701801.08 0.92771 1.19413 1.13492 1.05217 0.9994307 2.08194191.09 0.91965 1.21945 1.15199 1.05856 0.9992042 2.1072199

1.10 0.91177 1.24500 1.16908 1.06494 0.9989280 2.13284741.11 0.90408 1.27078 1.18621 1.07129 0.9985987 2.15882001.12 0.89656 1.29680 1.20338 1.07763 0.9982131 2.18513371.13 0.88922 1.32305 1.22057 1.08396 0.9977681 2.21178461.14 0.88204 1.34953 1.23779 1.09027 0.9972611 2.2387690

1.15 0.87502 1.37625 1.25504 1.09658 0.9966898 2.26608351.16 0.86816 1.40320 1.27231 1.10287 0.9960518 2.29372501.17 0.86145 1.43038 1.28961 1.10916 0.9953454 2.32169031.18 0.85488 1.45780 1.30693 1.11544 0.9945686 2.34997671.19 0.84846 1.48545 1.32426 1.12172 0.9937201 2.3785813

1.20 0.84217 1.51333 1.34161 1.12799 0.9927984 2.40750161.21 0.83601 1.54145 1.35898 1.13427 0.9918023 2.43673531.22 0.82999 1.56980 1.37636 1.14054 0.9907309 2.46627991.23 0.82408 1.59838 1.39376 1.14682 0.9895833 2.49613341.24 0.81830 1.62720 1.41116 1.15309 0.9883588 2.5262936

1.25 0.81264 1.65625 1.42857 1.15938 0.9870568 2.55675861.26 0.80709 1.68553 1.44599 1.16566 0.9856768 2.58752651.27 0.80164 1.71505 1.46341 1.17195 0.9842187 2.61859571.28 0.79631 1.74480 1.48084 1.17825 0.9826822 2.64996431.29 0.79108 1.77478 1.49827 1.18456 0.9810671 2.6816308

1.30 0.78596 1.80500 1.51570 1.19087 0.9793736 2.71359361.31 0.78093 1.83545 1.53312 1.19720 0.9776018 2.74585141.32 0.77600 1.86613 1.55055 1.20353 0.9757519 2.77840281.33 0.77116 1.89705 1.56797 1.20988 0.9738242 2.81124631.34 0.76641 1.92820 1.58538 1.21624 0.9718191 2.8443809

1.35 0.76175 1.95958 1.60278 1.22261 0.9697371 2.87780521.36 0.75718 1.99120 1.62018 1.22900 0.9675787 2.91151821.37 0.75269 2.02305 1.63757 1.23540 0.9653445 2.94551871.38 0.74829 2.05513 1.65494 1.24181 0.9630352 2.9798058

1.39 0.74396 2.08745 1.67231 1.24825 0.9606516 3.0143783

Tabla 2

k = 1.4

1.40 0.73971 2.12000 1.68966 1.25469 0.9581944 3.04923541.41 0.73554 2.15278 1.70699 1.26116 0.9556645 3.08437621.42 0.73144 2.18580 1.72430 1.26764 0.9530629 3.11979971.43 0.72741 2.21905 1.74160 1.27414 0.9503903 3.15550521.44 0.72345 2.25253 1.75888 1.28066 0.9476479 3.1914918

1.45 0.71956 2.28625 1.77614 1.28720 0.9448367 3.22775891.46 0.71574 2.32020 1.79337 1.29377 0.9419577 3.26430551.47 0.71198 2.35438 1.81058 1.30035 0.9390120 3.30113111.48 0.70829 2.38880 1.82777 1.30695 0.9360008 3.33823491.49 0.70466 2.42345 1.84493 1.31357 0.9329253 3.3756163

1.50 0.70109 2.45833 1.86207 1.32022 0.9297865 3.41327481.51 0.69758 2.49345 1.87918 1.32688 0.9265858 3.45120961.52 0.69413 2.52880 1.89626 1.33357 0.9233244 3.48942021.53 0.69073 2.56438 1.91331 1.34029 0.9200034 3.52790611.54 0.68739 2.60020 1.93033 1.34703 0.9166243 3.5666667

1.55 0.68410 2.63625 1.94732 1.35379 0.9131883 3.60570151.56 0.68087 2.67253 1.96427 1.36057 0.9096966 3.64501001.57 0.67768 2.70905 1.98119 1.36738 0.9061507 3.68459181.58 0.67455 2.74580 1.99808 1.37422 0.9025517 3.72444631.59 0.67147 2.78278 2.01493 1.38108 0.8989011 3.7645732

1.60 0.66844 2.82000 2.03175 1.38797 0.8952003 3.80497201.61 0.66545 2.85745 2.04852 1.39488 0.8914504 3.84564241.62 0.66251 2.89513 2.06526 1.40182 0.8876529 3.88658381.63 0.65962 2.93305 2.08197 1.40879 0.8838092 3.92779601.64 0.65677 2.97120 2.09863 1.41578 0.8799206 3.9692786

1.65 0.65396 3.00958 2.11525 1.42280 0.8759884 4.01103121.66 0.65119 3.04820 2.13183 1.42985 0.8720140 4.05305341.67 0.64847 3.08705 2.14836 1.43693 0.8679987 4.09534511.68 0.64579 3.12613 2.16486 1.44403 0.8639439 4.13790571.69 0.64315 3.16545 2.18131 1.45117 0.8598509 4.1807351

1.70 0.64054 3.20500 2.19772 1.45833 0.8557211 4.22383291.71 0.63798 3.24478 2.21408 1.46552 0.8515557 4.26719881.72 0.63545 3.28480 2.23040 1.47274 0.8473562 4.31083261.73 0.63296 3.32505 2.24667 1.47999 0.8431237 4.35473401.74 0.63051 3.36553 2.26289 1.48727 0.8388597 4.3989027

1.75 0.62809 3.40625 2.27907 1.49458 0.8345654 4.44333851.76 0.62570 3.44720 2.29520 1.50192 0.8302421 4.4880412

1.77 0.62335 3.48838 2.31128 1.50929 0.8258910 4.53301041.78 0.62104 3.52980 2.32731 1.51669 0.8215134 4.57824611.79 0.61875 3.57145 2.34329 1.52412 0.8171106 4.6237478

Tabla 2

k = 1.4

1.80 0.61650 3.61333 2.35922 1.53158 0.8126838 4.66951561.81 0.61428 3.65545 2.37510 1.53907 0.8082342 4.71554901.82 0.61209 3.69780 2.39093 1.54659 0.8037630 4.76184801.83 0.60993 3.74038 2.40671 1.55415 0.7992715 4.80841241.84 0.60780 3.78320 2.42244 1.56173 0.7947607 4.8552419

1.85 0.60570 3.82625 2.43811 1.56935 0.7902319 4.90233631.86 0.60363 3.86953 2.45373 1.57700 0.7856862 4.94969561.87 0.60158 3.91305 2.46930 1.58468 0.7811247 4.99731951.88 0.59957 3.95680 2.48481 1.59239 0.7765485 5.04520781.89 0.59758 4.00078 2.50027 1.60014 0.7719588 5.0933604

1.90 0.59562 4.04500 2.51568 1.60792 0.7673566 5.14177721.91 0.59368 4.08945 2.53103 1.61573 0.7627430 5.19045791.92 0.59177 4.13413 2.54633 1.62357 0.7581190 5.23940251.93 0.58988 4.17905 2.56157 1.63144 0.7534857 5.28861081.94 0.58802 4.22420 2.57675 1.63935 0.7488441 5.3380826

1.95 0.58618 4.26958 2.59188 1.64729 0.7441951 5.38781781.96 0.58437 4.31520 2.60695 1.65527 0.7395398 5.43781641.97 0.58258 4.36105 2.62196 1.66328 0.7348790 5.48807811.98 0.58047 4.41638 2.63991 1.67293 0.7292804 5.54873931.99 0.57907 4.45345 2.65182 1.67939 0.7255452 5.5893904

2.00 0.57735 4.50000 2.66667 1.68750 0.7208739 5.64044082.01 0.57565 4.54678 2.68145 1.69564 0.7162008 5.69175392.02 0.57397 4.59380 2.69618 1.70382 0.7115269 5.74332962.03 0.57231 4.64105 2.71085 1.71203 0.7068530 5.79516772.04 0.57068 4.68853 2.72546 1.72027 0.7021799 5.8472682

2.05 0.56906 4.73625 2.74002 1.72855 0.6975084 5.89963092.06 0.56747 4.78420 2.75451 1.73686 0.6928394 5.95225582.07 0.56589 4.83238 2.76895 1.74521 0.6881737 6.00514272.08 0.56433 4.88080 2.78332 1.75359 0.6835119 6.05829162.09 0.56280 4.92945 2.79764 1.76200 0.6788548 6.1117024

2.10 0.56128 4.97833 2.81190 1.77045 0.6742032 6.16537502.11 0.55978 5.02745 2.82610 1.77893 0.6695578 6.21930922.12 0.55829 5.07680 2.84024 1.78745 0.6649193 6.27350502.13 0.55683 5.12638 2.85432 1.79601 0.6602883 6.32796242.14 0.55538 5.17620 2.86835 1.80459 0.6556655 6.3826812

2.15 0.55395 5.22625 2.88231 1.81322 0.6510516 6.43766142.16 0.55254 5.27653 2.89621 1.82188 0.6464472 6.49290282.17 0.55115 5.32705 2.91005 1.83057 0.6418529 6.54840552.18 0.54977 5.37780 2.92383 1.83930 0.6372692 6.60416932.19 0.54840 5.42878 2.93756 1.84806 0.6326969 6.6601942

Tabla 2

k = 1.4

2.20 0.54706 5.48000 2.95122 1.85686 0.6281363 6.71648012.21 0.54572 5.53145 2.96482 1.86569 0.6235882 6.77302692.22 0.54441 5.58313 2.97837 1.87456 0.6190529 6.82983462.23 0.54311 5.63505 2.99185 1.88347 0.6145311 6.88690302.24 0.54182 5.68720 3.00527 1.89241 0.6100232 6.9442322

2.25 0.54055 5.73958 3.01863 1.90138 0.6055297 7.00182212.26 0.53930 5.79220 3.03194 1.91040 0.6010511 7.05967262.27 0.53805 5.84505 3.04518 1.91944 0.5965879 7.11778372.28 0.53683 5.89813 3.05836 1.92853 0.5921404 7.17615522.29 0.53561 5.95145 3.07149 1.93765 0.5877091 7.2347872

2.30 0.53441 6.00500 3.08455 1.94680 0.5832945 7.29367962.31 0.53322 6.05878 3.09755 1.95599 0.5788969 7.35283242.32 0.53205 6.11280 3.11049 1.96522 0.5745167 7.41224542.33 0.53089 6.16705 3.12338 1.97448 0.5701543 7.47191862.34 0.52974 6.22153 3.13620 1.98378 0.5658100 7.5318521

2.35 0.52861 6.27625 3.14897 1.99311 0.5614842 7.59204572.36 0.52749 6.33120 3.16167 2.00249 0.5571773 7.65249932.37 0.52638 6.38638 3.17432 2.01189 0.5528894 7.71321302.38 0.52528 6.44180 3.18690 2.02134 0.5486211 7.77418672.39 0.52419 6.49745 3.19943 2.03082 0.5443725 7.8354204

2.40 0.52312 6.55333 3.21190 2.04033 0.5401439 7.89691402.41 0.52206 6.60945 3.22430 2.04988 0.5359356 7.95866742.42 0.52100 6.66580 3.23665 2.05947 0.5317479 8.02068072.43 0.51996 6.72238 3.24894 2.06910 0.5275811 8.08295372.44 0.51894 6.77920 3.26117 2.07876 0.5234353 8.1454865

2.45 0.51792 6.83625 3.27335 2.08846 0.5193107 8.20827902.46 0.51691 6.89353 3.28546 2.09819 0.5152077 8.27133122.47 0.51592 6.95105 3.29752 2.10797 0.5111264 8.33464302.48 0.51493 7.00880 3.30951 2.11777 0.5070671 8.39821442.49 0.51395 7.06678 3.32145 2.12762 0.5030298 8.4620454

2.50 0.51299 7.12500 3.33333 2.13750 0.4990148 8.52613592.51 0.51203 7.18345 3.34516 2.14742 0.4950223 8.59048592.52 0.51109 7.24213 3.35692 2.15737 0.4910523 8.65509532.53 0.51015 7.30105 3.36863 2.16737 0.4871052 8.7199642

2.54 0.50923 7.36020 3.38028 2.17739 0.4831809 8.7850925

2.55 0.50831 7.41958 3.39187 2.18746 0.4792797 8.85048012.56 0.50741 7.47920 3.40341 2.19756 0.4754016 8.91612712.57 0.50651 7.53905 3.41489 2.20770 0.4715468 8.98203342.58 0.50562 7.59913 3.42631 2.21788 0.4677153 9.04819902.59 0.50474 7.65945 3.43767 2.22809 0.4639074 9.1146238

Tabla 2

k = 1.4

2.60 0.50387 7.72000 3.44898 2.23834 0.4601230 9.18130782.61 0.50301 7.78078 3.46023 2.24863 0.4563623 9.24825102.62 0.50216 7.84180 3.47143 2.25896 0.4526253 9.31545342.63 0.50131 7.90305 3.48257 2.26932 0.4489120 9.38291492.64 0.50048 7.96453 3.49365 2.27972 0.4452227 9.4506355

2.65 0.49965 8.02625 3.50468 2.29015 0.4415573 9.51861522.66 0.49883 8.08820 3.51565 2.30063 0.4379158 9.58685402.67 0.49802 8.15038 3.52657 2.31114 0.4342983 9.65535182.68 0.49722 8.21280 3.53743 2.32168 0.4307049 9.72410862.69 0.49642 8.27545 3.54824 2.33227 0.4271356 9.7931245

2.70 0.49563 8.33833 3.55899 2.34289 0.4235903 9.86239922.71 0.49485 8.40145 3.56969 2.35355 0.4200691 9.93193302.72 0.49408 8.46480 3.58033 2.36425 0.4165721 10.00172562.73 0.49332 8.52838 3.59092 2.37498 0.4130992 10.07177722.74 0.49256 8.59220 3.60146 2.38576 0.4096504 10.1420876

2.75 0.49181 8.65625 3.61194 2.39657 0.4062258 10.21265692.76 0.49107 8.72053 3.62237 2.40741 0.4028253 10.28348502.77 0.49033 8.78505 3.63274 2.41830 0.3994488 10.35457202.78 0.48960 8.84980 3.64307 2.42922 0.3960965 10.42591772.79 0.48888 8.91478 3.65334 2.44018 0.3927681 10.4975222

2.80 0.48817 8.98000 3.66355 2.45117 0.3894639 10.56938552.81 0.48746 9.04545 3.67372 2.46221 0.3861836 10.64150752.82 0.48676 9.11113 3.68383 2.47328 0.3829272 10.71388832.83 0.48606 9.17705 3.69389 2.48439 0.3796948 10.78652772.84 0.48538 9.24320 3.70389 2.49554 0.3764863 10.8594259

2.85 0.48469 9.30958 3.71385 2.50672 0.3733015 10.93258272.86 0.48402 9.37620 3.72375 2.51794 0.3701405 11.00599822.87 0.48335 9.44305 3.73361 2.52920 0.3670033 11.07967232.88 0.48269 9.51013 3.74341 2.54050 0.3638896 11.15360502.89 0.48203 9.57745 3.75316 2.55183 0.3607996 11.2277964

2.90 0.48138 9.64500 3.76286 2.56321 0.3577330 11.30224632.91 0.48073 9.71278 3.77251 2.57462 0.3546900 11.3769548

2.92 0.48010 9.78080 3.78211 2.58607 0.3516702 11.45192182.93 0.47946 9.84905 3.79167 2.59755 0.3486738 11.52714742.94 0.47884 9.91753 3.80117 2.60908 0.3457006 11.6026316

2.95 0.47821 9.98625 3.81062 2.62064 0.3427505 11.67837422.96 0.47760 10.05520 3.82002 2.63224 0.3398234 11.75437542.97 0.47699 10.12438 3.82937 2.64387 0.3369193 11.83063502.98 0.47638 10.19380 3.83868 2.65555 0.3340381 11.90715312.99 0.47578 10.26345 3.84794 2.66726 0.3311797 11.9839297

Tabla 2

k = 1.4

3.00 0.47519 10.33333 3.85714 2.67901 0.3283439 12.06096473.50 0.45115 14.12500 4.26087 3.31505 0.2129476 16.24200094.00 0.43496 18.50000 4.57143 4.04687 0.1387562 21.06808104.50 0.42355 23.45833 4.81188 4.87509 0.0916979 26.53866515.00 0.41523 29.00000 5.00000 5.80000 0.0617163 32.6534743

6.00 0.40416 41.83333 5.26829 7.94059 0.0296509 46.81520577.00 0.39736 57.00000 5.44444 10.46939 0.0153515 63.55262638.00 0.39289 74.50000 5.56522 13.38672 0.0084878 82.86546819.00 0.38980 94.33333 5.65116 16.69273 0.0049639 ###

10.00 0.38758 116.50000 5.71429 20.38750 0.0030448 ###

Tabla 2

Choque normal unidimensional de un gas perfecto( Calor específico y peso molecular constantes )

k = 1.0

464.36139

Tabla 2

Línea de Fanno; flujo de un gas perfecto, unidimensional, adiabático yde área constante

( Calor específico y peso molecular constantes )

k = 1.4

0 1.20000

0.01 1.19998 109.543416 57.873843 7134.404540.02 1.19990 54.770065 28.942130 1778.449880.03 1.19978 36.5115513 19.300542 787.0813870.04 1.19962 27.3817471 14.481486 440.352214

0.05 1.19940 21.9034271 11.591444 280.0203060.06 1.19914 18.2508495 9.665910 193.0310820.07 1.19883 15.6415534 8.291525 140.6550140.08 1.19847 13.6843088 7.261610 106.7182160.09 1.19806 12.1617653 6.461342 83.4961172

0.10 1.19760 10.9435131 5.821829 66.921560.11 1.19710 9.94656388 5.299230 54.68789550.12 1.19655 9.11559228 4.864318 45.4079620.13 1.19596 8.4122961 4.496859 38.20700310.14 1.19531 7.80931667 4.182400 32.511306

0.15 1.19462 7.28659101 3.910343 27.93196750.16 1.19389 6.82907187 3.672739 24.197830.17 1.19310 6.42525257 3.463509 21.11517820.18 1.19227 6.0661835 3.277926 18.54265450.19 1.19140 5.74479918 3.112259 16.3751637

0.2 1.19048 5.45544726 2.963520 14.53326650.21 1.18951 5.19355203 2.829294 12.95602190.22 1.18850 4.95536975 2.707602 11.59605440.23 1.18744 4.73780779 2.596812 10.41608990.24 1.18633 4.53828896 2.495562 9.38648053

0.25 1.18519 4.35464843 2.402710 8.483408840.26 1.18399 4.18505446 2.317287 7.687566580.27 1.18276 4.02794666 2.238471 6.983169530.28 1.18147 3.88198758 2.165554 6.357214490.29 1.18015 3.74602426 2.097928 5.79891264

0.3 1.17878 3.61905747 2.035065 5.299253110.31 1.17737 3.50021693 1.976507 4.850663440.32 1.17592 3.38874115 1.921851 4.446743470.33 1.17442 3.28396095 1.870745 4.08205470.34 1.17288 3.1852859 1.822876 3.75195255

0.35 1.17130 3.09219303 1.777969 3.452451750.36 1.16968 3.00421752 1.735778 3.180117520.37 1.16802 2.92094477 1.696086 2.931977190.38 1.16632 2.84200386 1.658696 2.70544783

0.39 1.16457 2.76706191 1.623433 2.49827682Tabla 2

k = 1.4

0.40 1.16279 2.69581933 1.590140 2.308492650.41 1.16097 2.62800577 1.558673 2.134364080.42 1.15911 2.56337663 1.528905 1.974366030.43 1.15721 2.50171007 1.500718 1.827150970.44 1.15527 2.44280443 1.474005 1.69152484

0.45 1.15329 2.38647598 1.448672 1.566426690.46 1.15128 2.33255695 1.424629 1.450911350.47 1.14923 2.28089388 1.401795 1.344134760.48 1.14714 2.23134609 1.380097 1.245341290.49 1.14502 2.18378439 1.359468 1.15385301

0.50 1.14286 2.13808994 1.339844 1.069060310.51 1.14066 2.0941532 1.321168 0.990413940.52 1.13843 2.05187308 1.303388 0.917417990.53 1.13617 2.01115611 1.286454 0.849623870.54 1.13387 1.97191578 1.270321 0.78662509

0.55 1.13154 1.93407182 1.254948 0.728052570.56 1.12918 1.89754974 1.240294 0.673570710.57 1.12678 1.86228027 1.226326 0.622873820.58 1.12435 1.8281989 1.213007 0.575683020.59 1.12189 1.79524553 1.200308 0.53174348

0.60 1.11940 1.76336404 1.188200 0.490822050.61 1.11688 1.73250201 1.176654 0.452705090.62 1.11433 1.70261038 1.165646 0.417196570.63 1.11175 1.67364325 1.155151 0.384116380.64 1.10914 1.64555755 1.145148 0.35329885

0.65 1.10650 1.61831287 1.135616 0.324591370.66 1.10383 1.59187127 1.126535 0.297853230.67 1.10114 1.56619706 1.117887 0.272954520.68 1.09842 1.54125665 1.109655 0.249775190.69 1.09567 1.5170184 1.101822 0.22820414

0.70 1.09290 1.4934525 1.094373 0.208138510.71 1.09010 1.47053078 1.087294 0.189482920.72 1.08727 1.44822667 1.080571 0.172148850.73 1.08442 1.42651504 1.074192 0.15605410.74 1.08155 1.40537213 1.068144 0.14112224

0.75 1.07865 1.38477543 1.062417 0.127282140.76 1.07573 1.36470364 1.056999 0.11446756

0.77 1.07279 1.34513655 1.051881 0.102616760.78 1.06982 1.32605498 1.047053 0.091672160.79 1.06684 1.30744075 1.042505 0.08157997

1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!

M #VALUE! #VALUE! #VALUE! #VALUE!1.20000 #DIV/0! #DIV/0! #DIV/0!

0.80 1.06383 1.28927656 1.038230 0.072289970.81 1.06080 1.27154597 1.034219 0.063755190.82 1.05775 1.25423336 1.030464 0.055931670.83 1.05469 1.23732385 1.026959 0.048778270.84 1.05160 1.22080325 1.023696 0.04225644

0.85 1.04849 1.20465808 1.020669 0.036330040.86 1.04537 1.18887545 1.017871 0.030965150.87 1.04223 1.17344308 1.015297 0.026129950.88 1.03907 1.15834925 1.012941 0.021794540.89 1.03589 1.14358274 1.010798 0.01793083

0.90 1.03270 1.12913287 1.008863 0.014512390.91 1.02950 1.11498939 1.007131 0.011514360.92 1.02627 1.10114253 1.005597 0.008913340.93 1.02304 1.0875829 1.004258 0.006687290.94 1.01978 1.07430155 1.003108 0.00481545

0.95 1.01652 1.06128988 1.002145 0.003278220.96 1.01324 1.04853965 1.001365 0.002057140.97 1.00995 1.03604297 1.000763 0.001134790.98 1.00664 1.02379227 1.000337 0.00049470.99 1.00333 1.01178027 1.000084 0.00012133

1.00 1.00000 1 1.000000 01.01 0.99666 0.98844475 1.000083 0.000116831.02 0.99331 0.97710808 1.000330 0.000458691.03 0.98995 0.9659838 1.000738 0.001013171.04 0.98658 0.95506595 1.001305 0.0017685

1.05 0.98320 0.9443488 1.002029 0.002713581.06 0.97982 0.93382684 1.002907 0.003837851.07 0.97642 0.92349476 1.003938 0.005131351.08 0.97302 0.91334746 1.005119 0.00658461.09 0.96960 0.90337999 1.006449 0.00818865

1.10 0.96618 0.89358761 1.007925 0.0099351.11 0.96276 0.88396575 1.009547 0.011815581.12 0.95932 0.87450999 1.011312 0.013822731.13 0.95589 0.86521607 1.013219 0.015949211.14 0.95244 0.85607987 1.015267 0.01818811

1.15 0.94899 0.84709743 1.017454 0.02053289

1.16 0.94554 0.83826492 1.019780 0.022977351.17 0.94208 0.82957862 1.022242 0.025515561.18 0.93861 0.82103495 1.024840 0.028141931.19 0.93515 0.81263047 1.027573 0.03085112

Tabla 2

k = 1.4

1.20 0.93168 0.80436182 1.030440 0.033638071.21 0.92820 0.79622576 1.033440 0.036497951.22 0.92473 0.78821916 1.036572 0.039426191.23 0.92125 0.78033899 1.039835 0.042418431.24 0.91777 0.77258232 1.043229 0.04547052

1.25 0.91429 0.76494631 1.046753 0.048578521.26 0.91080 0.7574282 1.050406 0.051738691.27 0.90732 0.75002532 1.054189 0.054947441.28 0.90383 0.7427351 1.058100 0.058201391.29 0.90035 0.73555502 1.062138 0.0614973

1.30 0.89686 0.72848265 1.066305 0.064832091.31 0.89338 0.72151564 1.070598 0.068202831.32 0.88989 0.71465171 1.075018 0.071606731.33 0.88641 0.70788863 1.079565 0.075041141.34 0.88292 0.70122424 1.084239 0.07850352

1.35 0.87944 0.69465647 1.089038 0.081991471.36 0.87596 0.68818327 1.093964 0.08550271.37 0.87249 0.68180268 1.099015 0.089035011.38 0.86901 0.67551278 1.104193 0.092586331.39 0.86554 0.6693117 1.109496 0.09615468

1.40 0.86207 0.66319764 1.114926 0.099738171.41 0.85860 0.65716883 1.120481 0.103335011.42 0.85514 0.65122357 1.126162 0.106943491.43 0.85168 0.64536019 1.131969 0.110561971.44 0.84822 0.63957707 1.137903 0.11418891

1.45 0.84477 0.63387263 1.143963 0.117822821.46 0.84133 0.62824535 1.150150 0.121462321.47 0.83788 0.62269372 1.156463 0.125106041.48 0.83445 0.6172163 1.162904 0.128752731.49 0.83101 0.61181166 1.169471 0.13240118

1.50 0.82759 0.60647843 1.176167 0.136050221.51 0.82416 0.60121527 1.182991 0.139698761.52 0.82075 0.59602087 1.189943 0.143345761.53 0.81734 0.59089395 1.197024 0.146990221.54 0.81393 0.58583326 1.204234 0.15063121

1.55 0.81054 0.5808376 1.211574 0.154267821.56 0.80715 0.57590577 1.219044 0.157899211.57 0.80376 0.57103664 1.226644 0.161524561.58 0.80038 0.56622907 1.234376 0.16514311.59 0.79701 0.56148197 1.242239 0.16875411

Tabla 2

k = 1.4

1.6 0.79365 0.55679425 1.250235 0.172356891.61 0.79030 0.55216489 1.258364 0.175950781.62 0.78695 0.54759286 1.266626 0.179535171.63 0.78361 0.54307715 1.275022 0.183109461.64 0.78027 0.53861681 1.283553 0.18667309

1.65 0.77695 0.53421087 1.292219 0.190225531.66 0.77363 0.52985842 1.301021 0.193766281.67 0.77033 0.52555853 1.309960 0.197294861.68 0.76703 0.52131033 1.319037 0.200810831.69 0.76374 0.51711296 1.328252 0.20431376

1.7 0.76046 0.51296555 1.337606 0.207803261.71 0.75718 0.5088673 1.347100 0.211278941.72 0.75392 0.50481738 1.356735 0.214740461.73 0.75067 0.500815 1.366511 0.218187471.74 0.74742 0.4968594 1.376430 0.22161967

1.75 0.74419 0.49294982 1.386492 0.225036751.76 0.74096 0.48908551 1.396698 0.228438441.77 0.73774 0.48526575 1.407049 0.231824481.78 0.73454 0.48148984 1.417546 0.235194641.79 0.73134 0.47775707 1.428190 0.23854867

1.8 0.72816 0.47406677 1.438982 0.241886371.81 0.72498 0.47041828 1.449923 0.245207551.82 0.72181 0.46681093 1.461013 0.248512011.83 0.71866 0.46324411 1.472255 0.25179961.84 0.71551 0.45971718 1.483648 0.25507015

1.85 0.71238 0.45622952 1.495194 0.258323531.86 0.70925 0.45278055 1.506894 0.261559591.87 0.70614 0.44936968 1.518750 0.264778211.88 0.70304 0.44599632 1.530761 0.26797931.89 0.69995 0.44265993 1.542930 0.27116274

1.9 0.69686 0.43935993 1.555257 0.274328441.91 0.69379 0.4360958 1.567743 0.277476331.92 0.69073 0.43286701 1.580391 0.28060634

1.93 0.68769 0.42967302 1.593200 0.283718391.94 0.68465 0.42651334 1.606172 0.28681244

1.95 0.68162 0.42338747 1.619309 0.289888441.96 0.67861 0.4202949 1.632611 0.292946341.97 0.67561 0.41723517 1.646080 0.295986121.98 0.67262 0.4142078 1.659717 0.299007751.99 0.66964 0.41121232 1.673523 0.30201122

Tabla 2

k = 1.4

2.00 0.66667 0.40824829 1.687500 0.30499652.01 0.66371 0.40531526 1.701649 0.30796362.02 0.66076 0.40241278 1.715971 0.310912512.03 0.65783 0.39954044 1.730467 0.313843232.04 0.65491 0.3966978 1.745139 0.31675578

2.05 0.65200 0.39388446 1.759989 0.319650172.06 0.64910 0.39110002 1.775017 0.322526422.07 0.64621 0.38834406 1.790225 0.325384562.08 0.64334 0.3856162 1.805614 0.328224612.09 0.64047 0.38291606 1.821187 0.33104661

2.10 0.63762 0.38024325 1.836944 0.333850582.11 0.63478 0.37759742 1.852886 0.336636582.12 0.63195 0.37497818 1.869016 0.339404652.13 0.62914 0.3723852 1.885334 0.342154822.14 0.62633 0.3698181 1.901843 0.34488716

2.15 0.62354 0.36727655 1.918543 0.347601722.16 0.62076 0.36476022 1.935437 0.350298552.17 0.61799 0.36226875 1.952525 0.352977712.18 0.61523 0.35980184 1.969810 0.355639272.19 0.61249 0.35735915 1.987292 0.35828328

2.20 0.60976 0.35494037 2.004975 0.360909822.21 0.60704 0.35254518 2.022858 0.363518952.22 0.60433 0.35017329 2.040944 0.366110742.23 0.60163 0.34782439 2.059234 0.368685272.24 0.59895 0.34549818 2.077731 0.37124261

2.25 0.59627 0.34319437 2.096435 0.373782842.26 0.59361 0.34091269 2.115349 0.376306032.27 0.59096 0.33865283 2.134473 0.378812272.28 0.58833 0.33641454 2.153811 0.381301642.29 0.58570 0.33419753 2.173363 0.38377421

2.30 0.58309 0.33200154 2.193131 0.38623008

2.31 0.58049 0.32982631 2.213117 0.388669332.32 0.57790 0.32767157 2.233323 0.391092042.33 0.57532 0.32553707 2.253751 0.39349832.34 0.57276 0.32342256 2.274401 0.39588821

2.35 0.57021 0.3213278 2.295277 0.398261842.36 0.56767 0.31925253 2.316381 0.400619292.37 0.56514 0.31719652 2.337712 0.402960662.38 0.56262 0.31515954 2.359275 0.405286022.39 0.56011 0.31314135 2.381070 0.40759548

1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!1.20000 #DIV/0! #DIV/0! #DIV/0!

M #VALUE! #VALUE! #VALUE! #VALUE!1.20000 #DIV/0! #DIV/0! #DIV/0!

2.4 0.55762 0.31114172 2.403100 0.409889132.41 0.55514 0.30916043 2.425366 0.412167062.42 0.55267 0.30719726 2.447870 0.414429362.43 0.55021 0.30525199 2.470615 0.416676132.44 0.54777 0.30332441 2.493602 0.41890747

2.45 0.54533 0.3014143 2.516832 0.421123462.46 0.54291 0.29952146 2.540309 0.423324222.47 0.54050 0.29764568 2.564035 0.425509822.48 0.53810 0.29578675 2.588010 0.427680372.49 0.53571 0.29394449 2.612237 0.42983596

2.5 0.53333 0.2921187 2.636719 0.431976692.51 0.53097 0.29030917 2.661457 0.434102662.52 0.52862 0.28851573 2.686453 0.436213962.53 0.52627 0.28673819 2.711709 0.438310692.54 0.52394 0.28497635 2.737228 0.44039294

2.55 0.52163 0.28323005 2.763012 0.442460822.56 0.51932 0.28149909 2.789063 0.444514422.57 0.51702 0.27978331 2.815382 0.446553832.58 0.51474 0.27808252 2.841972 0.448579152.59 0.51247 0.27639657 2.868836 0.45059049

2.6 0.51020 0.27472527 2.895975 0.452587922.61 0.50795 0.27306847 2.923392 0.454571562.62 0.50571 0.271426 2.951089 0.45654152.63 0.50349 0.26979769 2.979068 0.458497832.64 0.50127 0.26818339 3.007331 0.46044064

2.65 0.49906 0.26658294 3.035881 0.462370042.66 0.49687 0.26499619 3.064720 0.464286122.67 0.49469 0.26342298 3.093850 0.466188962.68 0.49251 0.26186316 3.123274 0.468078682.69 0.49035 0.26031658 3.152993 0.46995536

2.7 0.48820 0.25878311 3.183011 0.47181909

2.71 0.48606 0.25726258 3.213329 0.473669962.72 0.48393 0.25575486 3.243951 0.475508082.73 0.48182 0.25425982 3.274878 0.477333542.74 0.47971 0.2527773 3.306113 0.47914641

2.75 0.47761 0.25130718 3.337658 0.480946812.76 0.47553 0.24984932 3.369515 0.482734812.77 0.47345 0.24840358 3.401688 0.484510522.78 0.47139 0.24696984 3.434179 0.486274012.79 0.46933 0.24554797 3.466989 0.48802539

1.20000 #DIV/0! #DIV/0! #DIV/0!Tabla 2

k = 1.4

2.8 0.46729 0.24413783 3.500123 0.489764732.81 0.46526 0.24273931 3.533581 0.491492142.82 0.46323 0.24135227 3.567368 0.493207692.83 0.46122 0.2399766 3.601484 0.494911482.84 0.45922 0.23861218 3.635934 0.4966036

2.85 0.45723 0.23725888 3.670719 0.498284132.86 0.45525 0.23591659 3.705842 0.499953152.87 0.45328 0.23458519 3.741306 0.501610772.88 0.45132 0.23326456 3.777113 0.503257052.89 0.44937 0.2319546 3.813266 0.50489209

2.9 0.44743 0.23065519 3.849768 0.506515972.91 0.44550 0.22936623 3.886622 0.508128782.92 0.44358 0.22808759 3.923829 0.50973062.93 0.44167 0.22681918 3.961393 0.511321512.94 0.43977 0.22556089 3.999317 0.5129016

2.95 0.43788 0.22431262 4.037603 0.514470952.96 0.43600 0.22307425 4.076255 0.516029632.97 0.43413 0.2218457 4.115274 0.517577742.98 0.43226 0.22062685 4.154664 0.519115352.99 0.43041 0.21941762 4.194428 0.52064255

3.00 0.42857 0.21821789 4.234568 0.522159413.10 0.41068 0.20672301 4.657311 0.536776593.20 0.39370 0.19607994 5.120958 0.550443783.30 0.37760 0.1862086 5.628647 0.563231913.40 0.36232 0.17703802 6.183699 0.57520672

3.50 0.34783 0.16850509 6.789621 0.586428983.60 0.33408 0.16055357 7.450111 0.596954723.70 0.32103 0.15313316 8.169066 0.606835573.80 0.30864 0.14619883 8.950585 0.61611903

3.90 0.29688 0.13971012 9.798973 0.62484877

4.00 0.28571 0.13363062 10.718750 0.633064934.10 0.27510 0.12792751 11.714652 0.640804434.20 0.26502 0.12257111 12.791640 0.648101194.30 0.25543 0.11753458 13.954904 0.654986394.40 0.24631 0.11279356 15.209867 0.66148873

4.50 0.23762 0.10832593 16.562195 0.66763464.60 0.22936 0.10411155 18.017795 0.673448314.70 0.22148 0.10013209 19.582828 0.678952254.80 0.21398 0.09637078 21.263710 0.68416705

Tabla 2

k = 1.4

4.9 0.20683 0.09281233 23.067119 0.689111755 0.20000 0.08944272 25.000000 0.693803926 0.14634 0.06375767 53.179784 0.729875287 0.11111 0.04761905 104.142857 0.752802168 0.08696 0.03686049 190.109375 0.768191619 0.06977 0.02934836 327.189300 0.77898519

10 0.05714 0.02390457 535.937500 0.78683083

0.00000 0

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