metodos numericos jose gonzalez cod 2063307

7/29/2019 Metodos Numericos Jose Gonzalez Cod 2063307

1/39

Ti 375 Vm 1.70725 b 0.0010538

Tf 378 Tc 647.1 a 1.84972488

f(t) #REF! Pc 22048.32 w 0.345

Iteraciones a g(a) b m g(m)

0 375 -0.304369209 378 376.5 0.1053521 375 -0.304369209 376.5 375.75 -0.099507

2 375.75 -0.099507106 376.5 376.125 0.002923

3 375.75 -0.099507106 376.125 375.9375 -0.048292

4 375.9375 -0.048292067 376.125 376.0313 -0.022685

5 376.03125 -0.02268462 376.125 376.0781 -0.009881

6 376.078125 -0.009880915 376.125 376.1016 -0.003479

7 376.101563 -0.003479067 376.125 376.1133 -0.000278

8 376.113281 -0.000278144 376.125 376.1191 0.001322

9 376.113281 -0.000278144 376.1191 376.1162 0.000522

10 376.113281 -0.000278144 376.1162 376.1147 0.000122

11 376.113281 -0.000278144 376.1147 376.114 -7.81E-05

12 376.114014 -7.80863E-05 376.1147 376.1144 2.19E-05

13 376.114014 -7.80863E-05 376.1144 376.1142 -2.81E-05

14 376.114197 -2.80719E-05 376.1144 376.1143 -3.06E-06

15 376.114288 -3.06469E-06 376.1144 376.1143 9.44E-06

16 376.114288 -3.06469E-06 376.1143 376.1143 3.19E-06

17 376.114288 -3.06469E-06 376.1143 376.1143 6.12E-0818 376.114288 -3.06469E-06 376.1143 376.1143 -1.5E-06

19 376.114294 -1.50174E-06 376.1143 376.1143 -7.2E-07

20 376.114297 -7.20261E-07 376.1143 376.1143 -3.3E-07

21 376.114298 -3.29523E-07 376.1143 376.1143 -1.34E-07

Ecuaciones no lineales

1. La temperatura con la ecuacin de peng robinson dado la P, Vm y las propiedades

crticas (Tc, Pc y w). R = constante de los gases (8,31451 J/molK)

METODO DE BISECCION

0.0025


2/39

0

0.0005

0.001

0.0015

0.002

0 2 4 6 8 10 12

ERROR

ITERACIONES

Series1


3/39

Vm^2-2bVm-b^2 2.91110325

R/(Vm-b) 0.270502302

p 100

g(a)*g(m) error

-0.03206587 0.0019960.030286899 0.000997

-0.000290837 0.0004988

0.004805404 0.0002493

0.001095487 0.0001246

0.000224145 6.232E-05

3.43764E-05 3.116E-05

9.67681E-07 1.558E-05

-3.67795E-07 7.789E-06

-1.45215E-07 3.895E-06

-3.39256E-08 1.947E-06

2.17192E-08 9.737E-07

-1.71341E-09 4.868E-07

2.19203E-09 2.434E-07

8.60315E-11 1.217E-07

-2.89273E-11 6.085E-08

-9.76751E-12 3.043E-08

-1.87604E-13 1.521E-084.60235E-12 7.607E-09

1.08164E-12 3.803E-09

2.37342E-13 1.902E-09

4.42069E-14 #DIV/0!


4/39

ITERACION ERROR

0 0.002

1 0.001

2 0.00012

3 6.20E-05

4 3.10E-05

5 1.60E-05

6 7.80E-06

7 3.90E-06


5/39


6/39


7/39

Ti 375 Vm 1.70725 b

Tf 378 Tc 647.1 a

f(t) -104.296 Pc 22048.32 wxi 375

f(X) -2.4622E-10

Iteraciones xi g(xi) g'(xi) xi+1 error

0 375 -0.304369209 0.294727 376.0327 0.304369

1 376.0327 -0.022284047 0.29466 376.1083 0.022284

2 376.1083 -0.00162707 0.294655 376.1139 0.001627

3 376.1139 -0.000118777 0.294655 376.1143 0.000119

4 376.1143 -8.67065E-06 0.294655 376.1143 8.67E-06

5 376.1143 -6.32952E-07 0.294655 376.1143 6.33E-07

6 376.1143 -4.62051E-08 0.294655 376.1143 4.62E-08

7 376.1143 -3.37295E-09 0.294655 376.1143 3.37E-098 376.1143 -2.46217E-10 0.294655 376.1143 2.46E-10

9 376.1143 -1.79767E-11 0.294655 376.1143 1.8E-11

10 376.1143 -1.32161E-12 0.294655 376.1143 1.32E-12

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 2 4 6 8 10 12

ERROR

ITERACIONES

Series1

METODO DE NEWTON RAPSON


8/39

0.001054 Vm^2-2bV 2.911103

1.849725 R/(Vm-b) 0.270502

0.345 p 100


9/39

g 9.8 c ? v 50

m 68.1 t 28

Iteracion a g(a) b m g(m)

0 13 1.091966 14 13.5 -0.7565

1 13 1.091966 13.5 13.25 0.151443

2 13.25 0.151443 13.5 13.375 -0.3065

3 13.25 0.151443 13.375 13.3125 -0.07853

4 13.25 0.151443 13.3125 13.28125 0.036202

5 13.28125 0.036202 13.3125 13.29688 -0.021236 13.28125 0.036202 13.29688 13.28906 0.007471

7 13.28906 0.007471 13.29688 13.29297 -0.00688

8 13.28906 0.007471 13.29297 13.29102 0.000293

9 13.29102 0.000293 13.29297 13.29199 -0.0033

10 13.29102 0.000293 13.29199 13.2915 -0.0015

11 13.29102 0.000293 13.2915 13.29126 -0.0006

12 13.29102 0.000293 13.29126 13.29114 -0.00016

13 13.29102 0.000293 13.29114 13.29108 6.84E-05

14 13.29108 6.84E-05 13.29114 13.29111 -4.4E-05

15 13.29108 6.84E-05 13.29111 13.29109 1.23E-05

16 13.29109 1.23E-05 13.29111 13.2911 -1.6E-05

17 13.29109 1.23E-05 13.2911 13.2911 -1.7E-06

18 13.29109 1.23E-05 13.2911 13.29109 5.3E-06

19 13.29109 5.3E-06 13.2911 13.29109 1.8E-06

20 13.29109 1.8E-06 13.2911 13.2911 4.66E-08

2. Modelo de cada libre

Un paracaidista con masa, m = 68.1 kg salta de un globo fijo y a los 28 segu

adquiere una velocidad de 50 m/s. Si la aceleracin debida a la gravedad es

m/s2, Cul es el coeficiente de resistencia (kg/s)?.

2a Ley de Newton F = m x a. Despejando a y representndola como la razn

cambio de la velocidad respecto altiempo.dv/dt = F/m ; F = FD + FU ;FD = mg ;FU = -cv ; dv/dt = (mg - cv) / m

Simplificando: dv/dt = g - cv / m

EDO que relaciona la aceleracin de un cuerpo que cae, con las fuerzas que


10/39

21 13.2911 4.66E-08 13.2911 13.2911 -8.3E-07

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0 5 10 15 20 25

ERROR

ITERACIONES

Series1


11/39


12/39

-3.9E-14 #DIV/0!


13/39

xi 15

f(X) 0

Iteraciones xi g(xi) g'(xi) xi+1 error

0 15 -5.60129 -2.934 13.0909 5.601285

1 13.0909 0.746108 -3.81589 13.28643 0.746108

2 13.28643 0.01715 -3.709 13.29105 0.017153 13.29105 0.000154 -3.70653 13.29109 0.000154

4 13.29109 1.33E-06 -3.7065 13.2911 1.33E-06

5 13.2911 1.15E-08 -3.7065 13.2911 1.15E-08

6 13.2911 9.89E-11 -3.7065 13.2911 9.89E-11

7 13.2911 8.6E-13 -3.7065 13.2911 8.6E-13

8 13.2911 0 -3.7065 13.2911 0

9 13.2911 0 -3.7065 13.2911 0

10 13.2911 0 -3.7065 13.2911 0

METODO DE NEWTON RAPSON


14/39

AbrevaderoMtodo Secante

Datos

Longitud 160

Diametro 80

Volumen 386000

Radio 40 Iter Xi g(Xi) Xi+1 g(xi+1) xi+2 Error Iterati

1 0.1 0.2 13563.8703 0.1 -

2 0.2 13563.8703 0.1 14843.861 1.2596851 14843.861

3 0.1 14843.861 1.2596851 2.55599429 1.25988482 2.55599429

4 1.2596851 2.55599429 1.25988482 0.00080936 1.25988488 0.00080936

5 1.25988482 0.00080936 1.25988488 0 1.25988488 0

6 1.25988488 0 1.25988488 0 #DIV/0! 0

7 1.25988488 0 #DIV/0! #DIV/0! #DIV/0! #DIV/0!

8 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

9 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!10 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!







15/39

Error Abs

92.061508

0.01585247

5.0213E-06

0

#DIV/0!

#DIV/0!

#DIV/0!

#DIV/0!

#DIV/0!#DIV/0!

#DIV/0!

#DIV/0!

#DIV/0!

#DIV/0!

#DIV/0!


16/39

AbrevaderoMtodo BiseccinDatos

Longitud 160

Diametro 80

Volumen 386000

Radio 40

Iter Xa g(Xa) Xb g(xb) m1 1 3325.19312 2 -9465.46967 1.5

2 1 3325.19312 1.5 -3071.63939 1.25

3 1.25 126.464208 1.5 -3071.63939 1.375

4 1.25 126.464208 1.375 -1472.67358 1.3125

5 1.25 126.464208 1.3125 -673.125205 1.28125

6 1.25 126.464208 1.28125 -273.335506 1.265625

7 1.25 126.464208 1.265625 -73.4368857 1.2578125

8 1.2578125 26.5133538 1.265625 -73.4368857 1.26171875

9 1.2578125 26.5133538 1.26171875 -23.461843 1.25976563

10 1.25976563 1.52573614 1.26171875 -23.461843 1.2607421911 1.25976563 1.52573614 1.26074219 -10.9680583 1.26025391

12 1.25976563 1.52573614 1.26025391 -4.72116226 1.26000977

13 1.25976563 1.52573614 1.26000977 -1.59771336 1.2598877

14 1.25976563 1.52573614 1.2598877 -0.03598868 1.25982666

15 1.25982666 0.74487371 1.2598877 -0.03598868 1.25985718

16 1.25985718 0.35444251 1.2598877 -0.03598868 1.25987244

17 1.25987244 0.15922691 1.2598877 -0.03598868 1.25988007

18 1.25988007 0.06161911 1.2598877 -0.03598868 1.25988388

19 1.25988388 0.01281521 1.2598877 -0.03598868 1.25988579

20 1.25988388 0.01281521 1.25988579 -0.01158673 1.25988483

21 1.25988483 0.00061424 1.25988579 -0.01158673 1.25988531

22 1.25988483 0.00061424 1.25988531 -0.00548625 1.25988507

23 1.25988483 0.00061424 1.25988507 -0.002436 1.25988495

24 1.25988483 0.00061424 1.25988495 -0.00091088 1.25988489

25 1.25988483 0.00061424 1.25988489 -0.00014832 1.25988486

26 1.25988486 0.00023296 1.25988489 -0.00014832 1.25988488

27 1.25988488 4.2319E-05 1.25988489 -0.00014832 1.25988489

28 1.25988488 4.2319E-05 1.25988489 -5.3001E-05 1.25988488

29 1.25988488 4.2319E-05 1.25988488 -5.3411E-06 1.25988488

30 1.25988488 1.8489E-05 1.25988488 -5.3411E-06 1.25988488

31 1.25988488 6.574E-06 1.25988488 -5.3411E-06 1.2598848832 1.25988488 6.1642E-07 1.25988488 -5.3411E-06 1.25988488

33 1.25988488 6.1642E-07 1.25988488 -2.3623E-06 1.25988488

34 1.25988488 6.1642E-07 1.25988488 -8.73E-07 1.25988488

35 1.25988488 6.1642E-07 1.25988488 -1.2817E-07 1.25988488

36 1.25988488 2.4412E-07 1.25988488 -1.2817E-07 1.25988488

37 1.25988488 5.7917E-08 1.25988488 -1.2817E-07 1.25988488

38 1.25988488 5.7917E-08 1.25988488 -3.5157E-08 1.25988488


17/39

g(m) g(Xa)*g(m)Error Itera Error Abs-3071.63939 -10213794.2 - 20

126.464208 420517.913 20 9.09090909

-1472.67358 -186240.498 9.09090909 4.76190476

-673.125205 -85126.2458 4.76190476 2.43902439

-273.335506 -34567.1582 2.43902439 1.2345679

-73.4368857 -9287.13758 1.2345679 0.62111801

26.5133538 3352.99028 0.62111801 0.30959752

-23.461843 -622.052144 0.30959752 0.15503876

1.52573614 40.4523821 0.15503876 0.07745933

-10.9680583 -16.7343629 0.07745933 0.03874467-4.72116226 -7.20324789 0.03874467 0.01937609

-1.59771336 -2.43768902 0.01937609 0.00968898

-0.03598868 -0.05490924 0.00968898 0.00484473

0.74487371 1.13648074 0.00484473 0.0024223

0.35444251 0.26401491 0.0024223 0.00121114

0.15922691 0.05643679 0.00121114 0.00060557

0.06161911 0.00981142 0.00060557 0.00030278

0.01281521 0.00078966 0.00030278 0.00015139

-0.01158673 -0.00014849 0.00015139 7.5695E-05

0.00061424 7.8716E-06 7.5695E-05 3.7848E-05

-0.00548625 -3.3699E-06 3.7848E-05 1.8924E-05

-0.002436 -1.4963E-06 1.8924E-05 9.4619E-06

-0.00091088 -5.595E-07 9.4619E-06 4.731E-06

-0.00014832 -9.1105E-08 4.731E-06 2.3655E-06

0.00023296 1.4309E-07 2.3655E-06 1.1827E-06

4.2319E-05 9.8586E-09 1.1827E-06 5.9137E-07

-5.3001E-05 -2.243E-09 5.9137E-07 2.9568E-07

-5.3411E-06 -2.2603E-10 2.9568E-07 1.4784E-07

1.8489E-05 7.8243E-10 1.4784E-07 7.3921E-08

6.574E-06 1.2155E-10 7.3921E-08 3.6961E-08

6.1642E-07 4.0523E-12 3.6961E-08 1.848E-08-2.3623E-06 -1.4562E-12 1.848E-08 9.2402E-09

-8.73E-07 -5.3813E-13 9.2402E-09 4.6201E-09

-1.2817E-07 -7.9008E-14 4.6201E-09 2.31E-09

2.4412E-07 1.5048E-13 2.31E-09 1.155E-09

5.7917E-08 1.4139E-14 1.155E-09 5.7751E-10

-3.5157E-08 -2.0362E-15 5.7751E-10 2.8875E-10

1.135E-08 6.5738E-16 2.8875E-10 #DIV/0!


18/39

metodo de newton para sistemas no lineales

0.4 2 -0.48952 0.979048

1.2214 1 0.597905 -0.19581

-0.4895 0.97905 2.96 -2.644732

0.5979 -0.1958 -1.2214 2.008934

1.

( + ) = ;

+ =

2.

+ = ;

+ =

,

,

= ,

y=1

=A =

( = , , = ) = + = , ; = , , = = + = ,

= = =


19/39

ITERACION

1

X 0.2 Y 1

PASO 1 0.4 2 PASO 2 -0.48952 0.979046 2.961.221403 1 0.597905 -0.195809 -1.2214

PASO 3 2.96 -0.48952 0.979046 -2.644797

-1.2214 0.597905 -0.19581 2.008959

PASO 4 0.2 -2.6448 -2.444797

1 2.008959 3.008959

2

X -2.4448 Y 3.008959

PASO 1 -4.88959 6.017919 PASO 2 -0.18479 1 .112038 -11.0309

0.086744 1 0.016029 0.903538 -2.0957

PASO 3 -11.0309 -0.18479 1.112038 -0.292132

-2.0957 0.016029 0.903538 -2.070363

=

+ =

=


20/39

PASO 4 -2.4448 -0.29213 -2.736929

3.008959 -2.07036 0.938597

3

X -2.73693 Y 0.938597

PASO 1 -5.47386 1.877194 PASO 2 -0.17872 0 .335486 -4.37174

0.064769 1 0.011575 0.978271 -0.00337

PASO 3 -4.37174 -0.17872 0.335486 0.780175

-0.00337 0.011575 0.978271 -0.053897

PASO 4 -2.73693 0.780175 -1.956753

0.938597 -0.0539 0.8847

4X -1.95675 Y 0.8847

PASO 1 -3.91351 1.7694 PASO 2 -0.24018 0.424974 -0.61158

0.141316 1 0.033941 0.939944 -0.02602

PASO 3 -0.61158 -0.24018 0.424974 0.135832

-0.02602 0.033941 0.939944 -0.045212

+ =

=

+ =

=


21/39

PASO 4 -1.95675 0.135832 -1.820921

0.8847 -0.04521 0.839488

5

X -1.82092 Y 0.839488

PASO 1 -3.64184 1.678976 PASO 2 -0.25552 0 .429008 -0.02049

0.161877 1 0.041362 0.930554 -0.00136

PASO 3 -0.02049 -0.25552 0.429008 0.004651

-0.00136 0.041362 0.930554 -0.002118

PASO 4 -1.82092 0.004651 -1.81627

0.839488 -0.00212 0.837371

6X -1.81627 Y 0.837371

PASO 1 -3.63254 1.674741 PASO 2 -0.25609 0 .428881 -2.6E-05

0.162631 1 0.041648 0.93025 -1.8E-06

PASO 3 -2.6E-05 -0.25609 0.428881 5.94E-06

-1.8E-06 0.041648 0.93025 -2.72E-06

+ =

=

+ =

=

=


22/39

PASO 4 -1.81627 5.94E-06 -1.816264

0.837371 -2.7E-06 0.837368

+ =+ = = ,

= ,


23/39

con x=1con y=1

con z=1

X 1 Y 1 z 1

-1 3 1 0.21844565 0.2815543 0.34466305 0.34

1.

+ , = ;

+ , = + ;

, = ;

, = ;

, =

3.

+ , = ;

+ , = ;

+ ,

+

1 3 11 1 2

1


24/39

PASO 1 1 1 -2 PASO 2 0.31692081 0.1830792 0.04923758 0.09

2.718282 -2.71828 1 0.26768323 -0.2676832 0.19695031 -0.59

norma

0.34 0.2184457 0.2815543 0.34466305 -0.1037398 0.115228

PASO 3 0.09 0.3169208 0.1830792 0.04923758 0.09518003

-0.59 0.2676832 -0.2676832 0.19695031 -0.0492799

1 -0.1037398 0.89626

PASO 4 1 0.09518 1.09518

1 -0.0492799 0.95072

X 0.89626 Y 1.09518 z 0.95072

-0.75131 3.042453 0.981566 0.2389304 0.3048389 0.3451069 0.07301

PASO 1 1.09518 1 -1.90144 PASO 2 0.29348846 0.1609893 0.01803313 0.012302

2.450422 -2.98972 1 0.29196829 -0.2656709 0.20825651 -0.00142

norma

0.0730105 0.2389304 0.3048389 0.3451069 0.02070425 0.021566

PASO 3 0.0123025 0.2934885 0.1609893 0.01803313 0.02338267

-0.001421 0.2919683 -0.2656709 0.20825651 0.01775238

0.89626 0.0207042 0.916964

=

+ =

=


25/39

PASO 4 1.09518 0.0233827 1.118563

0.95072 0.0177524 0.968473

X 0.89626 Y 1.09518 z 0.95072

-0.75131 3.042453 0.981566 0.2389304 0.3048389 0.3451069 0.07301PASO 1 1.09518 1 -1.90144 PASO 2 0.29348846 0.1609893 0.01803313 0.012302

2.450422 -2.98972 1 0.29196829 -0.2656709 0.20825651 -0.00142

norma

0.0730105 0.2389304 0.3048389 0.3451069 0.02070425 0.021566

PASO 3 0.0123025 0.2934885 0.1609893 0.01803313 0.02338267

-0.001421 0.2919683 -0.2656709 0.20825651 0.01775238

0.89626 0.0207042 0.916964

PASO 4 1.09518 0.0233827 1.118563

0.95072 0.0177524 0.968473

X 0.89626 Y 1.09518 z 0.95072

-0.75131 3.042453 0.981566 0.2389304 0.3048389 0.3451069 0.07301

PASO 1 1.09518 1 -1.90144 PASO 2 0.29348846 0.1609893 0.01803313 0.012302

2.450422 -2.98972 1 0.29196829 -0.2656709 0.20825651 -0.00142

=

=

+ =


26/39

norma

0.0730105 0.2389304 0.3048389 0.3451069 0.02070425 0.021566

PASO 3 0.0123025 0.2934885 0.1609893 0.01803313 0.02338267

-0.001421 0.2919683 -0.2656709 0.20825651 0.01775238

0.89626 0.0207042 0.916964

PASO 4 1.09518 0.0233827 1.1185630.95072 0.0177524 0.968473

X 0.916964 Y 1.118563 z 0.968473

-0.75063 3.12518 1.025682 0.23447044 0.2980517 0.33681757 -0.05709

PASO 1 1.118563 1 -1.93695 PASO 2 0.28377567 0.1578019 0.01459002 0.002257

2.501685 -3.06045 1 0.28191072 -0.2626861 0.20204064 0.000295

norma

-0.057093 0.2344704 0.2980517 0.33681757 -0.0126147 0.013142

PASO 3 0.0022567 0.2837757 0.1578019 0.01459002 -0.0158412

0.0002949 0.2819107 -0.2626861 0.20204064 -0.0166284

0.916964 -0.0126147 0.90435

PASO 4 1.118563 -0.0158412 1.102721

0.968473 -0.0166284 0.951844

=

+ =

=

+ =


27/39

, = 2 .


28/39

D3 B3 D4 B4 D5

Propano 11.57094 8.56238 6.76773 5.81176 3.95255

n-butano 30.69344 25.17339 20.84461 17.81885 11.70061

i-butano 33.819624 32.02329 29.91337 23.71197 15.83681

Pentano 22.735882 32.53703 37.8993 46.49406 53.23297Hexano 0.974395 0.89049 2.27396 3.25458 8.51728

Heptano 0.202999 0.68499 1.42122 1.45294 3.0609

C8+ 0.002598 0.10275 0.75799 1.15073 2.98105

Agua 0.000122 0.02569 0.12182 0.30512 0.71785

caudal D3 B3 D4 B4 D5

100 100.00001 100 100.00001 100.00002

1 0 0 0 0

2.65263151 1 0 0 0

2.92280696 2.84371508 1 0 0

1.96491227 6.3858478 3.21407061 1 0

0.08421053 0.06886565 0.78884605 0.13368086 1

0.01754386 0.19588742 0.34159458 0.0406318 0.33049586

0.00022453 0.04070308 0.33426273 0.05409246 0.27389834

1.0544E-05 0.01039117 0.04803926 0.01420393 0.06064294

BALANCE GENERAL

MATRIZ L

11.57094 8.56238 6.76773 5.81176 3.95255 1.25631

0 2.46055104 2.89231618 2.40239232 1.21595134 0.11617251

0 6.99710612 10.1326016 6.7253174 4.28426934 1.98145838

0 15.7127045 24.6013043 35.0744615 45.466556 66.5054711

0 0.16944743 1.70404586 2.76516861 8.18443367 11.3241855

0 0.481991 1.218221 1.249941 2.857901 5.339561

0 0.100152 0.755392 1.148132 2.978452 2.953432

0 0.025568 0.121698 0.304998 0.717728 0.738888

11.57094 8.56238 6.76773 5.81176 3.95255 1.25631

0 2.46055104 2.89231618 2.40239232 1.21595134 0.11617251

0 0 1.9076785 -0.10640186 0.82645017 1.65109686

0 0 6.13141339 19.7331498 37.7016758 65.7636111

0 0 1.50486464 2.59972631 8.10069639 11.3161852

0 0 0.65165264 0.77934256 2.61971143 5.31680427


29/39

0 0 0.63766583 1.05034724 2.92895904 2.94870342

0 0 0.09164346 0.28003434 0.70509284 0.73768083

11.57094 8.56238 6.76773 5.81176 3.95255 1.25631

0 2.46055104 2.89231618 2.40239232 1.21595134 0.11617251

0 0 1.9076785 -0.10640186 0.82645017 1.651096860 0 0 20.0751329 35.0454066 60.4568692

0 0 0 2.683661 7.44875444 10.0137239

0 0 0 0.81568886 2.33740052 4.75279852

0 0 0 1.08591342 2.65270754 2.39680327

0 0 0 0.2851458 0.66539079 0.65836337

11.57094 8.56238 6.76773 5.81176 3.95255 1.25631

0 2.46055104 2.89231618 2.40239232 1.21595134 0.11617251

0 0 1.9076785 -0.10640186 0.82645017 1.65109686

0 0 0 20.0751329 35.0454066 60.4568692

0 0 0 0 2.7638544 1.93179776

0 0 0 0 0.91344243 2.29632687

0 0 0 0 0.75701512 -0.87345779

0 0 0 0 0.16760825 -0.20036184

11.57094 8.56238 6.76773 5.81176 3.95255 1.25631

0 2.46055104 2.89231618 2.40239232 1.21595134 0.11617251

0 0 1.9076785 -0.10640186 0.82645017 1.65109686

0 0 0 20.0751329 35.0454066 60.45686920 0 0 0 2.7638544 1.93179776

0 0 0 0 0 1.6578757

0 0 0 0 0 -1.40257399

0 0 0 0 0 -0.31751173

11.57094 8.56238 6.76773 5.81176 3.95255 1.25631

0 2.46055104 2.89231618 2.40239232 1.21595134 0.11617251

0 0 1.9076785 -0.10640186 0.82645017 1.65109686

0 0 0 20.0751329 35.0454066 60.45686920 0 0 0 2.7638544 1.93179776

0 0 0 0 0 1.6578757

0 0 0 0 0 0

0 0 0 0 0 0


30/39

B5 D6 B6 A

1.25631 0.65309 0.00147 500 11.57094 8.56238

3.4487 1.84694 0.03712 1400 30.69344 25.17339

5.65341 2.99769 0.10016 1700 33.819624 32.02329

68.97401 49.63492 47.13193 4000 22.735882 32.5370311.42998 17.76408 15.08222 800 0.974395 0.89049

5.54256 10.776 10.31011 500 0.202999 0.63220823

2.95603 13.58429 19.38348 800 0.002598 0.10207449

0.73901 2.74298 7.95351 300 0.000122 0.02565828

B5 D6 B6 100

100.00001 99.99999 100

0 0 0 11.57094 8.56238 6.76773

0 0 0 0 2.46055104 2.89231618

0 0 0 0 0 1.9076785

0 0 0 0 0 0

0 0 0 0 0 0

1 0 0 0 0 0

-0.84600672 1 0 0 0 0

-0.19151721 0.19411757 1 0 0 0

50073.6842469

29.0595142

0.65309 0.00147 -746.391852

0.11453289 0.03322063 829.675242

1.088834 0.09586347 222.990693

48.3516554 47.1290416 788.954179

17.7090829 15.0820962 147.677509

10.573001 10.107111

13.581692 19.380882

2.742858 7.953388

0.65309 0.00147

0.11453289 0.03322063

0.76313509 0.00139346

47.6202658 46.9168997

17.7011956 15.0798085

10.5505654 10.1006035

SUSTITUCION

HACIA

ADEL

ANTE


31/39

13.5770302 19.3795298

2.74166787 7.9530428

0.65309 0.00147

0.11453289 0.03322063

0.76313509 0.0013934645.1674958 46.912421

17.0991995 15.0787092

10.2898826 10.1001275

13.3219425 19.379064

2.70500743 7.95297586

0.65309 0.00147

0.11453289 0.03322063

0.76313509 0.00139346

45.1674958 46.912421

11.0611698 8.80741651

8.4546458 8.1939912

10.8787214 16.8414556

2.06345143 7.28663506

0.65309 0.00147

0.11453289 0.03322063

0.76313509 0.00139346

45.1674958 46.91242111.0611698 8.80741651

4.79897496 5.28317652

7.84908534 14.4291188

1.39266958 6.75252744

0.65309 0.00147

0.11453289 0.03322063

0.76313509 0.00139346

45.1674958 46.91242111.0611698 8.80741651

4.79897496 5.28317652

11.9090504 18.8987217

2.31175588 7.76434667

AL OBSERVAR EST

YA QUE NO ES MUY


32/39

6.76773 5.81176 3.95255 1.25631 0.65309 0.00147

20.84461 17.81885 11.70061 3.4487 1.84694 0.03712

29.91337 23.71197 15.83681 5.65341 2.99769 0.10016

37.8993 46.49406 53.23297 68.97401 49.63492 47.131932.27396 3.25458 8.51728 11.42998 17.76408 15.08222

1.33695314 1.35190173 2.927244 5.36160153 10.5844587 10.1071368

0.75691154 1.1494369 2.97933946 2.95371408 13.5818386 19.3808823

0.12176936 0.30505928 0.71776967 0.73890125 2.74286489 7.95338802

5.81176 3.95255 1.25631 0.65309 0.00147

2.40239232 1.21595134 0.11617251 0.11453289 0.03322063

-0.10640186 0.82645017 1.65109686 0.76313509 0.00139346

20.0751329 35.0454066 60.4568692 45.1674958 46.912421

0 2.7638544 1.93179776 11.0611698 8.80741651

0 0 1.6578757 4.79897496 5.28317652

0 0 0 11.9090504 18.8987217

0 0 0 0 4.09577282

(L x U)

MATRIZ U

SUSTITUCION

HACIA

ATRS

-80.8529036418.174893

-71.1195379

-390.420602

153.718681

-6.53568043

9.03013842

36.0560792

SUSTITUCION

HACIA

ATRS


33/39

METODO, NO ES MUY FACTIBLE UTILIZARLO

CERTADO PARA LA SOLUCION DE EL PROBLEMA


34/39

Compuesto CH4

Datos

Presion 850

Vol Molar 7.31382327

ratura Critica 342.7

resion Critica 667.8tor Acentrico 0.011

R 10.7314

a 9260.50201

b 0.42843183

Iteraciones xi Tr(Xi) (Xi) g(Xi) Xi+1 Tr(Xi+1) (Xi+1) g(Xi+1) Xi+2 Error

0 500 1.45900204 0.84381758 -201.876858 500.1 1.45929384 0.8437307 -201.707495 619.197329 201.7074946

1 500.1 1.45929384 0.8437307 -201.707495 619.197329 1.80682033 0.74862055 -1.30127615 619.97065 1.3012762

2 619.197329 1.80682033 0.74862055 -1.30127615 619.97065 1.80907689 0.74805208 -0.00763075 619.975212 0.0076308

3 619.97065 1.80907689 0.74805208 -0.00763075 619.975212 1.8090902 0.74804872 -2.6309E-07 619.975212 0.0000003

4 619.975212 1.8090902 0.74804872 -2.6309E-07 619.975212 1.8090902 0.74804872 0 619.975212 0.0000000

3. En un laboratorio se realizaron pruebas a un gas a una determinada presin,

temperatura y volumen molar. Se desea ajustar estos datos con la ecuacin de vander

Waals para obtener las constantes crticas.

Los datos reportados fueron:Calcular la Tc y Pc del gas y determinar cul gas es con el cual estaban

trabajando. Para todos los ejercicios calcular la norma de los deltas y los residuos

.

= , = , = , = ,

.

= , = , = , = ,


35/39


36/39

Compuesto CH4

850

7.31382327

342.7667.8

0.011

10.7314

9260.50201

0.42843183

Iteraciones a Tr(a) (a) F(a) b Tr(b)

0 600 1.75080245 0.76291861 -33.444269 700 2.04260286

1 600 1.75080245 0.76291861 -33.444269 650 1.89670266

2 600 1.75080245 0.76291861 -33.444269 625 1.82375255

3 612.5 1.7872775 0.75356785 -12.5085816 625 1.82375255

4 618.75 1.80551503 0.74894965 -2.04962673 625 1.82375255

5 618.75 1.80551503 0.74894965 -2.04962673 621.875 1.81463379

6 618.75 1.80551503 0.74894965 -2.04962673 620.3125 1.81007441

7 619.53125 1.80779472 0.74837501 -0.74266742 620.3125 1.81007441

8 619.921875 1.80893456 0.74808791 -0.08922174 620.3125 1.81007441

9 619.921875 1.80893456 0.74808791 -0.08922174 620.117188 1.80950449

10 619.921875 1.80893456 0.74808791 -0.08922174 620.019531 1.80921953

11 619.970703 1.80907704 0.74805204 -0.00754262 620.019531 1.80921953

12 619.970703 1.80907704 0.74805204 -0.00754262 619.995117 1.80914828

13 619.970703 1.80907704 0.74805204 -0.00754262 619.98291 1.80911266

14 619.970703 1.80907704 0.74805204 -0.00754262 619.976807 1.8090948515 619.973755 1.80908595 0.74804979 -0.00243769 619.976807 1.80909485

16 619.973755 1.80908595 0.74804979 -0.00243769 619.975281 1.8090904

17 619.974518 1.80908818 0.74804923 -0.00116145 619.975281 1.8090904

18 619.974899 1.80908929 0.74804895 -0.00052334 619.975281 1.8090904

19 619.97509 1.80908985 0.74804881 -0.00020428 619.975281 1.8090904

20 619.975185 1.80909012 0.74804874 -4.475E-05 619.975281 1.8090904

21 619.975185 1.80909012 0.74804874 -4.475E-05 619.975233 1.80909026

22 619.975209 1.80909019 0.74804873 -4.8678E-06 619.975233 1.80909026

23 619.975209 1.80909019 0.74804873 -4.8678E-06 619.975221 1.80909023

24 619.975209 1.80909019 0.74804873 -4.8678E-06 619.975215 1.80909021

25 619.975209 1.80909019 0.74804873 -4.8678E-06 619.975212 1.8090902

26 619.975211 1.8090902 0.74804872 -2.3752E-06 619.975212 1.8090902

27 619.975211 1.8090902 0.74804872 -1.1289E-06 619.975212 1.8090902

28 619.975212 1.8090902 0.74804872 -5.0569E-07 619.975212 1.8090902

29 619.975212 1.8090902 0.74804872 -1.9411E-07 619.975212 1.8090902

30 619.975212 1.8090902 0.74804872 -3.8325E-08 619.975212 1.8090902

b

Datos

Presion

Vol Molar

Temperatura CriticaPresion Critica

Factor Acentrico

R

a

3. En un laboratorio se realizaron pruebas a un gas a un

temperatura y volumen molar. Se desea ajustar estos d

Waals para obtener las constantes crticas.

Los datos reportados fueron:

Calcular la Tc y Pc del gas y determinar cul gas es con

trabajando. Para todos los ejercicios calcular la norma


37/39

(b) F(b) M Tr(M) (M) F(M) F(a)*F(M)

0.69212175 133.418029 650 1.89670266 0.726408 50.1597591 -1677.55647

0.726408 50.1597591 625 1.82375255 0.74436881 8.40352185 -281.049645

0.74436881 8.40352185 612.5 1.7872775 0.75356785 -12.5085816 418.340367

0.74436881 8.40352185 618.75 1.80551503 0.74894965 -2.04962673 25.6379232

0.74436881 8.40352185 621.875 1.81463379 0.74665459 3.17766787 -6.51303299

0.74665459 3.17766787 620.3125 1.81007441 0.74780096 0.56420133 -1.15640212

0.74780096 0.56420133 619.53125 1.80779472 0.74837501 -0.74266742 1.522191

0.74780096 0.56420133 619.921875 1.80893456 0.74808791 -0.08922174 0.06626208

0.74780096 0.56420133 620.117188 1.80950449 0.74794442 0.23749262 -0.0211895

0.74794442 0.23749262 620.019531 1.80921953 0.74801616 0.07413615 -0.00661456

0.74801616 0.07413615 619.970703 1.80907704 0.74805204 -0.00754262 0.00067297

0.74801616 0.07413615 619.995117 1.80914828 0.7480341 0.03329681 -0.00025115

0.7480341 0.03329681 619.98291 1.80911266 0.74804307 0.0128771 -9.7127E-05

0.74804307 0.0128771 619.976807 1.80909485 0.74804755 0.00266724 -2.0118E-05

0.74804755 0.00266724 619.973755 1.80908595 0.74804979 -0.00243769 1.8387E-050.74804755 0.00266724 619.975281 1.8090904 0.74804867 0.00011478 -2.798E-07

0.74804867 0.00011478 619.974518 1.80908818 0.74804923 -0.00116145 2.8313E-06

0.74804867 0.00011478 619.974899 1.80908929 0.74804895 -0.00052334 6.0783E-07

0.74804867 0.00011478 619.97509 1.80908985 0.74804881 -0.00020428 1.0691E-07

0.74804867 0.00011478 619.975185 1.80909012 0.74804874 -4.475E-05 9.1415E-09

0.74804867 0.00011478 619.975233 1.80909026 0.74804871 3.5014E-05 -1.5669E-09

0.74804871 3.5014E-05 619.975209 1.80909019 0.74804873 -4.8678E-06 2.1784E-10

0.74804871 3.5014E-05 619.975221 1.80909023 0.74804872 1.5073E-05 -7.3374E-11

0.74804872 1.5073E-05 619.975215 1.80909021 0.74804872 5.1028E-06 -2.4839E-11

0.74804872 5.1028E-06 619.975212 1.8090902 0.74804872 1.1747E-07 -5.718E-13

0.74804872 1.1747E-07 619.975211 1.8090902 0.74804872 -2.3752E-06 1.1562E-11

0.74804872 1.1747E-07 619.975211 1.8090902 0.74804872 -1.1289E-06 2.6812E-12

0.74804872 1.1747E-07 619.975212 1.8090902 0.74804872 -5.0569E-07 5.7086E-13

0.74804872 1.1747E-07 619.975212 1.8090902 0.74804872 -1.9411E-07 9.8163E-14

0.74804872 1.1747E-07 619.975212 1.8090902 0.74804872 -3.8325E-08 7.4394E-15

0.74804872 1.1747E-07 619.975212 1.8090902 0.74804872 3.9571E-08 -1.5165E-15

a determinada presin,

atos con la ecuacin de vander

l cual estaban

de los deltas y los residuos


38/39

Error

50.1597591

8.4035219

12.5085816

2.0496267

3.1776679

0.5642013

0.7426674

0.0892217

0.2374926

0.0741361

0.0075426

0.0332968

0.0128771

0.0026672

0.00243770.0001148

0.0011615

0.0005233

0.0002043

0.0000448

0.0000350

0.0000049

0.0000151

0.0000051

0.0000001

0.0000024

0.0000011

0.0000005

0.0000002

0.0000000

0.0000000


39/39

metodos numericos jose gonzalez cod 2063307

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