Frank M. Whithe dices

8/7/2019 Frank M. Whithe dices

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F ig ur a A . !, V i sc o si da d a bs olu tad e fluid os c om une s a l atm .

5-2 0 20 8 0 1 0 00 60 120Tempera tura ,D C

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2/31

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F ig ur a A .2 . Vi s cos id a d c i nema t ic ade fiu idos c om une s a 1 atm .

P ro pi ed ad es fi si ca s d e lo s fi uid os 8 15

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1 X 10-7- 2 0

Temperatura, - c


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.--- - - -~ - -- - --~--- -8 1 6 A pendice A

Tabla A. l . Viscosidad I ,oC p, kglm 3 /J ., N . slm! v,m!/s T , of p, s l u g l f t " l /J .,lb . s i r e II, ft2/s -d en si da d d el. ag ua .---. a 1 atm . 0 1000- 1 .7 8 8 >


4/31

P ro pie da de s ffs ic as d e lo s tlu id os 81 7T a b l a A.3 . Propiedadesd e lf qu id o s usuales a 1 atm .. '.y 2 0 C (68 O F ) .

Modulo Pa rame t rovolnm etrico de v t scosdadNfm: C '. kgfm3 IL , kgf(m . s) Y. N/m"iquido

Amoniaco 608 ~ .~O X 10 -4 2.13 X 10 -2. 9.10 X lOS _=::..:::::===::~~~ ..-_~_B e_ncen _ ~! _~~~10~2 ..88X LQ :-2 .__LOLK l0 4 . . . . . . l . . 4 . _ X . l ( } 9 . .

Te trac loruro de carbo no 15 90 9 .67 X 10 -4 2 .70 X 10 -2 1.20 X 10 4 9.65 X 10 1Etanol 7 8 9 1.20 X 10-) 2 .28 X 10 -2 5 .7 X 10 3 9 .0 X 10 8E t il eno g li co lF re 6n 1 2GasolinaGlicerinaQuerosenoMercurio

.. Me t 1 U 1 0 1 . " . .. . . . .A ceite S A E 10 WA ce ite S AE 10 W 30A ceite S AE 30 WAcei te SAE 5 0 WAguaA g ua d e m ar (3 0% )

1.05_ _ 4 _ 1 !4.455 .7211.71.763.6828 .05 .561.07

. .. .. . 4 . 0 .3 . .. .15.714.018.320.2

Tabla A .l7 .28

2.14 X 10 -1 4 .84 X 10 -22.62 X 10 -42.92 X 10 -4 2.16 X 10 -21.49 6.33 X 10 -21.92 X 10 -3 2 .8 X 10 -21.56 X 10 -3 4.84 X 10 -1~ .98 . : > < J ! t _ 4 .2 .25 X . 1 O ~ . 21.04 X 10 - 1 + 3 .6 X 10 -21. 7 X 10 -1 +2 .9 X lO- l+ 3 .5 X 10- 28 .6 X lO-l;1.00 X 10 -3 7.28 X 10 -21.07 X 10 -3 7.28 X 10 -2

1. 2 X 1 Q I1 1 7132768 0

1260804

13 ,550.]918 7 08 768 919029 98

1025

5 .51 X 10 4 9 .58 X 10 81. 4 X 1 0 - 2 4.34 X 1 0 93.11 X 10 3 1. 6 X 10 91 . 1 X 10 -3 2.55 X 10 10J .34 X 1Q~ . _ . 8 ) X 10~ . . .. . .

1.31 X 10 91.38 X 10 9

2.34 X 10 3 2.19 X 10 92.34 X 1 Q l 2.33 X 10 9

* E n c o nt a c t o c o n a i r e .t La var iac i6n viscos idad-temperatura de e st es l fq u id o s puede ajustarse m e di an te l a e x pr e si on emp fr ic a~ - r ' (2 9 3 K )]" ' exp C--Ilk2o'c T KCOD un a precis ion de 6% e n e l rango 0 ~ T ~ 100 "C .

. t V al or e s r e pr e se n ta ti v e s. L a c la sific ac ic n d ea ce ite s' S A E pe rm ite u na va ria cio n d e v is cos id ad ba sta 5 0% ;' e spe cia lm ente abajas t~mpera tu ras.

T a b l a A .4 . P ro pie da de s d e g ase s P e s o I R a n o d e c alo r E x po ne nt e le ycom une s a 1 atm y 2 0 C (68 o F ) . ~!Gas molecular R, m2 / ( s 2 . K) o s . N/m3 jJ., N s/m! especiflco putcncilllllH2 2 .016 4124 0 .8 22 9.05 X 10 -6 1.41 0 .68He 4 .003 207 7 1.63 1.97 X 10 -5 1.66 0 .67Hp 18 .02 461 7 .35 1.02 X 10 -5 1.33 1.15A r 39 .9 44 208 16.3 2 .24 X 10 -5 1.67 0 .72Aire seco 28 .9 6 28 7 11.8 1.80 X 10 -5 1.40 0 .67CO 2 44.01 18 9 17 .9 1.48 X 10 -5 1.30 0 .79CO 28 .01 29 7 11.4 1.82 X 10 -5 1.40 0 .7 1N 2 28 .02 29 7 11.4 1.76 X 10 - 5 1.40 0 .67 2 32 .00 260 13 .1 2 .00 X 10 - 5 l A O 0.69NO 30 .01 27 7 12 .1 1.90 X 10 -5 lA O 0 .78Np 44 .02 18 9 17.9 lA S X 10 -5 1.31 0 .89Cl 2 70 .91 11 7 28.9 1.03 X 10 - 5 1.34 1.00CH 4 16.04 518 6.5 4 1 .3 4 X 10 -5 1.32 0 .87_-- ~-. ---* L a curv a de la le y po tenc ia l. E cuac i6n (1 .2 7 ) , ~U,91 x '" (T r293 )n , ajusta este s gase s con un 4% en e~ ~~2 50 S -T s ''tOOO K . L a'tem pe ratu ra debe e stare n k e lV inS :-- -


5/31

-- ---. - ----.. . - - _ - -8 1 8 A pe nd ic e A

T a b la A . S. Tens ion T , C T a p ia A . 6. p, kglm Js u p e rf ic i al ._ p r . es i6 n _ Y , N /m P u , k P a a . O I l s Propiedades Z , m T, K p, P a a , m /sd e v ap or y velocidad 0 Q0756 0 .611 1402 d e la a tm osfe ra -5 00 291.41 - .. 107,508 1.2854 342.2d el so nid o e n e l agu a. 10 0:0742 1.227 1447 e s t a n d a r , 0 288.16 101,350 1.2255 340.320 0.0728 2.337 1482 500 284.91 95 ,480 1.167 7 338 .4

30 0.0712 4.242 1509 1000 2Rl.1l1l R 9 ,RR9 1 .1 1 20 . . 336.5 ..~40 0.0696 7 .375 1529 1500 278.41 84,565 1.05 83 334.550 0.0679 12 .34 - 1542 2000 275.16 79 ,500 1.0067 332.660 0.0662 19 .9 2 1551 2500 271.91 74,68 4 0.9 570 330.67 0 0.0644 31.16 1553 3000 268.66 70,107 0.9 092 328 .680 0.0626 47.35 15 54 3500 265.41 65,759 0.8633 326.690 0.0608 70.11 1550 4000 262.16 61,633 0.8191 324.610 0 0.0589 101.3 1543 4500 258.91 57,718 0.7768 322.6

5000 255.66 54,008 0.7361 320.6,120 0.0550 198.5 151 .8 . . ' 55 00 .252.41 50,49 3 0..69 70 318.5.. . .140 0.0509 361.3 1483 6000 249.16 47 ,166 0.6596 316.5160 0.0466 617.8 1440 6500 245.91 44,018 0.6237 314.418 0 0 .0422 1002 1389 7000 242.66 41,043 0.5 89 3 312.3200 0 .037 7 1554 1334 7500 239.41 38,233 0.5 564 310.2220 0 .0331 2318 1268 8000 236.16 35 ,581 0.5 25 0 308 .1240 0.0284 3344 1192 8500 232.91 33,080 0.4949 306.0260 0 .0237 4688 1110 9000 229.66 30,7 23 0.4661 303.8280 0 .0190 6412 1022 9500 226.41 28,504 0.438 7 301.7300 0.0144 85 81 920 10,000 223.16 26,416 0.4125 299.5320 0 .009 9 11,274 800 10,500 219.91 24,455 0.387 5 297 .3340 0 .0056 14,586 630 11,000 216.66 22,612 0.3637 295 .136 0 0.0019 18 ,651 370 11,500 216.66 20,897 0.3361 295 .1374* 0 .0* 22,090* 0* 12,000 216.66 19 ,312 0 .3106 295.1

12,500 216.66 17 ,8 47 0 .287 0 295 .1* Punt o e n ri co . 13,000 216.66 16,494 0 .2652 295 .113,500 216.66 15,243 0 .2451 295 .114,000 216.66 14,087 0.2265 295.114,500 216.66 13 ,018 0 .2094 295.115,000 216.66 12 ,031 0 .19 35 295 .115,500 216.66 11,118 0 .17 88 295.116,000 216.66 10,275 0 .1652 295 .116,500 216.66 9496 0 .15 27 295 .117,000 216.66 8775 0 .1411 295 .117,500 216.66 8110 0 .1304 295 .118,000 216.66 7495 0 .1205 295.118,500 216.66 6926 0 .1ll4 29 5 .119,000 216.66 6401 0.1029 295.119,500 216.66 5915 0 .09 51 29 5 .120,000 216.66 5467 0 .08 79 295.122,000 218.6 4048 0.0645 296.424,000 220.6 2972 0.0469 297.826,000 222.5 2189 0 .0343 29 9 .128,000 224.5 1616 0.0251 300.430,000 226.5 1197 0 .0184 301.740,000 250.4 28 7 0 .0040 317 .2) O , O O f l 7 . 7 0. 7 . ' 80 nrmn 1 2 Q 960,000 255.7 22 0 .0003 320 .670,000 219.7 6 0 .0001 29 7 .2


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"e~ " . - T a b l a s _ - d e - f l u j o c o m p r e s i b l e

T a b l a B.l. Flujo M a pipil p l p u T I T o A.IA* M a p l p o p l p o TITo ; i i t1 ' "i so e nt r6 pi co d eu n g as p erfe cto , 0 .00 1.0000 1.0000 1.0000 00 1.75 0 .187 8 0 .3029 0 .6202 1.3865k = 1.4 . 0.05 0 .9 9 83 0 .9 9 88 0 .9 9 9 5 11.5 9 14 1.80 0 .1740 0.2868 0 .6068 !.439 00.10 0 .9 9 30 0 .9 9 50 0 .9980 5.8218 1.8 5 0.1612 0 .2715 0 .5 9 36~ 1 .4 95 2 .

0 .15 0 .9 8 44 0 .9 8 88 0 .9 9 5 5 3.9103 1.90 0.1492 0 .2570 0 .5 8 07 1.5 5 5 30 .20 0 .9 7 25 0 .9 8 03 0 .9921 2.9635 1.95 0.1381 0 .2432 0 .5 680 1.6193

. 0 .25 0 .9 5 75 0 .9 694 0 .9 8 7 7 2.4027 2 .00 0 .1278 0 . 23 0 0 . . 05556- ... 1 .6 87 50 .30 0 .9 395 0 .9 5 64 0.98 23 2.0351 2 .05 0 .1182 0 .2176 0 .5 433 1.7600

0.35 0 .9 18 8 0 .9 413 0.97 61 1:77 8 0 2 .10 0 .1094 0.2058 0 .5 313 1.8 3690 .40 0 .8 9 56 0 .9 243 0.9 69 0 1.5 9 01 2.15 O . L O l l 0 .19 46 0 .5 196 1.91850.45 0.87 03 0.905 5 0.9611 , 1 .4 48 7 2.20 0 .09 35 0.1841 0 .5081 2.00500.50 0.8430 0.88 5 2 0.9 524 1.3398 2.25 0 .08 65 0 .17 40 0.4969 2.09640.55 0.8 142 0.8634 0.9 430 1.25 49 2.30 0 .08 00 0.1646 0.48 5 9 2 .19 31 ,0.60 0.7 840 0.8405 0 .9 328 1.18 82 2.35 0 .07 40 0 .15 56 0 .47 5 2 2 .29 530.65 0.7 528 0.8164 0 .9 221 1.1356 2.40 0 .0684 0.1472 0.4647 2.4031. '0 .70 0 .7 209 0.79 16 0 .9 107 1.0944 2.45 0.0633 0.1392 0.4544 2.516g.0 .7 5 0 .6886 0.7660 0 .8989 1.0624 2 .5 0 0 .05 85 0.1317 0.4444 2 .63670 .8 0 0.6560 0.7400 0 .8 865 1.038 2 2 .5 5 0 .05 42 0.1246 0.4347 2.76300 .8 5 0 .6235 0 .7 136 0 .8 7 37 1.0207 2 .60 0 .05 01 0.117 9 0.425 2 2.89600 .9 0 0 .5 913 0.6870 0 .8 606 1.008 9 2 .65 0.0464 0.1115 0.415 9 3.035 90 .9 5 0 .5 5 95 0 .6604 0 .8 471 1.0021 2 .7 0 0.0430 0.1056 0.4068 3.18301.00 0 .5 283 0 .6339 0 .8 333 1.0000 2 .7 5 0.039 8 0.09 9 9 0.398 0 3.33771.05 0 .49 79 0.6077 0.819 3 1.0020 2 .8 0 0.0368 0.09 46 0 .389 4 3.50011.10 0 .4684 0 .5 8 17 0.805 2 1.007 9 2 .8 5 0.0341 0.08 96 0 .3810 3.67071.15 0 .4398 0 .5 5 62 0.79 08 1.017 5 2 .9 0 0.0317 0.0849 0.3729 3 .84981.20 0 .4124 0 .5 311 0.77 64 1.0304 2 .9 5 0.029 3 0.08 04 0 .3649 4.03761.25 0 .38 61 0.5067 0.7619 1.0468 3 .00 0.027 2 0.0762 0 .3571 4.23461.30 0 .3609 0 .48 29 0.747 4 1.0663 3 .05 0.025 3 0.0723 0 .3496 4.44101.35 0.3370 0 .4598 0.7329 1.08 9 0 s . r o 0.0234 0.0685 0.3422 4.6573. 1 .4 0 " 0:3142 0.4374 0 :7184 1.1149 3 .15 0.0218 0 .065 0 0 .3351 4 .88381.45 0.29 27 Oc415_ _Q70_40 1.1440 3 .20 0.0202 0 .0617 0.3281 5.12101.50 0.27 24 0.39 5 0 0 .689 7 1.1762 3 .25 0 .018 8 0 .058 5 0.3213 5.36911.5 5 0.25 33 0 .3750 0 .675 4 1.2116 3 .30 0 .0175 0 .0555 0.3147 5.62861.60 0.235 3 0.35 5 7 0 .6614 1.25 02 3.35 0.0163 0 .05 27 0 .3082 5 .90001.65 0 .218 4 0.3373 0 .647 5 1.29 22 3.40 0 .0151 0 .05 01 0.3019 6.18371.70 0 .2026 0.319 7 0 .6337 1.3376 3.45 0.0141 0.0476 0 .2958 6.4801

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820 A pendice BT ab la B .1(Gon t inuac i6n ) . M a - - p !P jI _ .- p l p o T IT o MA* M a p l p o P ( P n T I T o MA*. . ._ . - a. . $ a. o . _~ 0 . 2 6 2 3lujo isoentropico 3 . 4 5 0 ; 9 1 4 1 0 . 0 4 7 6 0 .2 9 5 8 6 . 4 8 0 1 3 . 7 5 0 . 0 0 9 2 0 . 0 3 5 2 8 . 5 5 1 7d e u n g as pe rfe cto , 3 . 5 0 0 . 0 1 3 1 0 . 0 4 5 2 0 .2 8 9 9 6 . 7 8 9 6 3 . 8 0 0 . 0 0 8 6 0 . 0 3 3 5 0 . 2 5 7 2 8 . 9 5 0 6~1-:4. 3 S 5 0 0 1 2 2 0 0 4 3 0 0 . 2 8 4 1 7 . 1 1 2 8 3 . 8 5 0 . 0 0 8 ) 0 .Q 3 2 Q _ _ _ 0 .2 ~ .2 f 9 . 3 6 6 1- -- 3 . 6 0 0 . 0 1 1 4 - 0 . 0 4 0 9 0 . 2 7 8 4 7 . 4 5 0 1 - 3 . 9 0 0 1 m 5 0 ] 3 0 4 - 0 .2 4 7 4 - 9 . 7 9 9 0 ---- .. _ _

3 . 6 5 0 . 0 1 0 6 _ Q , _ 0 3 8 9 0 . 2 7 2 9 7 . 8 0 2 0 3 . 9 5 0 .0 0 7 0 0 . 0 2 9 0 0 . 2 4 2 7 l O . 2 4 9 63 . 7 0 0 . 0 0 9 9 0 . 0 3 7 0 0 . 2 6 7 5 8 . 1 6 9 1 4 .0 0 0 .0 0 6 6 0 . 0 2 7 7 0 . 2 3 8 1 1 0 . 7 1 8 8

T ab la B . 2. R e la ci on e s Ma < 1 Mad P 2 1 P I V 1 I V 1 = P 2 f p l 7 2 f T I P 0 2 1 P O I AiIA'i- . . d e o nd a-d e c h oq u e, . ..n orm al p ara u n gas 1 . 0 0 1 .0 0 0 0 1 . 0 0 0 0 1 . 0 0 0 0 1 . 0 0 0 0 1 . 0 0 0 0 1 . 0 0 0 01 . 0 5 0 . 9 5 3 1 1 . 1 1 9 6 . 1 .0 8 4 0 1 . 0 3 2 8 0 . 9 9 9 9 1 . 0 0 0 1perfecto, k = 104.

L l O 0 . 9 1 1 8 1 . 2 4 5 0 1 . 1 6 9 1 1 . 0 6 4 9 0 .9 9 8 9 l . 0 0 1 11 . 1 5 0 . 8 7 5 0 1 . 3 7 6 3 1 . 2 5 5 0 1 . 0 9 6 6 0 .9 9 6 7 1 .0 0 3 31 . 2 0 0 . 8 4 2 2 1 . 5 1 3 3 1 . 3 4 1 6 1 . 1 2 8 0 0 .9 9 2 8 1 . 0 0 7 31 . 2 5 0 . 8 1 2 6 1 .6 5 6 3 1 .4 2 8 6 1 . 1 5 9 4 0 .9 8 7 1 1 . 0 1 3 11 . 3 0 0 . 7 8 6 0 1 . 8 0 5 0 1 . 5 1 5 7 1 . 1 9 0 9 0 .9 7 9 4 . - . C 0 2 U1 . 3 5 0 . 7 6 1 8 1 . 9 5 9 6 1 . 6 0 2 8 1 . 2 2 2 6 0 .9 6 9 7 1 . 0 3 1 21 . 4 0 0 .7 3 9 7 2 . 1 2 0 0 1 . 6 8 9 7 1 . 2 5 4 7 0 . 9 5 8 2 1 . 0 4 3 61 . 4 5 0 .7 1 9 6 2 . 2 8 6 3 1 . 7 7 6 1 1 . 2 8 7 2 0 . 9 4 4 8 1 . 0 5 8 41 . 5 0 0 .7 0 1 1 2 . 4 5 8 3 1 . 8 6 2 1 1 . 3 2 0 2 0 . 9 2 9 8 1 . 0 7 5 51 . 5 5 0 . 6 8 4 1 2 . 6 3 6 3 1 . 9 4 7 3 1 . 3 5 3 8 0 . 9 1 3 2 1 . 0 9 5 11 . 6 0 0 .6 6 8 4 2 . 8 2 0 0 2 .0 3 1 7 1 . 3 8 8 0 0 . 8 9 5 2 1 . 1 1 7 1. ......... . . . . . . . . . .. . ".." .. . - . . . . . _ ' 1 . 6 5 . 0 .6 5 4 0 ' 3 .0 0 9 6 . . . . . " '" 2 : r 1 5 2 1 : 4 2 2 8 0 .8 7 6 0 ' '. . . U 4 1 6 '1 . 7 0 0 .6 4 0 5 3 . 2 0 5 0 2 . 1 9 7 7 1 .4 5 8 3 0 . 8 5 5 7 . . 1 .1 6 8 61 . 7 5 0 .6 2 8 1 3 . 4 0 6 3 2 . 2 7 9 1 1 .4 9 4 6 0 . 8 3 4 6 1 . 1 9 8 21 . 8 0 0 . 6 1 6 5 3 . 6 1 3 3 2 . 3 5 9 2 1 .5 3 1 6 0 . 8 1 2 7 1 . 2 3 0 51 . 8 5 0 . 6 0 5 7 3 . 8 2 6 3 2 . 4 3 8 1 1 .5 6 9 3 0 . 7 9 0 2 1 . 2 6 5 5l .9 0 0 . 5 9 5 6 4 .0 4 5 0 2 . 5 1 5 7 1 .6 0 7 9 0 . 7 6 7 4 1 . 3 0 3 2. .' . . 1 . 9 5 0 , 5 8 6 2 4 .2 6 9 6 2 . 5 9 1 9 1 .6 4 7 3 0 . 7 4 4 2 1 . 3 4 3 72 . 0 0 0 . 5 7 7 4 4 .5 0 0 0 2 . 6 6 6 7 1 .6 8 7 5 0 . 7 2 0 9 1 . 3 8 7 22 . 0 5 0 . 5 6 9 1 4 . 7 3 6 3 2 . 7 4 0 0 1 .7 2 8 5 0 .6 9 7 5 1 . 4 3 3 72 . 1 0 0 .5 6 1 3 . 4 . 9 7 8 3 2 . 8 1 1 9 1 .7 7 0 5 0 .6 7 4 2 1 . 4 8 3 22 . 1 5 0 . 5 5 4 0 5 .2 2 6 3 2 . 8 8 2 3 1 . 8 1 3 2 0 . 6 5 1 1 1 . 5 3 6 02 . 2 0 0 . 5 4 7 1 5 .4 8 0 0 2 . 9 5 1 2 1 .8 5 6 9 0 .6 2 8 1 1 . 5 9 2 02 . 2 5 0 . 5 4 0 6 5 . 7 3 9 6 3 . 0 1 8 6 1 . 9 0 1 4 0 .6 0 5 5 l . 6 5 1 4

'. . 2 . 3 0 0 . 5 3 4 4 6 . 0 0 5 0 3 . 0 8 4 5 1 . 9 4 6 8 0 .5 8 3 3 1 .7 1 4 42 . 3 5 0 . 5 2 8 6 6 .2 7 6 3 3 .1 4 9 0 1 .9 9 3 1 0 . 5 6 1 5 1 . 7 8 1 02 . 4 0 0 .5 2 3 1 6 . 5 5 3 3 3 . 2 1 1 9 2 .0 4 0 3 0 .5 4 0 t 1 .8 5 1 42 . 4 5 0 . 5 1 7 9 6 .8 3 6 3 3 . 2 7 3 3 2 . 0 8 8 5 0 .5 1 9 3 1 .9 2 5 62 .5 0 _ 0 . 5 1 3 0 _ _ 7 j _ 2 5 0 _ _ _ ~ . 3 3 3 3 2 . 1 3 7 5 0 . 4 9 ~ 0 2 . 0 0 3 9 ---2 . 5 5 0 .5 0 8 3 7 . 4 1 9 6 3 . 3 9 1 9 2 .1 8 7 5 0 .4 7 9 3 2 . 0 8 6 52 . 6 0 0 . 5 0 3 9 7 . 7 2 0 0 3 . 4 4 9 0 2 .2 3 8 3 0 .4 6 0 1 2 . 1 7 3 32 .6 5 0 .4 9 9 6 8 . 0 2 6 2 3 . 5 0 4 7 2 . 2 9 0 2 0 . 4 4 1 6 2 . 2 6 4 72 . 7 0 0 . 4 9 5 6 8 . 3 3 8 3 3 .5 5 9 0 2 .3 4 2 9 0 . 4 2 3 6 2 .3 6 0 82 . . 7 5 . . 0.4918 . 8 ,6 5 6 '7 , , 3 ,6 1 1 9 . 2 . 1 9 1 \ 6 0 . 4 0 6 2 2 .4 6 1 72 . 8 0 0 . 4 8 8 2 8 . 9 8 0 0 3 . 6 6 3 6 2 . 4 5 1 2 0 . 3 8 9 5 2 .5 6 7 62 . 8 5 0 . 4 8 4 7 9 . 3 0 9 6 3 .7 1 3 9 2 . 5 0 6 7 0 . 3 7 3 3 2 .6 7 8 82 . 9 0 0 . 4 8 1 4 9 . 6 4 5 0 3 .7 6 2 9 2 . 5 6 3 2 0 . 3 5 7 7 2 . 7 9 5 42 . 9 5 0 . 4 7 8 2 9 . 9 8 6 2 3 . 8 1 0 6 2 . 6 2 0 6 0 . 3 4 2 8 2 .9 1 7 63 . 0 0 0 . 4 7 5 2 1 0 . 3 3 3 3 3 . 8 5 7 1 2 . 6 7 9 0 0 . 3 2 8 3 3 .0 4 5 6


8/31

-------------T ab la s d e ft uj o c om p re si ble 82 1

T ab la B .2 (Con t inuac i6n ) .R e lac ione s d e o nd a d e c hoq uen orm a l p ara u n g as p erfe cto ,k = 1.4 .

0 . 4 7520 . 4 7230 .4695

- .~. ~~-~~~_-::"-::_-_-'"I-.t-'i--~'~6Q--9 --I-tl:4096----3:98960 .46430 .46190 . 4 5960 . 4 5730 . 4 5520 . 4 5310 .45120 . 44920 . 4 474 0 . 4 4560 .44390 .44230 .44070 . 43920 . 43770 .43630 . 43500 .4336

3 .003 .053. .103 . 203 .253 .303 .353 . 403 .453 . 503 . 55

.. -- - - - '-- ' -.- . - - . . - . 3 ..603 .653 . 703 . 753 . 803 . 853 . 903 . 954 . 004 .05

10 .3333 3 .8 5 7 110 .68 63 3 .9 02511 .045 0 3 .9 46611 . 7 80012 .156312 . 538312 . 926313 .320013 . 719614 . 125014 . 5363

. - - 14 . 953315 . 3 76315 . 805016 .239616 .680017 .126317 . 5 78318 .036318 . 500018 . 9696

4 .03154 . 0 7234 .11204 .15074 . 18844 . 22514 .26094 . 2 9574 .3 29 6 .. ,.4 . 36274 . 3 9494 .42624 .45684 .48664 . 51564 . 54394 . 5 7144 . 5 983- - -- -4 .10 -- --0 .4 32 4 - 19 .4 45 0 4 .6245

4 .15 0 .43 11 19 .9 263 4 .65 004 .204 .254 . 304 .354 . 404 .454 . 504 . 554 .604 .654 . 704 . 754 . 804 . 854 .904 . 955 . 00

0 .4 29 9 20 .41330 .4 28 8 20 .9 063'0 .4 27 7 . ... 21 .4 05 00 .4 266 21 .9 09 60 .4 25 5 22 .4 2000 .4 245 22 .9 3620 .4236 23 .4 5 8 30 .42260 .42170 .42080 .41990 .41910 .41830 .41750 .41670 .41600 .4152

23 . 9 86224 . 520025 . 0 59625 . 605026 .156226 . 713327 . 2 76227 . 845028 . 419629 . 0000

4 .67494 . 69924 . 72294 . 74604 . 76854 . 7 9044 . 81194 . 83284 . 8 5324 . 8 7314 . 8 9264 . 91164 . 93014 . 94824 . 96594 . 9 8315 . 0000

2 . 67902 . 73832 . 7 9862 . 92202 . 9 8513 . 04923 .11423 .18023 . 24723 .31513 . 3 8393 .4 5 37 --3 . 5 2453 . 5 9623 .66893 . 74263 . 81723 . 8 9283 . 96944 .04694 .12544 .20484 . 2 8524 .36664 . 44894 . 53224 .61654 . 70174 . 7 8794 . 8 7514 . 96325 . 0 5235 .14245 . 23345 . 32545 . 41845 . 51245 . 60735 . 70325 . 8000

0 .32 8 3 3 .045 60 .314 5 3 .17 9 60 .30 12 3 .319 9

- 0"1 8 8 J- j:q6 6 70 .2 7 62 3 .62020 .264 5 3 .7 8 060 .2 5 33 3 .9 48 30 .2 425 4 .12340 .2 322 4 .30620 .22 24 4 .4 9 690 .2129 4 .69 600 .2 039 4 .9 03 60 .1953 . ._. ..- ' -5 . 1200 '0 .18 7 1 5 .345 60 .17 9 2 5 .5 8 060 .17 17 " 5 .8 25 30 .1645 6 .0 8 0 10 .15 7 6 6 .345 40 .15 10 6 .62130 .1448 6 .9 08 40 .138 8 7 .20 690 .1330 7 .5 17 20 .127 6 7 .8 3 9 70 .1223 8 .17 47 ..-0 . 11730 .11260 .10800 .10360 . 0 9950 . 0 9550 .09170 . 0 8810 . 0 8460 .08130 . 0 7810 . 0 7500 . 0 7210 .06940 .06670 .06420 .0617

8 .5 22 7 .8 . 8 840. . . . .9 . 2 5919 .648 4 .10 . 0 52210 .471110 . 905411 . 3 556 ,1 1.8 22 2 ,12.305. .7 . :12.8 0 6 i (13 . 325113 . 862014 .417714 . 9 92815 . 5 87816 .2032

-_._ ---- ..., ~_~. "t,"1. .... ....___.~' ' _


9/31

-- - -- -- --- --- ----.-- - .. --822 A pend ic e BT ab la B .3 . F lu jo v i sc o so M a fU D p I p * " T I 1 ' * p * l p = V I V * P o / p ~ad iabatic oea una tube ria de area

. c o ns ta n te para k = 1.4 . 0.00 .- - -.---~ 0 .0000, 00 00 1.2 00 0 . 00~ 0.05 28 0 .0203 21.9034 1.1994 0 .0548 11.5 9140.10 66.9 216 10 .9435 1.1976 0 .109 4 5 .82180.15 27 .9 320 7 .2866 !.l946 .-- 0.1639 3 .91030.20 - 14.5333 5 .4554 1.1905 0 .218 2 2 .96350.25 8 .4834 4 .3546 1.1852 0 .2722 2 .40270.30 5 .29 93 3 .6191 1.1788 0 .3257 2 .03510.35 3 .4525 3 .0922 1.1713 0 .378 8 1.7 7800.40 2 .3085 2 .6958 1.1628 0 .4313 1.59010 .45 1.5664 2 .3865 1.1533 0 .4833 1.44870 .50 1.0691 2 .1381 1.1429 0 .5345 1.33980 .55 0 .7281 1.9341 1.1315 0 .585 1 1.2549. .. . "_,,, .. ...... . . . . . . . . . . , , . . _ _ .. 0 .6 0 0 .4 90 8 ...... 1.7 63 4 __ . . 1 .1 19 4 .. . 0. 63 4 8 . .. . _ . .. 1. 1882 .- . . . . . . . . . ' . . ,-"0.65 0 .3246 1.6183 1.1065 0 .6837 1.13560 .70 0 .2081 1.49 35 1.0929 0 .7318 1.09440 .75 0 .1273 1.3848 1.0787 0 .7789 1.06240 .80 0 .07 23 1.289 3 1.0638 0 .825 1 1.038 20 .85 0 .0363 1.2047 1.0485 0 .8704 1.02070 .90 0 .0145 1.129 1 1.0327 0 .9146 1.00890 .95 0 .0033 1.0613 1.0165 0 .9578 1 .00211.00 0 .0000 1.0000 1.0000 1.0000 1.00001.05 0 .0027 0 .9443 0 .9832 1.0411 1.00201.10 0 .0099 0 .8936 0.9662 1.0812 1.00791.15 0 .0205 0 .8471 0 .9490 1.1203 1.01751.20 0 .0336 0 .8044 0 .9317 1.1583 1.03041.25 0 .0486 0 .7649 0 .9143 1.195 2 1.04681.30 0 .0648 0 .7285 0 .8969 . L 23n 1.06631.35 0 .0820 0 .6947 0 .8794 1.2660 1.08901.40 0 .09 97 0.6632 0 .8621 1.2999 1.11491.45 0 .1178 0.6339 0 .8448 1.3327 1.14401.50 0.1361 0.6065 0 .8276 1.3646 1.17621.55 0 .15 43 0 .5808 0 .8105 1.3955 1.21161 . 6 0 0 .1724 0 .5568 0 .7937 1.4254 1.25021.65 0 .1902 0 .5342 0 .7770 1.4544 1.29221.70 0 .2078 0 .5130 0 .7605 1.4825 1.33761.75 0 .2250 0 .4929 0 .7442 1.5097 1.38651.80 0 .2419 0 .4741 0 .7282 1.5360 1.43901.85 0 .2583 0 .4562 0 .7124 1.5614 1.49521.90 0 .2743 0 .4394 0.6969 1.5861 1.55531.95 0 .2899 . 0.4234 0.6816 1.609 9 1.61932 .00 0 .3050 0 .4082 0.6667 1.6330 1.68752.05 0 .3197 0 .3939 0 .6520 1.6553 1.76002.10 0 .3339 0 .3802 0 .6376 1.6769 1.8369

_ 2 .15 _ 0 .3476 .0 .3673 0.6235 1.6977 1.91852.20 0.3609 0 .3549 0 .6098 1.717 9 2 .005 02.25 0 .3738 0 .3432 0 .5963 1.7374 2 .09642 .30 0 .3862 0 .3320 0 .5831 1.7563 2 .19312 .35 0 .3983 0.3213 0 .5702 1.7745 2 .2953? 40 0 .4099 0 .3111 0 .5576 179 22 2 .40312A 5 0.4211 0.3014 0 .5453 1.8092 2 .51682 .50 0 .4320 0 .2921 0 .5333 1.8257 2.63672 .55 0 .4425 0 .2832 0 .5216 1.8417 2 .76302.60 0 .4526 0 .2747 0 .5102 1.8571 2 .89602.65 0 .4624 0.2666 0 .4991 1.8721 3 .035 9


10/31

- ------~ -- - - - - -T ab la s d e fl uj o c om pr es ib le 8 2 3

T ab la B J (Cont inuac ion) . Flujo Ma fU D p I p " TIP fJ* ip = v r v * P O / P bv isc o s o ad ia ba tic o e n u na tu be riad e a re a c on stan te p ara k = 1.4 . 2.65 O A 6 2 4 0 .2666 0.49 91 1.8721 3.0359

2.70 0.4718 0 .25 8 8 0.48 82 1.8 865 3.~8302 ' .75 0.4809 __ 0 .25 J~ ______ 0.47 76, 1.9005 3.3377. -- . . . . _ . . . . . . . - - .- - --------- 2.8 0 0.48 98 0 .2441 0.4673 1.9 140 3.50012.85 0.4983 0.2373 0.45 72 1.9 271 3.67072.90 0.5065 0 .2307 0 .447 4 1.9398 3.84982.95 0.5 145 0 .2243 0.4379 1.9521 4.03763.00 0.5 222 0 .2182 0 .4286 1.9640 4.23463.05 0.5296 0 .2124 0 .419 5 1.9 75 5 4.44103.10 0.5 368 0 .2067 0 .4107 1.9 866 4.65733.15 0.5437 0 .2013 0.4021 1.9 9 74 4.88383.20 0 .5 5 04 0 .1961 0.3937 2.0079 5.1210'3 '.2 5 . . .. .. . r r. 5 5 69 . - .~ - .. 0.1911 "0.3855 2.0180 5.36913.30 0.5 632 0 .1862 0.37 76 2.0278 5.62863.35 0.5 693 0 .1815 0.3699 2.0373 5.90003 .40 0 .5 7 52 0 .17 7 0 0 .3623 2.0466 : .6 .18373.45 0 .5 8 09 0 .17 27 0 .3550 2 .0555 6.48013.50 0.5864 0 .168 5 0 .347 8 2.0642 6.78963.55 0 .5 918 0 .1645 0.3409 2.0726 7.11283 .60 0 .5 9 70 0 .1606 0.3341 2 .08 08 7 .45 013.65 0 .6020 0 .1568 0.3275 2 .08 8 7 7 .8 020

- - - - .. - . ___ 3.7 0 0.6068 0 .15 31 0 .3210 2 .0964 8 .16913.7 5 0.6115 0 .1496 0.3148 2 .1039 8 .5 517 '" .. .3 .8 0 0 .6161 0 .1462 0.3086 2.1111 8 .9506 .'3 .85 0 .6206 0 .1429 OJ027 2 .1182 9 .36613 .90 . 0 .6248 . . 0 ,1 39 7 ., ... 0 .2 969 2 .1250 9 ':7 -9 90 3 .95 0.6290 0 .1366 0.2912 2 .1316 10 .2496 4 .00 0 .6331 0 .1336 0.28 57 2 .1381 10.7187

T a b la B .4 . F lu jo n o v isc oso M a 1 ' 0 /1 6 . p l p ~ < T I T ' " p *lp :: : V IV * P o l p T te n tu be ria c on tra ns fe re nc iade c alor para k = lA . 0 .00 0.0000 2.4000 0 .0000 0.0000 1 .2679 . .. . ( ,

0 .05 0.0119 2.3916 0 .0143 0 .0060 1.26510 .10 0.0468 2.3669 0 .0560 0 .0237 1.25910.15 0.1020 2.3267 0 .1218 0,0524 1.24860 .20 0 .17 36 2.2727 0.2066 0 .0909 1.23460 .25 0 .2568 2.2069 0.3044 0 .137 9 1.217 70.30 0 .3469 2 .1314 0.4089 0.1918 1.1985-0 :35 0.4389 2 .048 7 0 .5 141 0 .2510 1.17 7 90 .40 0.5 290 1.9 608 0 .6151 0 .3137 1.15660 .45 0.6139 1.8 69 9 0 .7 08 0 0 .378 7 1.13510.50 0 .6914 1.77 7 8 0 .79 01 0 .4444 1.11410 .5 5 0 .75 9 9 1.6860 0 .8 59 9 0,5100 1.09400,60 0 .818 9 1.59 5 7 0 .9 167 0 ,5 745 1.07 5 30.65 0 .8683 1.5 08 0 0 .9 608 0,6371 1.05820.7 0 0 .908 5 1.4235 0 .9 929 0.6975 1.04310.75 0,9401 1.3427 1.0140 0 .7 55 2 1.03010.80 0.9639 - 1.265 8- 1.0255 0.8101 1.01930.85 0.9810 1.19 31 1.0285 0.8620 1.01090.90 0 .99 21 1.1246 1.0245 0 .9 110 1.00490,95 0 .99 81 1.0603 1.0146 0 .9 569 1.00121.00 1.0000 1.0000 1.0000 1.0000 1.0000


11/31

8 2 4 A p en d i c e B ----T a b l a B . 4 (Continuaci6n) . ~ '1 l1 -~ - ' l'D f T ' o p l p * TfT* p * / p = V fV* . P o fp ~F lu jo n o v i s c o s e e n t u b e r f a t:"c o n t r a ns fe re n c ia d e c alo r ~ 1 .0 0 1 .0 0 0 0 1 . 0 0 0 0 1 . 0 0 0 0 1 . 0 0 0 0 1 . 0 0 0 0E a r a k = 1 . 4 . 1 . 0 5 0 . 9 9 8 4 0 . 9 4 3 6 0 . 9 8 1 6 1 . 0 4 0 3 1 . 0 0 1 2

1 . 1 0 0 . 9 9 3 9 O . 8 9 ( ) 9 0 . 9 6 0 3 - - = - - : - ~ - 1 .0 7 8 0 - _ : ' .-=-:.- 1 ' . 0 0 4 9 - --US 0 . 9 8 7 2 0 . 8 4 1 7 0 . 9 3 6 9 1.1131 1.01091 .2 0 - 0 . 9 7 8 7 - 0 . 7 9 5 8 0 . 9 1 1 8 1 . 1 4 5 9 1 . 0 1 9 4 -1 . 2 5 0 . 9 6 8 9 0 . 7 5 2 9 0 . 8 8 5 8 1 . 1 7 6 5 1 . 0 3 0 31 . 3 0 0 . 9 5 8 0 0 . 7 1 3 0 0 . 8 5 9 2 1 . 2 0 5 0 1 . 0 4 3 71 . 3 5 0 .9 4 6 4 0 .6 7 5 8 0 . 8 3 2 3 1 . 2 3 1 6 1 . 0 5 9 41 . 4 0 0 .9 3 4 3 0 .6 4 1 0 0 . 8 0 5 4 1 . 2 5 6 4 1 . 0 7 7 71 . 4 5 0 .9 2 1 8 0 .6 0 8 6 0 . 7 7 8 7 1 . 2 7 9 6 1 . 0 9 8 31 . 5 0 0 .9 0 9 3 0 .5 7 8 3 0 . 7 5 2 5 1 .3 0 1 2 1 .1 2 1 51 . 5 5 0 .8 9 6 7 0 .5 5 0 0 0 . 7 2 6 8 1 . 3 2 1 4 1 . 1 4 7 3

._ ~ . .~.~. . . _ . _ . '" 1 '.6 0- " . - - 0 .8 8 4 2 - . . . . 0 .5 2 3 0 ' ' 0 . 7 0 1 7 _ . 1 .3 40 3 . . " 1 . 1 7 5 61 . 6 5 0 . 8 7 1 8 0 . 4 9 8 8 0 . 6 7 7 4 1 . 3 5 8 0 1 . 2 0 6 61 . 7 0 0 . 8 5 9 7 0 . 4 7 5 6 0 . 6 5 3 8 1 . 3 7 4 6 1 . 2 4 0 2- 1 . 7 5 0 . 8 4 7 8 0 . 4 5 3 9 0 . 6 3 1 0 1 . 3 9 0 1 1 . 2 7 6 71 . 8 0 0 .8 3 6 3 0 .4 3 3 5 0 . 6 0 8 9 1 . 4 0 4 6 1 . 3 1 5 91 . 8 5 0 . 8 2 5 0 0 . 4 1 4 4 0 . 5 8 7 7 1 . 4 1 8 3 1 . 3 5 8 11 . 9 0 0 .8 1 4 1 0 .3 9 6 4 0 . 5 6 7 3 1 . 4 3 1 1 1 . 4 0 3 31 . 9 5 0 .8 0 3 6 0 .3 7 9 5 0 . 5 4 7 7 1 . 4 4 3 2 1 . 4 5 1 62 . 0 0 0 .7 9 3 4 0 .3 6 3 6 0 . 5 2 8 9 1 .4 5 4 5 1 .5 0 3 12 . 0 5 0 . 7 8 3 5 0 . 3 4 8 7 0 . 5 1 0 9 1 . 4 6 5 2 1 . 5 5 7 92 . 1 0 0 . 7 7 4 1 0 . 3 3 4 5 0 . 4 9 3 6 1 . 4 7 5 3 1 . 6 1 6 22 . 1 5 0 . 7 6 4 9 0 . 3 2 1 2 0 . 4 7 7 0 1 . 4 8 4 8 1 . 6 7 8 02 . 2 0 0 .7 5 6 1 0 .3 0 8 6 0 . 4 6 1 1 1 . 4 9 3 8 1 . 7 4 3 4.. . .2 ,25 0 .7 4 7 7 .0 . 2 9 6 8 " 0 .4 4 5 8 1 5 0 2 3 .1 . 8 1 2 8 .... '" . _ . " ~2 . 3 0 0 . 7 3 9 5 0 . 2 8 5 5 0 . 4 3 1 2 1 . 5 1 0 3 1 . 8 8 6 02 . 3 5 0 . 7 3 1 7 0 . 2 7 4 9 0 . 4 1 7 2 1 . 5 1 8 0 1 . 9 6 3 42 . 4 0 0 . 7 2 4 2 0 . 2 6 4 8 0 . 4 0 3 8 1 . 5 2 5 2 2 . 0 4 5 12 . 4 5 0 . 7 1 7 0 0 . 2 5 5 2 0 . 3 9 1 0 1 . 5 3 2 0 2 . 1 3 1 12 . 5 0 0 . 7 1 0 1 0 . 2 4 6 2 0 . 3 7 8 7 1 . 5 3 8 5 2 . 2 2 1 82 . 5 5 0 . 7 0 3 4 0 . 2 3 7 5 0 . 3 6 6 9 1 . 5 4 4 6 2 . 3 1 7 32 . 6 0 0 . 6 9 7 0 0 . 2 2 9 4 0 . 3 5 5 6 1 . 5 5 0 5 2 . 4 1 7 72 . 6 5 0 .6 9 0 8 0 .2 2 1 6 0 . 3 4 4 8 1 . 5 5 6 0 2 . 5 2 3 32 . 7 0 0 . 6 8 4 9 0 . 2 1 4 2 0 . 3 3 4 4 1 . 5 6 1 3 2 . 6 3 4 32 . 7 5 0 . 6 7 9 3 0 . 2 0 7 1 0 . 3 2 4 4 1 . 5 6 6 3 2 . 7 5 0 82 . 8 0 0 .6 7 3 8 0 .2 0 0 4 0 . 3 1 4 9 1 . 5 7 1 1 2 . 8 7 3 12 . 8 5 0 .6 6 8 5 0 .1 9 4 0 0 . 3 0 5 7 1 . 5 7 5 7 3 . 0 0 1 42 . 9 0 0 .6 6 3 5 0 .1 8 7 9 0 . 2 9 6 9 1 . 5 8 0 1 3 . 1 3 5 92 . 9 5 0 . 6 5 8 6 0 . 1 8 2 0 0 . 2 8 8 4 1 . 5 8 4 3 3 . 2 7 6 83 . 0 0 0 .6 5 4 0 0 .1 7 6 5 0 . 2 8 0 3 1 . 5 8 8 2 3 . 4 2 4 53 . 0 5 0 .6 4 9 5 0 .1 7 1 1 0 . 2 7 2 5 1 . 5 9 2 0 3 . 5 7 9 03 . 1 0 0 .6 4 5 2 0 .1 6 6 0 0 . 2 6 5 0 1 . 5 9 5 7 3 . 7 4 0 8- - 3 ] 5 - 0 . 6 4 1 0 - - - 0 .1 6 1 2 0 . 2 5 7 7 1 . 5 9 9 2 3 . 9 1 0 1 - ----3 . 2 0 0 .6 3 7 0 0 .1 5 6 5 0 . 2 5 0 8 1 . 6 0 2 5 4 . 0 8 7 13 . 2 5 0 . 6 3 3 1 0 . 1 5 2 0 0 . 2 4 4 1 1 . 6 0 5 7 4 . 2 7 2 13 . 3 0 0 . 6 2 9 4 0 . 1 4 7 7 0 . 2 3 7 7 1 . 6 0 8 8 4 . 4 6 5 53 . 3 5 0 . 6 2 5 8 0 . 1 4 3 6 0 . 2 3 1 5 1 . 6 1 1 7 4 , 6 6 7 43 . 4 0 0 .6 2 2 4 0 .1 3 9 7 0 . 2 2 5 5 1 . 6 1 4 5 4 . 8 7 8 33 . 4 5 0 . 6 1 9 0 0 . 1 3 5 9 0 . 2 1 9 7 1 . 6 1 7 2 5 . 0 9 8 43 .5 0 0 .6 1 5 8 0 . 1 3 2 2 0 . 2 1 4 2 1 . 6 1 9 8 5 . 3 2 8 03 . 5 5 0 .6 1 2 7 0 .1 2 8 7 0 . 2 0 8 8 1 . 6 2 2 3 5 . 5 6 7 63 . 6 0 0 . 6 0 9 7 0 . 1 2 5 4 0 . 2 0 3 7 1 . 6 2 4 7 5 . 8 1 7 33 . 6 5 0 . 6 0 6 8 0 . 1 2 2 1 0 . 1 9 8 7 1 . 6 2 7 1 6 . 0 7 7 6


12/31

- ------ - Tabl as d e f lu jo c omp re si b1 e 8 2 5T abla B .4 (Con t i nuac ion ) . Ma To / n p / P ' ~ TIT~ p'~/p = VIV" PolptF lu jo n o viscose en tuberfacon transferencia d e c alo r 3.65 0.6068 0.1221 0.1987 1.6271 6.0776para k = 1 0 4 . 3.70 0.6040 0.1190 0.1939 1.6293 6.34883.75 0.6013 0.1160 0.1893 1.6314 6.6314- L6335-..r..---.,.. ..--___.. ____ .8 0 ~g,7 -1} .J .PJ.--_OJR 4& -- --- 6.9256----- -- 3.85 0.5962 0.1103 0.1805 1.6355 7 .2318- - 3.90 0.5937 0.1077 0.1763 1.6374 7 .5 505

3.95 0.5914 0.1051 0.1722 1.6392 7 .8 8204.00 0.5891 0.1026 0.1683 1.6410 8.2268

T abla B .S . F un cio n d e e xp an si6 nsupe rson i ca P randt l-Meye r para k= lA . . ... _ . .... " '"

Ma w , grades Ma w, grades Ma w, grades Ma w , g rados. L O a . ,".. . 0.00 . . . ' _ ' _ .. . _ . - .. . - _ .. ,.. ,," .." - .~. ' . . . . '_ .. _ .. . -- . ." ~, . . .. _ . .".. . . , _ M .1.05 0.49 3.05 50.71 5.05 77.38 7 .05 91.23.1.10 1.34 3.10 51.65 5.10 77 . 84 7.10 91.491.15 2.38 3.15 52.57 5.15 78.29 7 .15 91.751.20 3.56 3.20 53.47 5.20 78 . 73 7.20 "92.001.25 4.83 3.25 54.35 5.25 79.17 7.25 92.241.30 6.17 3.30 55.22 5.30 79.60 7 .30 9 2.491.35 7 .56 3 .35 56.07 5.35 80.02 7.35 92.731.40 8.99 3.40 56.91 5.40 80.43 7.40 92.971.45 10.44 3.45 57 . 73 5.45 80.84 7.45 93.21-1.50 1[9-1- . . "3 .50 5 8 .53-- . 5 .50 81.24 7.50 93.441.55 13.38 3.55 59.32 5.55 81.64 7.55 .", 93.67 .1.60 14 .8 6 3 .60 60.09 5.60 82.03 7.60 93.901.65 16.34 3.65 60.85 5.65 82.42 7.65 94.121.70 " 17.81 ' no .. . . 6 1 .6 0 ." 5.70 . E 2.8 0 ....-. 7.70 9~.341.75 19.27 3.75 62.33 5.75 83.17 7.75 94.561.80 20.73 3.80 63.04 5.80 83.54 7.80 94.781.85 22.16 3.85 63.75 5.85 83.90 7.85 95.001.90 23.59 3.90 64.44 5.90 84.26 7.90 95.211.95 24.9 9 3 .9 5 65.12 5.95 84.61 7.95 95.422.00 26.38 4.00 65.78 6.00 84.96 8.00 95.622.05 27.75 4.05 66.44 6.05 85.30 8.05 95 . 832.10 29.10 4.10 67.08 6.10 85.63 8.10 96.03 ;2.15 30.43 4 .15 67 .7 1 6.15 85 . 97 8.15 96.232.20 31.73 4 .20 68 .33 6.20 86.29 8.20 96.432.25 33.02 4.25 68.94 6.25 86.62 8.25 96.632.30 34.28 4.30 69.54 6.30 86.94 8.30 96.822.35 35.53 4.35 70.13 6.35 87.25 8.35 97.012.40 36.75 4.40 70.71 6.40 87 . 56 8.40 97.202.45 37.95 4.45 71.27 6.45 87 . 87 8.45 97.392.50 39.12 4.50 71.83 6.50 88.17 8.50 97 . 572.55 40.28 4 .5 5 72 .38 6.55 88.47 8 .55 . 97 . 762.60 41.41 4.60 72.92 6.60 88 .76 8.60 97 . 942.65 42.53 4.65 73.45 6.65 89.05 8.65 98.122.70 43.62 4.70 73.97 6.70 89.33 8.70 98.292.75 44.69 4.75 74.48 6.75 89.62 8.75 98.472.80 45.75 4.80 74.99 6.80 89 . 89 8.80 98.642.85 46.78 4.85 75.48 6.85 90.17 8.85 98 . 812.90 47.79 4.90 75~97 6.90 90.44 8.90 98 . 982.95 48.78 4.95 76.45 6.95 90.71 8.95 99.153.00 49.76 5.00 76.92 7.00 90.97 9.00 99.32

:' (.


13/31

_ ._ _ ~ 2 6 A pend ic e B

F i gu r a B . I. N iim ero de M ac haguas abajo de una onda dec he qu e o bli cu a p ara k = 1.4.

o

O n d a d e c h o q uedebil

4. 0

3. 0

3 5402. 04 5 50

1 . 0

1 . 0 4. 0

. .


14/31

-..,._._ ..-.--.~--,

F ig ur a B .2 . R e la ci on d e p re si on esaguas aba jo de una onda dec h oq u e o blic ua p ar a k = 1 .4 .

T ab la s d e ft uj o c om p re si ble 8 2 7

P 2P1

4 5

" ,

8 .0 - : :

"7 .0 -On da de c h oq ue f ue rt e

1 . 0 1 . 0

.',.


15/31

A Ie n_;__----t--__.- - a e - t f l f - P S - ~ p - r o n v p . r ~ i on -_ __ .. ,,_ _ _ _ _ _. 'VI && , _ ... "-J.& V&.&

. .

Du ra nt e e ste p erio do d e tra nsic i6 n b ay u na n ec esid ad c on sta nte d e re aliz ar c on v ersio ne se ntre u nidade s britanic as y e l S I (v ease T abla 1.2 ). A lgunas c onv ersione s adic ionale sson dadas aq uf, L os fac tores de conv ersion se m uestran en la pag, x iv .

.. t

Longitud V o l u m e n1 it = 1 2 ' in = 0 .3048 m Ift3 = 0 .0 28 31 7 m31 mi= 5280 ft = 1609 .344 m 1gal americano = 231 in3 = 0 :OO37854 "m31 m i li a n au ti c a (nmi ) = 60 76 ft = 1852 m 1 L = 0 .0 01 m3 = 0 .0 35 31 5 f r 1 yd = 3 ft = 0 .9 14 4 m 1 ooz a f iu id a ame ri c an a = 2 .9574 X 10 -1 m 31 angs t rom (A ) = 1. 0 X l O - , om 1 qu ar t ( q t) ame ri c an a = 9 .4635 X 1O -4m 3

Masa A r e a1 s lu g = 3 2 .1 74 Ibm = 14 .594 kg 1 f e : . : : . .0 92 90 3 m21 Ib m = 0 .4 536 kg 1 m i2 = 2 .78784 X 10 1 fe = 2 .59 X 106m l1 t on e la da ame ri c an a = 2 00 0 Ibm = 907 .185 k g 1 acre = 43 ,560 r t 2 = 4 04 6.9 m21 tooe l ada = 1000 kg 1 hec tarea (ha) = 10 ,0 00 m2

Velocidad A ce le racien1 ftIs = 0 .3 04 8 m ls 1 f t Is 2 = 0 .3048 mfsl1 mi/h = 1 .4 66 66 6 fils = 0 .4 47 04 m ls1 le n = 1 runi/h = 1 .6 8 7 8 f il s = 0 .5144 m ls

J . < ' lu j o m a s i c o Flujo vo lumet r ico ---I s lu g/ s = 1 4 .5 9 4 kg ls 1 ga l/m in = 0 . 002228 f e / s = 0 .0 63 09 L Is1 l bm l s = 0 .4 536 kgls 1 X 106 gal/dfa = 1.5472 ft3 / s = 0 .0 43 81 m3 /s

Presion Fuerza1 lbflf t2 = 4 7.8 8 P a 1 lbf =4 .4 48 22 2 N = 16 oz1 lbf / in2 = 1 4 4 I bf /f t2 = 6895 Pa 1 k gf = 2 .2 0 46 Ib f = 9 .80665NI atm = 2116. 2 lbf lf e = 1 4 .6 9 6 l bf /i o2 = 1 t on e la da ame ri c an a = 2 00 0 Ibf1 01 ,3 2 5 P a 1 d in a = 1. 0 X 10 -1

1 inR g (a 2 0C) = 3375 Pa I onza (oz) = 0 .2 78 01 N1 bar = 1.0 X IO 'P a .\

8 2 8


16/31

F ac tore s d e c onv ersion 8 29

Energfa Potenc ia

.. 'j:

1 ft lb f = 1 . 3 5 5 8 2 J1 B tu = 2 5 2 ca l = 1 0 5 5 . 0 5 6 J = 7 7 8 . 1 7 f t lb f1 k il o v a t i o h o r a ( k W h ) = 3 .6 " X 1 0 6 J

1 hp = 5 5 0 ft . lbf/s = 7 4 5 . 7 W1 ft . I b f / s = 1 .3 5 5 8 W

P e so e s pe c if ic o- - .. ---- - - - - _ .~ ~~~~~:=:~-~~~=====--;..;;.;--:;,;;;-=-+------------

Densidad1 I b f l t t 3 = 1 5 7 . 0 9 N /m 3 1 slug/t t ' = 5 1 5 . 3 8 kglm 3

1 lbmlfr = 1 6 . 0 1 8 5 kg/nr'1 g lc m3 = 1 00 0 k g/m 3

V lscosidad V iscoc idad c lnem atic a1 slugl(ft . s) = 4 7 . 8 8 kgl(m . s)1 po ise (P }= T g !( c in . s f= O .T R g !( in :" sr' _ '"

1 f t 2th = 0 . 0 0 0 0 2 5 8 0 6 m 2 /s. .. r - s t o k e s " ( S t ) = = I cm 2/s ' ': 0 . 0 0 0 1 r: 02/S ' ' ' - '

Tc = ~ ( T F - 3 2 )L e ct ura s d e e sc ala s d e t em p er at ura T K = Tc + 2 7 3 . 1 6R = T p + 4 5 9 . 6 9donde los subind ic es F , C , R Y K se re fie ren a las le cturas en las esc alas de F ah re nh eit , C elsius, R ank ine )K e l v in , r e sp e c t i v am e n t e .

Ca lo r e s pe c lf ic n 0 censtan te de gas" Conduc tiv tdad U \rm ica"1 ft . J b f/ ( s l u g . O R ) = 0 .1 6 7 2 3 N m / ( k g . K )1 B tu/flbm : O R ) = 4 1 8 6 . 8 J/(kg' K )

1 B tu I ( h . f t . O R ) = 1 . 7 3 0 7 W /(m . K )

. * A u nq ue la s e sc ala s d e t em p er atu ra a bs ol uta ( K elv in ) y C elsiu s te ng an d ife re nte p un to In rc ia l; e l i nte rv ale e s d e l m ism o ta-m afic : I g ra de K elv in = I g rad o C elsiu s. D el m ism o m od o p ara las e sc alas ab so lu ta s n o rn etr ic as (R an kin e) y Fahrenhe i t ;I g rad o R an kin e = I g ra de F ah re nh eit . E s h ab itu al e xp re sa r d ife re nc ia s d e te rn pe raru ra s e n u nid ad es d e te mp eratu rasabsolutas .

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17/31

-I -p e c

-----t--Eooaeiones-de - m o v i m i e n t oe n c o a r d e n a d a s c i l i n d r i c a s -

L as e cuac ione s de m ov im ie nto de un ftuido ne wtoniano inc om pre sible c on / 1 - , A y e cons-ptan te s se re co ge n aq ui e xp re sad as e n c oo rd en ad as c ilin dric as ( r , 8 , z ) , qu e e st an r ela ci on a-d as c on la s c oo rd en ad as c art es ia na s (x , y , z), com o indic a la Figura 4 .2 :

x = r cos 8 y = r sen 8 z = zL as c om pone nte s de v eloc idad son v r l v a Y v . Aqu i e st an la s e cu ac io ne s:. . . . . " . z . . .Continuidad: 1 a 1 a a--(rv) + --(v) t -(v) = 0

r a r r r a a e a z Z(D.2)

De ri va da t empora l c on ve ct iv a:a 1 a aV''V=v-t-v-tv-r a r r 0 a e Z a z (DJ)

Operador Lap la c iano:(DA)

L a ecuac i6n de cantidad de m ov im iento en la com ponente radial r :a V r 1 2 1 a p ( 2 v r 2 a v e )- t (V . 'V )v - -v = - - - t g + II 'Vv - - - --, a t r r e p a r r r r 2 r2 a a (D .5 )

L a e cuac i6n de c antidad de m ov im ie nto e n la c om pone nte ac im utal e :a V e 1 1 a p ( 2 v e 2 a v r)- + (V . ' ' 1 ) V e + - V r V I J = - - - + g o + v 'VV IJ - 2' +2:-a t r p r a a r r a e (D.6)

H i l i


18/31

E c ua c io ne s d e mo v im i en to e n c o or de na d as c ili nd ri ca s 8 31L a e cuac i6n d e c antidad de m ov im ie nto e n la dire cc i6 n ax ial z :

a V z 1 a p 2- + (V . V ') v, = - - - + g + v 'i/ v ,a t - p a z z - (D .7 )

[ a T 1 2 2 2 ? 2 ? 2pC p a t + (V , ' i / )T = A il T + , u [ 2 ( E r r + E( j8 + E~ ) + E ( j z + e ; z + E ~ ] (D .8 )donde a V rE r r =a r 1( a V f ) )E f ) f ) = - - + V rr a o. . . - . . . - . _ a v ~ - - - '

E =-Z Z a z

. . ._ . 1 a v z ' a v ~E =-+-8z r a e a z (D . 9 )B u , a v zE=-+-r z a z a r 1( a v r ) a V ( jEr9 = - - - V ( j +-r a e a r

Compo ne nt es e sfu erz os v is co so s:- - _ . . - 1 ' r r = 2 , u E r r

1 ' r z = , u E r z (D .1 0) ,:. /Compo ne nt es ve lo ci da d a ng ula r:

1 a v z a V ( j2w =---r r a e a za V r a v z2 W ( j = - - - a t . a r (0 .11 ) :

I.1 a 1 a V r2w = --(rv) ---z r a r 8 r a e


19/31

-e - E - - - - - - - - -

- -I n t r c d u c c i o n

~I I , . . . . .

EES e s u n a cr on imo d el s oftw are En gi ne er in g Equa ti on S o lv e r ( R es olv e do r d e e cu ac io ne se n la in ge ni crfa) . L a f u n c i o n basic a proporc ionada por E ES e s la soluc i6n num eric s dee cu ac io ne s a lg eb ra ic as n o li ne ale s y e cu ac io ne s c ti fe re nc ia le s. A d ema s, EES i nc orp orafu nc io ne s d e P I' p iedades te rmod inamica s y d e t ra ns po rt e p ara mu ch os f lu id os , i nc lu ye n-do el agua, e ire s co y a ir e humedo, r ef ri ge ra nt es , g as es d e c ombust i6 n, y o t ros . E1 usua riopuede a r i a d i r d at os d e p ro pi ed ade s ad ic io nale s. L a c om bi nac i6 n d e la c ap ac id ad d e re so -lu ci 6n d e e cu ac io ne s y la am plia b ase d e d at os re lac io nad os c on 1 a in ge nie rfa h ac en q ueE ES e a una h erram ie ntaw m uy v aliosa.

S e fac ili ta u na lic enc ia p ara EE S p ara t od os lo s d ep art am en to s d e i nsti tu cio ne s e du ca-c io na le s q u e u ti li ce n e st e li bro d e McG raw -H i ll. S i n ec e si ta m a s i nf ormac ion, c ont ac t e c ons u r ep re e nt an te lo ca l d e McG raw -IJ ill, llam e a ll-8 0 0 -~ 3 8 -3 9 8 7 , 0 v is it e la p ag in a w e bhttp : / /www.mhhe .com. La v e rs io n c omer ci al 0 p ro fe si on al d e EES p ue de o bt en ers e d e

F-Cha r t S o f t w a r eBo x 4 44 04 2Madison, W I 53744Te le fo no : ( 60 8 ) 8 3 6-8 5 31F ax : ( 60 8 ) 8 3 6-8 5 36http://fchart.com e-mail: info~fchar t.com I

I n f o r m a c io n Probab1em ente e l program a E ES este instalado en la red de orden adore s de su depar-tam ento. A dem as, e1 acuerdo de licenc ia para uso de E ES perm ite a los estudiantes yprofe sorado de un de partam ento partic ipante e n e l program a doc ente c opiar e 1 p rogra-rn a p ara u so e duc ac io nal e n s us p ro pi os ord en ad ore s p erso nale s. S olic ite in fo rm ac i6 nd et al1 ad a a s u i ns tru ct or.. Para empezar EES , pulse dos veces sobre e l icono del programa mostrado a la iz-quierda 0 b ie ns ob re c ualq ui er arc hiv o c re ad o p or EE S q ue !le va as oc iad o la e xte nsi on d earc hiv o .E E S. Iam bi en p ue de in ic iar e l p ro gram a d esd e la li ne a d e m an do s R u n d el m e nuS t a r t i nt ro du c ie ndo EES y puls ando en e1bo ton O K . EES empi ez a mo st ra nd o e n p an ta llau na v en tan a d e d ialo go q ue m ue st ra in fo rm ac io n so bre e l p ro ce so d e re gist ro , e l m irn erod e v ersi6 n d el p ro gram a y o tra i nfo rm ac i6 n. P ulse e l b oto n O K y la v ent an a d e d ialo goanterior desapare ce ra .

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20/31

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E a u a t i o n sA r r a y sS o l u t i o nR e s i d u a l sP a r a m e t r i c T a b le s- F ' i o t \ ~ I ' i ' r l d ' o v i f s ' - ' - " " . . . . . .L o o k u p T a b le sI n te g ra l T a b l e sD i a g r a m W i n d o w sF o r -m a t te d E q u a t io n sD e b u g 'V V i n d o wF u n c tio n s a n d P r o c e d u r e s- . .-.F l u id F ' r o p e t i y I n f o r m a t i o nM a t he m a t i c a l F u n c t i o n sS t r in g F u n c ti o n sT h e rm o p h y s i c a l' F u n c ti o n sI n t e rn a l F u n c t io n sI n te rn a l P r o c e d u re sL i b ra r y f ile sE x t e r n a l F u n c t i o n sE x t e r n a l P r o c e d u r e sI F . T H E N - E L S EL O O f < U PU n i t C o n v e rs io n s~ A o d u le s a n d S u b p r o g ra m sM u l t i p le E x te rn a l R o u t i n e sE E S F ile T ip es

Introducc i6n al E llS HI

M e n u C o m m a n d sF i le M e n uE d i t M e n uS e a rc h M e n uO p ti o n s M e n uC a lc u la te M e n u.' "., _.. _..... _ "w, ..._ ...... ........ ~.. .' ~....... , _....T a b le s M e n uP lo t t v le n lJW i n d o w s M e n uH e lp M e n uT e x t b o o k M e n u

I n p u t / O u tp u tS t r i n g V a r i a b l esC o m p le x N u m b e r sE '~ r o p e a n N L U n e r i c a l F o r r n e . iE x p o r t i n q r e s u t f s t o ; f d i s k f i r e .L o o k u p F ile F o rm a tsA r r a y ' R a n g e N o t a t i o nC o n s t a n t sP l o t sL a T eX /P D F R e p o r t g e n e r a to rGr e ek a n d s pe c ia l s v m b o l s

. .

S p e c ia l T o p ic s P r o f e s s io n a l V e r s io nD i r e c t i v e s D i f f e re n c e s f r o m C o m m e rc ia l \ / e r s i o nU n i t C h e c k i n g H o t a r e a s a n d C h i ld D i a g r a m \ N i n d o \ ' \ l sD i f f e re n tia l / I n t e g ra l E q u a t i o n s M a c r o F i l e sC o n f i g u r a t i o n O p t i o n s D y n a m ic D a t a E x c h a n g eC u r v e F itt ing -- . --:- D i s t r i b u t a b l e - P r o g r a m s2 - D I n te r p o la t i o n L ih r a r y M a n a g e r

- I 3 - D pIOt~3------ - -- F o r m a t te d t e x t i n D i a g r a m W i n do w sI D e b u g g in g H e lpF igu ra E .1. Indic e de ay udad el E E S.


21/31

--.----------------- 8 3 4 A pendic e E

S e p u ed e a c c e d e r a l a A y u d a D e ta l l a d a e n c u a l q u i e r p u n to d e l a e j e cu c i o n d e l a a p l i c a c io n- - - - E E S . P re s i o n a n d o l a t e c l a F l s e m u e s t r a u n a v e n t a n a d e A y u d a . r e l a c i o n a d a c o n l a v e n t a n a

. a c t i v a . P r e s i o n a n d o e l b o r o n C o n t e n ts s e p r e s e n ta e l H e lp I n d e x m o s t r a d o e n l a F ig u r a E .l .A I p u l s a r s o b r e u n a p a l a b ra s u b r a y a d a ( m o s t r a d a e n c o lo r v e r d e e n e l m o n i t o r) s e l e p ro p e r-c io na ra la a yu da re la ci on ad a c o n e s e l e m a . ~-'-7- - --_._ --- . ~-

L o s m a n do s d e E E S s e d is t r i b u y e n e n tr e o n c e m e n ti s d e s p le g a b le s . A c o n t i n u a c i 6 n s e d au n b re v e r e s u m e n m o s t r a n d o l a s f u n c i o n e s d e c a d a m e n u :

A l m e n u S y s t e m s e a c c e d e p re s i o n a n d o s o b r e e l i c o n o d e E E S s i t u a d o e n c im a 'd e l m e n uF i l e . E I m e n u S y s t e m n o e s u n m e n u p r o p i o d e E E S , s i n o m a s b i e n u n m e n u p r o p i od e l o s s i s t e m a s o p e r a t i v o s W i n d o w s . E n e l s e e n g l o b an m a n d o s q u e p e r r n i t e n m o v e r ,d i m e n s io n a r y a c t i v a r 0 d e s a c ti v a r l a i n t e rf a z d e l a a p li c a c i6 n .

E n e l m e n u F i l e s e e n cu en tr a n l a s o rd e n e s p a r a c a rg a r , u n i r y g u a r d a r l o s a r c h iv o s d e t r a b a j oy l i b re r i a s , e im p r im i r . E l c o m a n do L o a d T e x tb o o k e n e s t e m e n u l e e e l d is c o q u e a c o m -p a f i a a e s t e l i b r o y c r e a u n n u e v o m e nu a l a d e r e c h a d e l m e n u H e l p p a r a t e n e r u n a c c e s or a p id o a l o s p ro b l e m a s E E S q u e c o n t i e n e e s t e l i b ro .

E l m e n u E d i t c o n t i e n e l o s c o m a n do s d e e d ic i o n d e c o rt a r , c o p i a r y p e g a r i n f o r m a c i6 n .E l m e n u S ea r c h c o n t i e n e l o s c o m a n d o s d e F in d y R e p la c e ( b u sc a r y r e em p la z a r) p a r a u s o

d e n tr o d e l a v e n ta n a E q u a ti o n s .E l m e n u O p t i o n s c o n t i e n e l o s c o m a n d o s p a r a i n ic i a l i z a r e l v a l o r d e l a s v a r i a b le s , establecer

e l r a n g o d e v a r i a c i o n d e d ic h a s v a r i a b le s , e l e g ir e l s i s t e m a d e u n i d ad e s , f i j a r v a l e e s p o rd e f e c t o y p r e f e r e n c i a s . T a m b i e n d is p o n e d e u n a o rd e n p a r a m o s t r a r e n p a n ta l l a i n fo rm a -c i6 n s o b r e l a s f u n c i o n e s i n e o rp o r a d a s y l a s d e f i n id a s p o r e l u s u a r i o .

E I m e n u C a l c u l a t e d i s p o n e d e l o s c o m a n d o s p a r a c o m p ro b a r , d a r f o r m a t o y r e so lv e r e ls i s t e m a d e e c u ac i o n e s . T a m b i e n i n c l u y e u n a o rd en p a r a e h eq u e a r l a s u n i d ad es d e l a se c u a c i o n e s .

E l m e n u T a b le s c o n t i e n e c o m a n d o s p a r a i n tr o d u c i r y m o d if i c a r l o s v a l o re s d e l a P a ra m e t r i cT ab l e y l a L o o k u p T ab l e y p e r m i t e a d em a s h ac e r r e g re s i 6 n l i n e a l c o n l o s d a t o s d e l a sv a r i a b le s . L a P a r a m e tr i c T a b le , q u e e s s im i l a r a u n a h o j a d e c a l c u l o , p e r r n i t e q u e e lc o n ju n t o d e e cu a c io n e s s ea r e su e l t o d e u n m o d o r e p e ti t i v e m i e n t r a s s e v a r i a n l o s v a l o re sd e u n a 0 m a s v ar i a b le s . E l c o rn an d o L o o ku p T a b le g u a r d a d a t o s s u rn in is t r a d o s p o r e lu s u a r i o , q u e p u e d e n s e r i n te rp o l a d o s y u s a d o s e n l a s o lu c i 6 n d e l s i s te m a d e e cu a e io n e s.

E I m e n u P l o t s e o n t i e n e c o m a n d o s p a r a p re p a r a r u n n u e v o g r a f i c c d e d a t o s t o r n a d o s d e l aP a r a m e t r i c , L o o ku p , A r r a y , 0 I n t e g r a l T a b le s , 0 m o d i f ic a r u n a g r a f ic a e x is te n te . T a m -

- - - b ie n s e f a c i l i t a l o s e o m a n do s p a r a r e a l i z a r e l a j u st e d e c u rv as y e r e - a i -g ra f i c a s d e p ro p i e -d a d e s t e r m o d i n a m i c a s.

E l m e n u W in d o w s p r o p o re i o n a u n m o d o e f i c a z d e v is u a l i z a r l a s v en ta n a s s u p e r p o n ie n d o la so o rg an iz a n d o la s e n e l e n to m o d e t r a b a j o .

E l m e n u H e l p p e r n n t e e l a c c e s o a l a d o c u m e n ta c i 6 n d e a y u d a o n l i n e .E I m e n u F lu i d M e c h a n i c s p ro p o r c i o n a a c c e s o a l a s s o l u c i o n e s E E S d e l o s p ro b l e m a s d e

e s t e l i b r o . .


22/31

Introducc i6n a l EES 835U na capac idad basica de E ES es la soluc i6n de un sistem a de ec uac ione s algebraico noline al. P ara de mostrar e sta c apac idad, inic ie E ES e in trod uz ca e ste p roble ma se nc illo e nl a v e n ta na E q uatio ns W in do w :

L a e ntrada d e datos se re aliz a de fo rm a analoga a u n proc esador de te xtos c ualq uie ra . L asreglas q ue se h an de tene r en cuenta son:1 . ' No se d is ti ng ue ' e ntre le tra sri ia yti sc ula s y mim is cu la s. EES pOdr f( opC io n alm e n te )' "" '

c am biar la c aja de la v ariable p ara q ue c oin cida c on la form a prim era e n q ue ap are ci6l a va ri ab le .

2 . P ue de n introdu cirse lin eas y e sp ac io s e n b lan co p orq ue so n ig no rad os.3 . L os c om entarios de be n e nc errarse e n H av es { } 0 e ntre c om illas " " . L o s c om e ntario spueden abarc ar las lineas q ue sea necesario. L os com entarios entre H av es puedenanidarse , e n c uy o c aso tan solo e l c onjun to de llav es m as e xte rno e s re co noc ido . L osc om e ntario s e ntre c om illas se ran m o strad os e n la v en tan a F o rm a tt ed E q u at io ns .

( L os n o m b r e s de h is v ariable s deben em pezar por una le tra y estar c onstitu idos por ,c ualq uie r c arac te r d el te clad o, e xc ep tu an do lo s c arac te re s ( ) , I * / + - 1\ { } : " ; L as" /m atric es se id en tific an p or lo s c orc he te s q ue ro de an e l In dic e 0 los fndice s de la m atriz .(p or e je mp lo , X [5 ,3 ] ) . L a lo ngitud m ax im a de la v ariab le es de 3 0 c arac te re s.

5 . Puede introduc irse m as de una e cuac ion por line a si e stan separadas por un punto ycom a (;) . L a longitud m ax im a de linea es de 25 5 carac te re s.6 . E l sfrnbolo (") 0 * * se u sa p ara in dic ar e leva do a .

7 . E l orden en q ue se introducen las ecuac iones no im porta .8 . L a posic ion de v ariable s e incogn itas en la ecuac ion no im porta.. -S i 1 0 de se a, pu ede v isualiz ar las e cuac io ne s e n no tac io n m ate matic a se le cc ionan do e r. i :comando F orm a tte d E q ua tio ns de l m enu W i n d ow s 0 de l boron situado debajo de Iab arra d e m e nu s. l t 3 J t

y

X I n (X ) = I

S e le c ci on e . e l c omando So l ve de la barra de m enus C alcu late 0 p re sio ne F 2 . A p are c erau na v en tan a d e d ialo go in dic an do el prog re so d e la soluc ion, F in ali za do s lo s c alc ulo s, e lb ot6 n c am biara d e Abo r t a Con t inue .


23/31

P u ls e e n e l b o t o n C o n t i n u e . L a s o lu c i o n a e s t e s i s t e m a d e e c u a c i o n e s s e r a m o s t r a d a .

X = 1 .4 6 7 Y = 0 . 8 2 5 5

C a lc ula tio n tim e:: ,0 s ec

P r ob le m a e je m p lo : f r i c cio ne n u n a t u b er ia

P e rm i t a n o s a h o ra r e so lv e r e l P r o b l e m a P 6 . 5 5 d e l l i b ro , p a r a u n a t u b e r i a d e f u n d ic i 6 n ,c on e l f i n d e i l u s t r a r l a s c ap a c id ad e s d e l p ro g r a m a E E S . E s t e e je m p lo , s i n E E S , r e q u e ri r f ad e u n p ro ce s o i t e r a t i v o p a r a c a l c u la r e l m i m e r o d e R e y n o l d s , l a v e l o c i d ad y e l f a c to r d ef r i c c i o n , u n a t a re a a b ru m a d o r a . E I p ro b le m a d ic e :

P 6 .S 5 C o m o s e m u e s t r a e n l a F ig u ra E .2 , l o s t a n q u e s 1 y 2 e o n ti e n e n a g u a a 2 0 C .L a t u b e r f a e s d e f u n d ic i o n , c o n L = 4 5 0 0 m y D = 4 e m . L C u a l s e ra e l f l u jom a s i c o e n m 3J h s i 6 . z = 1 0 0 m ?

S e t r a t a d e u n p ro b l e m a r e p re s e n ta t i v o d e l f l u jo e n t u b e n a s ; y c o n a g u a e n u n a t u b e n ar a z o n a b le m e n te l a rg a ( n o c a p i l a r) , e l f l u jo s e r a p r o b a b l e m e n te t u r b u le n t o ( R e > 4 0 0 0 ) .

F igu ra E .2 . E sq ue ma de l siste mad e f lu j o.


24/31

In troduc c ion al EES 8 37

L a e cu ac i6 n d e c on se rv ac io n d e la e ne rg ia e n re gim e n e stac io nario ( 3.7 1) p ue de ap lic arsee ntre las supe rfic ie s libre s d e los tanq ue s 1 y 2 :

P I v t P 2 V~_c.::==========:::::,,:,~=--::~_--;~:L -2 . . l . ! - = - - = - - 2 - - t .Z2._t hi - - d o n d e- pg g _ pg g J

F ig ura E .3 . V e nta na d e d ia lo gop ara la s ele c cio n d e u nid ad es .

Como P I = P 2 = P a rm Y V I ::: ::V 2"" 0 , esta re lac ion se sim plifica aL V 2!u . = f D2g

donde V = Q IA es la v eloc idad en la tube ria. E l fac tor de fric c i6n f es una func i6n de ln t ime r c de R eyno l d s -y - la -r ugos idad r e la t iva de la tuber ia , S 1 e l flu jo e s tu rb ule nto ; d e':l a E c u ac i6 n ( 6 . 48 ) :

(E.l)

1 ( E I D 2.51)ll2 = -2.0Iog IO 3 .7 + Re l l 2F in alm ente , ne ce sitam os la de finic ion de l m im ero de R e ynolds Y de l flujo m asic o v olu -metrico : ..

si R e > 4 0 0 0 (E.2)

,11' 2Q = V-D4 ...,'.R e = p V D ( / - L .z: (B J') - y EA),

donde p Y fl s on la d en si da d Y v is co si da d d el f l u i d o , r es pe c ti v ame n te ... .H ay un to tal_ de onc e v ariable s im plic adas e n e ste proble ma: ( L , D , / ) .z~e , g , fl, p, V , . _Re,f , Q ). D e e lias, sie re p ue de n se r e sp ec ific ad as al c om ie nz o (L , D , / 5 . z , e, g , u, p) , mien-tras q ue c uatro (V , R e , f, Q ) de be n c alc ularse por m edio de las E cuac ione s (E . 1 -4 ). E stesistem a de cuatro ecuac iones y cuatro inc6gnitas e sta bien planteado y tiene soluc ion , .pe ro h a de obte ne rse por un labo rioso proc eso ite rativ o (e xac tam ente p ara 1 0 que EES fued is e fi ad o ) .

A rranq ue E ES 0 presione e l com ando N ew de l m enu F ile si ya h a e s ra do u t il iz a ndo 1e l program a. U na v en tana de ecuac iones (E quations W i ndow ) aparecera, Nue st ra r ec q .. .;:m endac ion: S ele cc ione inm ed iatam ente e l sistem a de unidades: Pu lse U nit S ystem de l 'm enu O ptions (F igura E J) . M arq ue S f, M ass y Degrees , aunq ue e n re alidad no te ne mosfu nc i6 n trig on om e tric a alg un a e n e ste c aso . S ele cc io nam os kPa para la pre sion y Cels iuspara la te mpe ratura y la s u nid ad es d e e ne rg ia e n k J , q ue se ra c 6m odo para usar las propie-dade s de l aguainco rporada s en E ES .


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- - 8 3 8 A pend ic e EA h o r a , s o b r e l a p a n ta l l a e n b la n co , i n tr o d u z c a l a s e c u a c i o n e s p a r a e s t e p r o b l e m a ( F ig u -

- r a EA) , c i n co d e l a s c u a l e s s o n v a l o re s d e e n tr a d a c o n o c i d o s , d o s s o n e v a l u ac i o n e s d ep r o p ie d a d e s y c u a tr o s o n l a s E c u a c io n e s (E . 1 - 4 ) .-----------------------:------------

F igu ra E .4 . V entan a d e e cu ac io ne s.

8 3 8

" P r o b l e m 6 . 5 5 f r o m , l= lu id M e c h a n i c s , 5 th e d ., , I = r a n , l i ; , 1 1 1 1 , W h it e "L = 4 5 0 0 " [ m t 'o = 4 l1 0 0 " [m]"D E L T f l Z = 1 0 0 " { m } "

. . . E p s = O . 26 /W O Q . _ "[mt . .. .. .... ......-' .9 = 9 . 8 0 7 " [ t r l s A 2 l "D E L T f l Z = f U O ' V " 2 f 2 / gM u = v is c o s i t y (w a t e r, T = 2 0 , P = 1 0 1 ) " r A g l m - s ] "R h o = d e n s it y (w a t er , T = 2 0 ,P = 1 0 1 ) " [ k ! J / r n A : 3 ] "R e = R h o * V *O /M u1 / f f l{ ) . 5 = - 2 .0 1 . ' l o g 1 0 ( E p s / O l 3 . 7 + 2 . S 1 / R e / f' 'O . 5 ) Q = V ' p i / 4 ; 'O i '2 1 . 'c o n v e r t( h r, s ) " [m A : ] l " " } "

N o t e c i e r t o s d e t a i l e s e n l a F ig u r a EA. P r i i n e r o , l a s c a n t i d a d e s e n c e r r a d a s e n c m i l l a s ,t a le s c om o "[m]", i n d i c a n l a s u n i d ad es d e l a v a r i a b le a l a i z q u ie r d a d e l s i g n o i g u a l . H a yo t r o s d o s m o d o s d is ti n to s d e i n t r o d u c ir l a s u n id a d e s d e l a s v a r i a b le s . L a s e sp e c i f i c a c io n e sn o a f e c t a n a l o s r e s u lt a d o s n um e r i c o s, p e r o E E S l a s u ti l i z a r a c u an d o r e a l i c e e l c h eq u e od im e n s io n a l. N o esta f o r z a d o a i n t r o d u c i r u n i d a d e s e n E E S ; p e r o e s u n a b u e n a i d e a ha-c e r l o p o r q u e E E S n o p u e d e c o m p r o b a r l a h o m o g e n e i d a d d im e n s i o n a l d e l a e c u a c i 6 n s in o s e i n tr o d u c e n l a s u n i d a d e s , y a d em a s c a b e r e c o r d a r q u e l a s c o n v e r s i o n e s d e u n i d ad e ss o n u n a f u e n t e p ro b ab le d e e r r o r e s . S e g u n d o , s e c o n v i r t i e ro n l a s u n i d a d e s d e E p s y D am e t r o s d ir e c t a m e n te p a r a m a n te n e r l a c o n s i s t e n c i a c o n e l s i s t e m a d e u n i d ad e s S I a d o p t a -d o . P o d r f a m o s h ab e r u sa d o l a f u n c i o n C o n v e r t p a r a c o n v e r t i r u n i d ad es t a l y c o m o s e h ah e c h e c o n l a u lt i m a e c u a c i 6 n . T e r c e ro ; r e c u rr im o s a E E S p a r a i n tr o d u c i r l o s v a l o re s d ev i s c o s i d a d y d e n s i d a d d e l a g u a a 20 C y 1 a t m , u n p ro ce d im i e n to b ie n e x p l i c a d o e n e lm e n u H e l p . P o r e j e m p l o , v is c o si t y (w a t e r , T = 2 0 , P = 1 0 1 ) s a ti s fa ce l o s r e q u is it o s d eq u e l a t e m p e r a tu ra (1 ) y l a p r e s i6 n (P ) e n t r e n e n C y k P a ; E E S e v a l u a r a l a f u n c i o n p . e n

- - - - k g /m - s . F in a lm e n t e , n o t e q u e E E S r e c o n o c e p i y - 'e a si g n a e l v a l o r 3 .1 4 1 5 9 3 .E n l a F ig u r a E .4 s e h a u t i l i z a d o l a f u n c i 6 n incorporada, l o g 1 0 . E x i s t e n m u c h a s m a s

f u n c i o n e s , q u e p u e d e n e n co n t r a r s e d e s p la z a n d o se h a c i a a b a j o e n e l c o m a n d o F u n c t i o nInformat ion e n . e l m e n u Options .. U n a v e z i n t r o d u c i d a s l a s e c u a c i o n e s , c o m p r u e b e i a s i n t a x i s p o r m e d i o d e l c o m a nd oCheck /Forma t d e l m e n u Calculate . S i 1 0 h a h e c h o b ie n , E E S i n f o r m a d e q u e e l s i s t e m ad e o n c e e c u ac i o n e s c o n o n c e i n c6 g n it a s p a r e c e O K . D e n o s e r a s f , E E S e m i t i r a p o s i b le sc a u s a s d e e r r o r . S i O K , p ro s i g a : E li j a e l c o m a nd o S o l v e d e l m e n u O p ti o n s . E E S e m i t ee l m e n sa j e " lo g a r i t r n o d e u n m im e r o n eg a t i v o - i n te n te l i m i ta r l a s v a r i a b le s " . P o d n am o sh ab e r l o s a b id o . S e l e c c i o n e e l c o m a n do V a r i a b le I n fo rm a t i o n e n e l m e n d O p t i o n s . A p a -r e ce ra u n a c a j a e n u m e r a n d o l a s o n c e v a r i a b l e s ( F i g u r a E . S ) . P o r d e f e c t o , e n E E S t o d a s l a se s t i m a c i o n e s d e v a r i a b le s s o n l a u n i d ad , y e l r a n g o d e d ic h a s v a r i a b le s e st a c o m p r e n d i d o


26/31

Epsf9L

. t v luQR e

R h oV

In troduc c i6n a l E ES 8 39

' 1 00 inf inity0 . 0 0 0 2 6 I - in fin ity lI')fin ity fl, 3

0 . 0 2 1 O . O O O O E + O O i n f i n i t y /l , 39 . 8 0 7 I - inf inity I inf inity ' A 3 N m / s ) \ 24 5 0 0 : -Inf inity I inf inity I A 3 1 N 1 m

0 . 0 0 1 0 0 2 I - ,In fin ity ! - ..._-.._nfinity I A 3 N k g / m - s "1 . 0 0 0 0 I O , O O O O E + O O I i n f i n i t ~ 1 F 4 N m J \ 3 ! h1 0 0 0 0 I O , Q O O O E + O O i n f i n i t y I A 3 N9 9 8 , 2 - inf inity j Inf inity A 3 N k g / m A3

1 , 0 0 0 0 I O . O o o O E + O O i n f i n i t y F 1 4 N m / s

F ig ura E .S . V e nta na d e in fo rm a ci6 n d e v aria ble s c on u nid ad es y v a lo re s e s ti m a d os y a i nt ro d uc id o s. ;1

entre -00y t oo , d em asia do e x te nso , In tro du zc a ( tal y com o se m uestra en la F igura E .5 ) :e stim ac io ne s p ara J= 0 .0 2 y R e = 10 ,0 00 , m ie ntra s V = 1 y Q = 1 p are ce n a de cu ad os, y otras Iv aria ble s e sta n fija da s. A s eg ure se d e q ue f,R e , V y Q DO pueden se r negativ as. L as colum - .nas "d isp lay " norm alm en te e stan pue stas e n " A ", autom atic o, 1 0 q ue re sulta satisfac torio ,para la m ay orfa d e v ariable s.N o sotros h em os c arnb iad o " A " a "F ' (d ec im al fijo) 'para Q y . : .V , para ase gurarnos d e q ue sus v alore s so n m ostrad os e n la pantalla c on c uatro c ifras d ec i-' ( :

U n i t Set t ings: [kJ] / [C]/[kPa] l[kg] /[deqrses Jo = 0 , 0 4 [m ] I J . Z = 1 0 0 [m ]f = 0 . 0 3 5 5 8 9 = 9 . 8 0 7 [ r n /s _ 4 _Io L = 0 .0 0 1 0 0 2 [ k g /m - s ] Q = 3 .1 6 6 6 [ m 3 / h ]p = 9 9 8 , 2 [ k g /m 3 j . _ . - - - . - V ~ O } O O O [ r n / s ]

Eps = 0 . 0 0 0 2 6 [m ]L = 4 5 0 0 [ r n ]R e = 2 7 8 9 1

N o u n it c on sis ten cy o r c on vers io n p ro blem s w ere d ets cted- .- ----_.

Ce lc u lefio n time = ,0 secF ig ura E .6 . V enta na d e so lu ci6 n p ara e l P ro ble m a P 6 . S S .


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-8 40 A pendice E- - : _ : : m ~ ~ a l e s . a c o l u m n a " U n i t s " m u e s t r a l a s u n id a d e s q u e f u e r o n a s i g n a d a s c o n c o m e n t a r io s

y c o r c h e te s e n l a v en fa n a eE q u a ti o n s . L a s u n i d ad e s t a m b ie n . p u ed en .s e r . i n tr o d u c id a s e ne s t a v e n ta n a d e d ia lo g o ,

N u e s t r as e s t im a c i o n e s y l f rn i t es s o n e x c e l e n te s y e l c o m a nd o S o lv e a h o ra i t e r a y n o si n fo rm a d e l c x i t o d e l o s c a l c u l o s : "max r e s i d u a l = 2 E fo '; : u n e r r o r d e sp r ec ia b le . ( E l a lg o -r i t m o p o r d e f e c t o r e a l i z a 1 0 0 i t e ra c i o n e s, v a l o r q u e p u ed e s er m c d i f i c ad o c o n e l c o m a n d oS to p C r i t e r i a d e l m e n u O p t i o n s . ) P u ls e e n C o n t i n u e y l a s o l u c i o n c om p le ta s e m o s t r a rap a r a t o d a s l a s v a r i a b l e s ( F ig u r a E .6 ). N o te c om o E E S t a m b ie n c om p ru e b a l a c o n s i s te n c iae n l a s u n i d ad e s d e t o d a s l a s e cu a c io n e s y n o e n c u e n t r a p ro b le m a a lg u n o .

E s t a e s l a s o lu c i 6 n c o rr e c t a a l P r o b l e m a P 6 .5 5 : e s t a t u b e r i a d e f u nd i c i o n , c o n u n ad i f e r e n c i a d e c o ta d e 1 00 m , e n t r e g a r a u n c a u d a l Q = 3 .1 7 m 3 J h d e a g u a . E E S r e a li z 6t o d o e l p r o c e so i t e ra ti v o p o r n o s o tr o s ., . , - _ . . ~ . . _ - - . . , . . _ . . " . . . . . . . . . . . . , . . _ o _ ' . _ . . . .

E s tu d io s p a ra m e tr ie o sc on e nt r a da d e d at o s t a bu la r

, ' . . . . . . .

F ig ura E .7 . N ue va tab lap a r a m e t r i c a mostrandolas v a r iab le s s e le c c ionadas,(V n o s e mu es tr a) .

U n o d e l o s p u n t o s f u e r t e s d e E E S e s l a c a p ac i d a d d e r e a l i z a r e s t u d i o s p ar a m e tr i c o s .P o r e j e m p lo , s u p o n g a q u e s e d e s e a c o n o c e r c 6 m o v a r i a n d o / 1 z . s e m o d if i c a e l c a u d a lQ . L o p rim e ro s e r a c o nv e r t i r l a e c u ac i o n D E L T A Z = 100 e n c om e n t a ri o , p a r a 1 0 q u el a e n ce r r a re m o s e n tr e H a v es { } . S i s e l e c c i o n a l a e c u ac i 6 n y p re s i o n a e l b o ro n d e r e ch o ,a p a r e c e r a u n m e n u c o n C om m e n t c o m o p r im e r i t em . S i p u l s a e s t e i t e m d e l m e nu , E E Sa u t o m a t i c am e n t e i n tr o d u c i r a l a s H a v e s. S e m o s t r a ra u n d ia lo g o ( F ig u r a E .7 ) e n u m e r a n -d o t o d a s l a s v a r i a b le s d e l p ro b l e m a . A c t i v e l a s v a r i a b le s q ue d e s e e v a r i a r : A z . A c t i v et a m b ie n l a s v a r i a b l e s q u e d e s e e c a l c u l a r y t a b u la r: V , Q , R e yI' "

H a g a c l i c e n e l b o t 6 n A d d y a c o n t i n u a c i 6 n c o n f i r r n e c o n O K y l a n u e v a t l a s e r av is u a l i z a d a ( F ig u r a E .8 ) . I n tr o d u z c a d ie z v a l o re s d e / 1 z q u e c u b r a n e l r a n g e d e i n te r e s ;n o s o tr o s h em o s s e le c c i o n a d o u n r a n go l i n ea l 1 0 m < / 1 z < 5 0 0 m . N o te q u e n o e s n e c e -s ar i o t e c l e ar e st o s v a lo re s, a u n q u e p u e d e h a c er l o s i 1 0 d e s e a . P u l s an d o e l i c o n o t r i a n g u la rs i t u ad o e n I ( ! .e s q u i n a s u p e r i o r d er e c h a e n l a c e l d a d e t i t u lo d e c a d a c o lu m n a a b re u n d ia -lo g o q u e p e r m i t e l a e n t r a d a a u to m a t i c a d e v a l o re s e n l a t a b la .


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-------In troducc ion al EE S 8 41

1 " 1 8 , 96 4 . 4 4

173.3

" , o r,"

It" ,q aram ente , la P aram e tric T ab le trab aja c om o u na h oja d e c alc ulo . S e le cc io ne Solve , 'Tab l e d e l ~ e ~ ti Calcula te 'y e l d i" alo g o'd e la v e n ta na S o lv e T a ble s e m o st ra ra e n p an ta lla(F igu ra E .9 ). L os v alo re s p ar d efe cto son satisfac to rio s; e l au to r n o h a c am biad o n ada,H aga c lic e n e l bo t6n O K, y lo s c a lc u lo s s er an r ea li za do s y se i r a c u br ie n do la P aram e- Itric T able , com o pue de v erse en la F igura E .lO .

L os c audales se m uestran e n la F igura E .I0 , pe ro siem pre , seg i in la e xp erie nc ia d ela uto r, u na g ra fic a e s m as ilu stra tiv a. S e le cc io ne N ew Plo t W indow de l m enu Plo t. L ac aja d e d ia lo go N ew Plot Se t up ( Fig ura E .ll) ap are ce ra . E li ja / j,z com o e je x y Q COgl-o .

. I,e je y,H e m os ariad id o lin eas d e re fe re nc ia . P ulse O K y e l grafic o de seado apare ce ra e n la

v en tan a P lo t (F igu ra E .l2 ). P ue de ob se rv arse la re lac i6 n n o lin eal, m as 0 m en os d el t ip orafz cuadrada, y ensefia q ue e l c au dal Q n o g uard a p ro po rc i6 n lin eal c on la c life re nc ia d ecota ! : J . z .

l' .. .. __ ,..-- - -----

F ig ura E .9 . D ialogo para resolvertabla.


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_----- - -8 42 Ap en dic e E

6 4 . 4 4 2 2 2 0 21 1 8 . 9 3 . 4 6 2 9 3 0 5 0 01 7 3 . 3 4 . 2 0 5 ' 1 3 7 0 3 82 2 7 . 8 - o ( )347-1 - 4 . 8 3 7 9 4 2 6 1 ' 1 ' 1 ' . 0 6 9 41 )2 8 2 . 2 0 .0 3 4 5 5 ' 5 . 3 9 8 ? 4 7 5 5 2 '1 . 1 ' 9 3 43 3 6 . 7 0 . 0 3 4 4 2 5 . 9 0 7 8 5 2 0 . 3 6 1 . 3 0 5 93 9 1 . 1 0 . 0 3 4 3 1 ' 6 . 3 1 7 3 5 6 ' 1 7 0 1 . 4 0 9 74 4 5 . 6 0 0 . 3 4 2 3 6 . 8 1 5 1 6 0 0 2 6 ' 1 . . 5 0 6 5

5 0 0 0 . 0 3 4 1 6 1 . 2 2 6 9 6 3 6 5 4 1.5975F ig ur a E .1 0. Ve nt an a d e t ab la p aram et ri ca , u na v e z re ali za do s lo s c alc ulo s .

,... . ~ .. ., - _ . _ - - _ _ . _ _ ---.i

Figura E.n. V en tan a d e N e w P lo t S et up .- _ . . . . .


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In t r oducc i6n al EE S 8 4

It

..~.- -4, .-- --I.

---',-- . _ . _ - . . . ' __ o . 4 _ . . . . . .I

F ig ura E .1 2. V en tan a d e P lo t pa ra c au dal fre nte a d ife re nc ia d e c ota ..,.'

L a a pa rie nc ia d el g rafic o e n la F ig ura E .1 2 p ue de m o dific arse d e v aria s m a ne ras. Pulsedos v ec e s e n e l re ctangu lo de l g rafico para v er alguna de e stas opc ione s . L a barra de h e-rram ie ntas a la d ere ch a d e la v en tan a P lot p erm ite in trod uc ir te xto 0 graficos,

P r o b l e m a s e je m p loe n d in am i ca d e f t u id o s E n e ste lib ro se ha in c lu ido un gran m im ero de prob lem as de d inarn ic a de fiu idospe nsados para se r re sue lto s c on E ES . E n la barra de m enus en la parte supe rio r de lapan ta lla , puede v erse e l m enu F lu id M ec h an ic s a la de re ch a de l m enu H elp . E ste m enupro po rc io na ac ce so a to das las so lu cio ne s d e pro ble m as E E S d esarrollad os e n e ste lib ro ,o rgan izados por c ap ftu los. C om o e jem plo , se le c cione C hap te r 6 de l m enu W h ite F lu idM e ch an ic s. U n a ~ en ~an a d ~ .~ ia lo go . a pare ce ra h ac ie nd o un a lis ta c on tod os los p ro b l e-m as de l C apitu lo 6 . E lija P rob lem P6 .5 5F I(} w B etw ee n R e se rv oirs . E ste p rob le ma e su na v aria nte d el e j_ ~ m plQ _ .9 .u ~c a_ Q am o sd e re so lv e r, c on sid era nd o p are d lis a e n lu ga rde rugosa. P roporc iona una v en tana D iag ram en la q ue pue de in troduc ir e l v alo r de / J . zy o tra in fo rm a ci6 n. In tro du zc a lo s v alo re s, y lu ego pu lse S olv e e n e l m enu C alc u la tepara v er e l e fe c to q ue p roduce en la so luc i6n ob ten ida.E n e ste p un to d eb eria e xplo rar la ap lic ac i6 n p or su c ue nta . In te nte c ua lq uie r c osa q uese Ie oc urra . L a ayuda e n line a Ie p roporc ionara los de ta lle s de los c om andos de E ES .E E S e s u na p ote nte h erram ie nta q ue le re su lta ra muy p ra ct ic a e n s us e stu di os .


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