MNIRH_TP6

UNIVERSIDAD NACIONAL AGRARIA LA MOLINA

SEMESTRE : 2015 – I

DOCENTE : Ing. Jose Arapa

ALUMNO : Aguedo Tahua Robert Henry.

CURSO : Métodos numéricos en ingeniería

de recursos hídricos.

TEMA : Flujo tránsito en tuberías.

CODIGO : 20150824

La Molina - Lima

ESCUELA DE POSTGRADO MAESTRIA EN RECURSOS HIDRICOS

Trabajo Nº 06

Maestría en recursos Hídricos - Universidad Nacional Agraria la Molina

2

INDICE

I. Reproducir en Hoja de Cálculo Excel, el Ejemplo 16.1 Pág. 329 del Texto Métodos Numéricos en

Recursos Hídricos del Prof. Abel Mejía................................................................................................ 2

II. Probar y ejecutar el código en MATLAB, proporcionado por el profesor en hora de clases, con el ejemplo

16.1 anteriormente referido, esto para verificar el código mismo y el ejemplo. ......................................... 7

III. Probar y ejecutar el código en MATLAB, proporcionado por el profesor en hora de clases, con datos

obtenidos de artículos de diseño, modelado y simulación de chimeneas de equilibrio, proporcionados por

el profesor de clases y/o obtenidos por otros medios como del Internet. ............................................... 10

I. Reproducir en Hoja de Cálculo Excel, el Ejemplo 16.1 Pág. 329 del Texto Métodos Numéricos en

Recursos Hídricos del Prof. Abel Mejía.

Datos

L = 12.69 D = 0.1016

DC = 0.187 F = 0.023

KE = 0.75 K0 = 1.3 Q0 = 0.013 Z0 = -0.66 N = 100

Calculo Previos

A = 0.008 AC = 0.027 A0 = 0.027

PERIODO = 13.153 C = 3584.640 E = 0.066 M = 2.770

DT = 0.132


3

Resultados experimentales.

t Z experim. 0 -0.66

4.14 0.665 10.82 -0.42 17.4 0.34

Aplicación del algoritmo Chimenea.

N t Z teórico V DV DZ

0 0 -0.66 0.4733368 0.0011811 0.0622579

1 0.1315298 -0.5977421 0.4745179 -0.0007806 0.0624132

2 0.2630595 -0.5353289 0.4737373 -0.0025924 0.0623106

3 0.3945893 -0.4730183 0.4711448 -0.004259 0.0619696

4 0.5261191 -0.4110488 0.4668859 -0.0057868 0.0614094

5 0.6576489 -0.3496394 0.461099 -0.0071835 0.0606483

6 0.7891786 -0.2889911 0.4539155 -0.0084573 0.0597034

7 0.9207084 -0.2292877 0.4454582 -0.0096169 0.058591

8 1.0522382 -0.1706967 0.4358413 -0.0106708 0.0573261

9 1.183768 -0.1133706 0.4251705 -0.0116275 0.0559226

10 1.3152977 -0.057448 0.413543 -0.0124952 0.0543932

11 1.4468275 -0.0030548 0.4010479 -0.0132815 0.0527497

12 1.5783573 0.049695 0.3877664 -0.0139937 0.0510028

13 1.7098871 0.1006978 0.3737728 -0.0146384 0.0491622

14 1.8414168 0.14986 0.3591343 -0.015222 0.0472369

15 1.9729466 0.1970969 0.3439123 -0.01575 0.0452347

16 2.1044764 0.2423316 0.3281624 -0.0162276 0.0431631

17 2.2360062 0.2854947 0.3119348 -0.0166595 0.0410287

18 2.3675359 0.3265234 0.2952753 -0.0170498 0.0388375

19 2.4990657 0.3653609 0.2782255 -0.0174025 0.0365949

20 2.6305955 0.4019559 0.260823 -0.0177209 0.034306

21 2.7621253 0.4362619 0.243102 -0.0180081 0.0319752

22 2.893655 0.468237 0.2250939 -0.0182668 0.0296066

23 3.0251848 0.4978436 0.2068271 -0.0184995 0.0272039

24 3.1567146 0.5250475 0.1883276 -0.0187082 0.0247707

25 3.2882444 0.5498182 0.1696195 -0.0188949 0.02231

26 3.4197741 0.5721282 0.1507246 -0.0190612 0.0198248

27 3.5513039 0.591953 0.1316634 -0.0192087 0.0173177

28 3.6828337 0.6092706 0.1124547 -0.0193386 0.0147911

29 3.8143634 0.6240617 0.093116 -0.019452 0.0122475

30 3.9458932 0.6363093 0.073664 -0.0195499 0.009689

31 4.077423 0.6459983 0.0541141 -0.019633 0.0071176

32 4.2089528 0.6531159 0.0344811 -0.019702 0.0045353

33 4.3404825 0.6576512 0.0147791 -0.0197574 0.0019439

34 4.4720123 0.6595951 -0.0049783 -0.0197956 -0.0006548

35 4.6035421 0.6589403 -0.0247739 -0.0197269 -0.0032585

36 4.7350719 0.6556818 -0.0445008 -0.0195155 -0.0058532

37 4.8666016 0.6498286 -0.0640163 -0.0191637 -0.0084201

38 4.9981314 0.6414086 -0.0831801 -0.0186765 -0.0109407

39 5.1296612 0.6304679 -0.1018566 -0.0180608 -0.0133972

40 5.261191 0.6170707 -0.1199173 -0.0173256 -0.0157727

41 5.3927207 0.601298 -0.1372429 -0.0164817 -0.0180515


4


42 5.5242505 0.5832465 -0.1537247 -0.0155412 -0.0202194

43 5.6557803 0.5630271 -0.1692659 -0.0145169 -0.0222635

44 5.7873101 0.5407636 -0.1837828 -0.0134226 -0.0241729

45 5.9188398 0.5165907 -0.1972054 -0.0122718 -0.0259384

46 6.0503696 0.4906523 -0.2094772 -0.0110783 -0.0275525

47 6.1818994 0.4630999 -0.2205555 -0.0098552 -0.0290096

48 6.3134292 0.4340902 -0.2304108 -0.008615 -0.0303059

49 6.4449589 0.4037844 -0.2390258 -0.0073691 -0.031439

50 6.5764887 0.3723454 -0.2463949 -0.006128 -0.0324083

51 6.7080185 0.3399371 -0.2525229 -0.0049011 -0.0332143

52 6.8395483 0.3067228 -0.257424 -0.0036964 -0.0338589

53 6.971078 0.2728639 -0.2611204 -0.0025207 -0.0343451

54 7.1026078 0.2385188 -0.2636411 -0.0013799 -0.0346767

55 7.2341376 0.2038421 -0.265021 -0.0002784 -0.0348582

56 7.3656674 0.168984 -0.2652995 0.0007801 -0.0348948

57 7.4971971 0.1340892 -0.2645194 0.0017931 -0.0347922

58 7.6287269 0.099297 -0.2627263 0.0027588 -0.0345563

59 7.7602567 0.0647407 -0.2599675 0.0036761 -0.0341935

60 7.8917864 0.0305472 -0.2562914 0.0045446 -0.0337099

61 8.0233162 -0.0031627 -0.2517468 0.0053644 -0.0331122

62 8.154846 -0.0362749 -0.2463824 0.0061361 -0.0324066

63 8.2863758 -0.0686815 -0.2402463 0.0068605 -0.0315995

64 8.4179055 -0.1002811 -0.2333858 0.0075388 -0.0306972

65 8.5494353 -0.1309783 -0.225847 0.0081723 -0.0297056

66 8.6809651 -0.1606839 -0.2176747 0.0087625 -0.0286307

67 8.8124949 -0.1893146 -0.2089121 0.0093111 -0.0274782

68 8.9440246 -0.2167927 -0.199601 0.0098196 -0.0262535

69 9.0755544 -0.2430462 -0.1897815 0.0102897 -0.0249619

70 9.2070842 -0.2680081 -0.1794918 0.010723 -0.0236085

71 9.338614 -0.2916166 -0.1687688 0.0111211 -0.0221981

72 9.4701437 -0.3138148 -0.1576478 0.0114855 -0.0207354

73 9.6016735 -0.3345501 -0.1461623 0.0118177 -0.0192247

74 9.7332033 -0.3537748 -0.1343445 0.0121191 -0.0176703

75 9.8647331 -0.3714451 -0.1222254 0.012391 -0.0160763

76 9.9962628 -0.3875214 -0.1098344 0.0126344 -0.0144465

77 10.127793 -0.4019679 -0.0972 0.0128505 -0.0127847

78 10.259322 -0.4147526 -0.0843494 0.0130403 -0.0110945

79 10.390852 -0.4258471 -0.0713092 0.0132045 -0.0093793

80 10.522382 -0.4352263 -0.0581046 0.013344 -0.0076425

81 10.653912 -0.4428688 -0.0447607 0.0134592 -0.0058874

82 10.785441 -0.4487562 -0.0313015 0.0135508 -0.0041171

83 10.916971 -0.4528733 -0.0177507 0.0136191 -0.0023347

84 11.048501 -0.455208 -0.0041316 0.0136644 -0.0005434

85 11.180031 -0.4557514 0.0095328 0.0136717 0.0012539

86 11.311561 -0.4544976 0.0232046 0.0135969 0.0030521

87 11.44309 -0.4514455 0.0368015 0.0134374 0.0048405

88 11.57462 -0.446605 0.0502389 0.0131949 0.0066079

89 11.70615 -0.4399971 0.0634338 0.0128719 0.0083434

90 11.83768 -0.4316537 0.0763057 0.0124719 0.0100365

91 11.969209 -0.4216172 0.0887776 0.0119995 0.0116769

92 12.100739 -0.4099403 0.100777 0.0114599 0.0132552

93 12.232269 -0.3966851 0.1122369 0.010859 0.0147625

94 12.363799 -0.3819226 0.1230959 0.0102035 0.0161908


5


95 12.495329 -0.3657319 0.1332994 0.0095 0.0175328

96 12.626858 -0.348199 0.1427993 0.0087556 0.0187824

97 12.758388 -0.3294167 0.151555 0.0079776 0.019934

98 12.889918 -0.3094827 0.1595326 0.0071729 0.0209833

99 13.021448 -0.2884994 0.1667055 0.0063486 0.0219267

100 13.152977 -0.2665726 0.1730541 0.0055111 0.0227618

101 13.284507 -0.2438109 0.1785652 0.0046668 0.0234866

102 13.416037 -0.2203242 0.183232 0.0038215 0.0241005

103 13.547567 -0.1962238 0.1870534 0.0029804 0.0246031

104 13.679097 -0.1716207 0.1900338 0.0021485 0.0249951

105 13.810626 -0.1466256 0.1921824 0.00133 0.0252777

106 13.942156 -0.1213479 0.1935124 0.0005287 0.0254526

107 14.073686 -0.0958952 0.1940411 -0.0002523 0.0255222

108 14.205216 -0.0703731 0.1937887 -0.0010102 0.025489

109 14.336745 -0.0448841 0.1927785 -0.0017428 0.0253561

110 14.468275 -0.019528 0.1910357 -0.0024483 0.0251269

111 14.599805 0.0055989 0.1885874 -0.0031252 0.0248049

112 14.731335 0.0304038 0.1854623 -0.0037725 0.0243938

113 14.862864 0.0547976 0.1816898 -0.0043895 0.0238976

114 14.994394 0.0786952 0.1773003 -0.0049757 0.0233203

115 15.125924 0.1020155 0.1723245 -0.0055311 0.0226658

116 15.257454 0.1246813 0.1667935 -0.0060554 0.0219383

117 15.388984 0.1466196 0.1607381 -0.006549 0.0211418

118 15.520513 0.1677614 0.1541891 -0.0070121 0.0202805

119 15.652043 0.1880419 0.147177 -0.0074451 0.0193582

120 15.783573 0.2074001 0.139732 -0.0078485 0.0183789

121 15.915103 0.225779 0.1318835 -0.0082229 0.0173466

122 16.046632 0.2431256 0.1236606 -0.0085688 0.016265

123 16.178162 0.2593906 0.1150917 -0.0088869 0.015138

124 16.309692 0.2745286 0.1062048 -0.0091778 0.0139691

125 16.441222 0.2884977 0.097027 -0.009442 0.0127619

126 16.572752 0.3012596 0.0875851 -0.0096801 0.01152

127 16.704281 0.3127797 0.077905 -0.0098927 0.0102468

128 16.835811 0.3230265 0.0680123 -0.0100802 0.0089456

129 16.967341 0.3319722 0.0579322 -0.0102431 0.0076198

130 17.098871 0.339592 0.047689 -0.0103819 0.0062725

131 17.2304 0.3458645 0.0373071 -0.0104968 0.004907

132 17.36193 0.3507715 0.0268104 -0.0105881 0.0035264

133 17.49346 0.3542979 0.0162223 -0.0106561 0.0021337

134 17.62499 0.3564316 0.0055662 -0.0107008 0.0007321

135 17.75652 0.3571637 -0.0051346 -0.010718 -0.0006754

136 17.888049 0.3564883 -0.0158526 -0.010679 -0.0020851

137 18.019579 0.3544032 -0.0265317 -0.0105788 -0.0034897

138 18.151109 0.3509135 -0.0371105 -0.0104181 -0.0048811

139 18.282639 0.3460324 -0.0475286 -0.0101983 -0.0062514

140 18.414168 0.339781 -0.0577268 -0.0099214 -0.0075928

141 18.545698 0.3321882 -0.0676482 -0.0095901 -0.0088978

142 18.677228 0.3232904 -0.0772383 -0.0092075 -0.0101591

143 18.808758 0.3131313 -0.0864458 -0.0087772 -0.0113702

144 18.940287 0.3017611 -0.095223 -0.0083034 -0.0125247

145 19.071817 0.2892364 -0.1035264 -0.0077902 -0.0136168

146 19.203347 0.2756196 -0.1113166 -0.0072424 -0.0146415

147 19.334877 0.2609782 -0.118559 -0.0066645 -0.015594


6


148 19.466407 0.2453841 -0.1252235 -0.0060614 -0.0164706

149 19.597936 0.2289135 -0.1312849 -0.0054377 -0.0172679

150 19.729466 0.2116456 -0.1367226 -0.0047983 -0.0179831

151 19.860996 0.1936626 -0.1415208 -0.0041475 -0.0186142

152 19.992526 0.1750484 -0.1456683 -0.0034897 -0.0191597

153 20.124055 0.1558886 -0.1491581 -0.0028291 -0.0196187

154 20.255585 0.1362699 -0.1519872 -0.0021694 -0.0199908

155 20.387115 0.1162791 -0.1541566 -0.0015142 -0.0202762

156 20.518645 0.0960029 -0.1556708 -0.0008666 -0.0204753

157 20.650175 0.0755275 -0.1565374 -0.0002295 -0.0205893

158 20.781704 0.0549382 -0.1567669 0.0003944 -0.0206195

159 20.913234 0.0343187 -0.1563725 0.001003 -0.0205676

160 21.044764 0.013751 -0.1553695 0.0015944 -0.0204357

161 21.176294 -0.0066847 -0.1537751 0.0021668 -0.020226

162 21.307823 -0.0269107 -0.1516083 0.0027188 -0.019941

163 21.439353 -0.0468517 -0.1488895 0.0032494 -0.0195834

164 21.570883 -0.0664351 -0.1456401 0.0037576 -0.019156

165 21.702413 -0.0855911 -0.1418824 0.0042428 -0.0186618

166 21.833943 -0.1042528 -0.1376396 0.0047043 -0.0181037

167 21.965472 -0.1223566 -0.1329353 0.0051418 -0.017485

168 22.097002 -0.1398415 -0.1277935 0.0055552 -0.0168086

169 22.228532 -0.1566502 -0.1222383 0.0059442 -0.016078

170 22.360062 -0.1727281 -0.1162941 0.0063089 -0.0152961

171 22.491591 -0.1880243 -0.1099852 0.0066493 -0.0144663

172 22.623121 -0.2024906 -0.1033359 0.0069656 -0.0135917

173 22.754651 -0.2160823 -0.0963703 0.0072579 -0.0126756

174 22.886181 -0.2287579 -0.0891124 0.0075264 -0.0117209

175 23.01771 -0.2404788 -0.081586 0.0077714 -0.010731

176 23.14924 -0.2512098 -0.0738147 0.007993 -0.0097088

177 23.28077 -0.2609186 -0.0658216 0.0081917 -0.0086575

178 23.4123 -0.2695761 -0.05763 0.0083674 -0.0075801

179 23.54383 -0.2771562 -0.0492625 0.0085206 -0.0064795

180 23.675359 -0.2836357 -0.040742 0.0086513 -0.0053588

181 23.806889 -0.2889945 -0.0320907 0.0087597 -0.0042209

182 23.938419 -0.2932154 -0.0233309 0.0088461 -0.0030687

183 24.069949 -0.2962841 -0.0144849 0.0089104 -0.0019052

184 24.201478 -0.2981893 -0.0055745 0.0089527 -0.0007332

185 24.333008 -0.2989225 0.0033782 0.0089712 0.0004443

186 24.464538 -0.2984782 0.0123493 0.0089461 0.0016243

187 24.596068 -0.2968538 0.0212954 0.0088723 0.002801

188 24.727598 -0.2940529 0.0301677 0.0087503 0.003968

189 24.859127 -0.2900849 0.038918 0.0085809 0.0051189

190 24.990657 -0.284966 0.0474989 0.0083656 0.0062475

191 25.122187 -0.2787185 0.0558645 0.0081062 0.0073478

192 25.253717 -0.2713707 0.0639707 0.0078049 0.0084141

193 25.385246 -0.2629566 0.0717756 0.0074642 0.0094406

194 25.516776 -0.253516 0.0792398 0.0070872 0.0104224

195 25.648306 -0.2430936 0.086327 0.0066768 0.0113546

196 25.779836 -0.231739 0.0930038 0.0062364 0.0122328

197 25.911366 -0.2195063 0.0992402 0.0057696 0.013053

198 26.042895 -0.2064532 0.1050098 0.0052798 0.0138119

199 26.174425 -0.1926413 0.1102896 0.0047707 0.0145064

200 26.305955 -0.178135 0.1150603 0.0042459 0.0151339


7

II. Probar y ejecutar el código en MATLAB, proporcionado por el profesor en hora de clases, con el

ejemplo 16.1 anteriormente referido, esto para verificar el código mismo y el ejemplo.

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 5 10 15 20 25 30Z (

m)

t (segundos)

Oscilación en la Chimenea de Equilibrio

Z teórico

Z experim.

%Flujo Transitorio en Tuberías

%Oscilacion de presiones en chimenea de equilibrio

clc;clear

%DATOS DE ENTRADA

L=12.69 ; %Longitud de la tuberia de presión (m)

D=0.1016; %Diámetro de la tuberia de presión (m)

Dc=0.187; %Diámetro de la chimenea

f=0.023; %Factor de fricción de Darcy

Ke=0.75; %Coeficiente en Tuberia

Ko=1.30; %Coeficiente en Chimenea

Qo=0.013; %Caudal inicial en la chimenea

Zo=-0.66; %Nivel inicial en la chmenea

N=100; %Numero de iteraciones recomendado

g=9.81; %Aceleracion de gravedad

%DATOS EXPERIMENTALES REGISTRADOS

tte=[0 4.14 10.82 17.40]; %Tiempos de experimentales

ZZe=[-0.66 0.665 -0.42 0.34]; %Niveles experimentales


8

Resultado en la ventana de comandos de Matlab.

%CALCULOS PREVIOS

A=pi*D^2/4;Ac=pi*Dc^2/4;Ao=Ac;

T=2*pi*sqrt(L*Ac/g/A);

C=1/(2*g*A^2)*(1+Ke+f*L/D);

E=Ko*Ac^2/(2*g*Ao^2);

M=C*Ac^2-E;Dt=T/N;

%CONDICIONES INICIALES (t=0)

Z=Zo;V=Qo/Ac;

DV=-(2*pi/T)^2*(Z+M*V*abs(V))*Dt;

DZ=V*Dt;

i=1;t(i)=0;Z(i)=Z;V(i)=V;DV(i)=DV;DZ(i)=DZ;

%CONDICIONES GENERALES (t>0)

while abs(Z(i))>=0.0001

i=i+1;

t(i)=t(i-1)+Dt;

Z(i)=Z(i-1)+DZ(i-1);

V(i)=V(i-1)+DV(i-1);

DV(i)=-(2*pi/T)^2*(Z(i)+M*V(i)*abs(V(i)))*Dt;

DZ(i)=V(i)*Dt;

ID(i)=i-1;

end

RESUL=[ID' t' Z' V' DV' DZ']';%Tabla de Resultados

fprintf('Iter Tiempo(s) Nivel Z(m) Velocidad(m/s) DV(m/s)

DZ(m) \n')

fprintf('%3.0i %8.4f %9.4f %12.4f %12.4f %8.4f\n',RESUL)

plot(t,Z,tte,ZZe);grid;%Grafico de Resultados

title('Osciliación en la Chimenea de Equilibrio');

xlabel('Tiempo t (s)');ylabel('Nivel en Chimenea Equilibrio

Z(m)')

Iter Tiempo(s) Nivel Z(m) Velocidad(m/s) DV(m/s) DZ(m)

0.0000 -0.6600 0.4733 0.0021 0.0623

1 0.1315 -0.5977 0.4754 0.0000 0.0625

2 0.2631 -0.5352 0.4755 -0.0018 0.0625

3 0.3946 -0.4727 0.4736 -0.0036 0.0623

4 0.5261 -0.4104 0.4701 -0.0052 0.0618

5 0.6576 -0.3486 0.4649 -0.0066 0.0611

6 0.7892 -0.2874 0.4582 -0.0080 0.0603

7 0.9207 -0.2271 0.4502 -0.0092 0.0592

8 1.0522 -0.1679 0.4410 -0.0104 0.0580

9 1.1838 -0.1099 0.4306 -0.0114 0.0566

10 1.3153 -0.0533 0.4193 -0.0123 0.0551

11 1.4468 0.0019 0.4069 -0.0132 0.0535

12 1.5784 0.0554 0.3938 -0.0139 0.0518

13 1.7099 0.1072 0.3798 -0.0146 0.0500

14 1.8414 0.1572 0.3652 -0.0153 0.0480

15 1.9729 0.2052 0.3499 -0.0159 0.0460

16 2.1045 0.2512 0.3341 -0.0164 0.0439

17 2.2360 0.2952 0.3177 -0.0168 0.0418

18 2.3675 0.3369 0.3008 -0.0173 0.0396

19 2.4991 0.3765 0.2836 -0.0177 0.0373

20 2.6306 0.4138 0.2659 -0.0180 0.0350


9

Iter Tiempo(s) Nivel Z(m) Velocidad(m/s) DV(m/s) DZ(m)

0.0000 -0.6600 0.4733 0.0021 0.0623

1 0.1315 -0.5977 0.4754 0.0000 0.0625

2 0.2631 -0.5352 0.4755 -0.0018 0.0625

3 0.3946 -0.4727 0.4736 -0.0036 0.0623

4 0.5261 -0.4104 0.4701 -0.0052 0.0618

5 0.6576 -0.3486 0.4649 -0.0066 0.0611

6 0.7892 -0.2874 0.4582 -0.0080 0.0603

7 0.9207 -0.2271 0.4502 -0.0092 0.0592

8 1.0522 -0.1679 0.4410 -0.0104 0.0580

9 1.1838 -0.1099 0.4306 -0.0114 0.0566

10 1.3153 -0.0533 0.4193 -0.0123 0.0551

11 1.4468 0.0019 0.4069 -0.0132 0.0535

12 1.5784 0.0554 0.3938 -0.0139 0.0518

13 1.7099 0.1072 0.3798 -0.0146 0.0500

14 1.8414 0.1572 0.3652 -0.0153 0.0480

15 1.9729 0.2052 0.3499 -0.0159 0.0460

16 2.1045 0.2512 0.3341 -0.0164 0.0439

17 2.2360 0.2952 0.3177 -0.0168 0.0418

18 2.3675 0.3369 0.3008 -0.0173 0.0396

19 2.4991 0.3765 0.2836 -0.0177 0.0373

20 2.6306 0.4138 0.2659 -0.0180 0.0350

21 2.7621 0.4488 0.2479 -0.0183 0.0326

22 2.8937 0.4814 0.2295 -0.0186 0.0302

23 3.0252 0.5116 0.2109 -0.0189 0.0277

24 3.1567 0.5393 0.1921 -0.0191 0.0253

25 3.2882 0.5646 0.1729 -0.0193 0.0227

26 3.4198 0.5873 0.1536 -0.0195 0.0202

27 3.5513 0.6075 0.1341 -0.0197 0.0176

28 3.6828 0.6252 0.1145 -0.0198 0.0151

29 3.8144 0.6402 0.0947 -0.0199 0.0125

30 3.9459 0.6527 0.0747 -0.0200 0.0098

31 4.0774 0.6625 0.0547 -0.0201 0.0072

32 4.2090 0.6697 0.0346 -0.0202 0.0045

33 4.3405 0.6743 0.0144 -0.0203 0.0019

34 4.4720 0.6762 -0.0059 -0.0203 -0.0008

35 4.6035 0.6754 -0.0262 -0.0202 -0.0034

36 4.7351 0.6719 -0.0464 -0.0200 -0.0061

37 4.8666 0.6658 -0.0664 -0.0196 -0.0087

38 4.9981 0.6571 -0.0860 -0.0191 -0.0113

39 5.1297 0.6458 -0.1051 -0.0185 -0.0138

40 5.2612 0.6320 -0.1237 -0.0178 -0.0163

. . . . . .

. . . . . .

. . . . . .

991 130.3460 -0.1307 0.0266 0.0039 0.0035

992 130.4775 -0.1272 0.0304 0.0037 0.0040

993 130.6091 -0.1232 0.0342 0.0036 0.0045

994 130.7406 -0.1187 0.0378 0.0034 0.0050

995 130.8721 -0.1137 0.0412 0.0033 0.0054

996 131.0037 -0.1083 0.0445 0.0031 0.0059

997 131.1352 -0.1024 0.0476 0.0029 0.0063

998 131.2667 -0.0962 0.0505 0.0027 0.0066

999 131.3982 -0.0895 0.0532 0.0025 0.0070

1000 131.5298 -0.0825 0.0556 0.0022 0.0073

1001 131.6613 -0.0752 0.0579 0.0020 0.0076

1002 131.7928 -0.0676 0.0599 0.0017 0.0079

1003 131.9244 -0.0597 0.0616 0.0015 0.0081

1004 132.0559 -0.0516 0.0631 0.0012 0.0083

1005 132.1874 -0.0433 0.0643 0.0010 0.0085

1006 132.3190 -0.0349 0.0653 0.0007 0.0086

1007 132.4505 -0.0263 0.0660 0.0004 0.0087

1008 132.5820 -0.0176 0.0665 0.0002 0.0087

1009 132.7135 -0.0089 0.0666 -0.0001 0.0088

1010 132.8451 -0.0001 0.0666 -0.0003 0.0088


10

Resultado en la en ventana de gráficos de Matlab:

III. Probar y ejecutar el código en MATLAB, proporcionado por el profesor en hora de clases, con

datos obtenidos de artículos de diseño, modelado y simulación de chimeneas de equilibrio,

proporcionados por el profesor de clases y/o obtenidos por otros medios como del Internet.

%Flujo Transitorio en Tuberías

%Oscilacion de presiones en chimenea de equilibrio

clc;clear

%DATOS DE ENTRADA

L=1820 ; %Longitud de la tuberia de presión (m)

D=3.1; %Diámetro de la tuberia de presión (m)

Dc=10; %Diámetro de la chimenea

f=0.05; %Factor de fricción de Darcy

Ke=0.75; %Coeficiente en Tuberia

Ko=1.30; %Coeficiente en Chimenea

Qo=16; %Caudal inicial en la chimenea

Zo=-3; %Nivel inicial en la chimenea

N=100; %Numero de iteraciones recomendado

g=9.81; %Aceleracion de gravedad


11

Resultado en la ventana de grafico de matlab.

%DATOS EXPERIMENTALES REGISTRADOS

tte=[0 80 220 350 490]; %Tiempos de experimentales

ZZe=[-3 5.5 -4 2.7 -2.2]; %Niveles experimentales

%CALCULOS PREVIOS

A=pi*D^2/4;Ac=pi*Dc^2/4;Ao=Ac;

T=2*pi*sqrt(L*Ac/g/A);

C=1/(2*g*A^2)*(1+Ke+f*L/D);

E=Ko*Ac^2/(2*g*Ao^2);

M=C*Ac^2-E;Dt=T/N;

%CONDICIONES INICIALES (t=0)

Z=Zo;V=Qo/Ac;

DV=-(2*pi/T)^2*(Z+M*V*abs(V))*Dt;

DZ=V*Dt;

i=1;t(i)=0;Z(i)=Z;V(i)=V;DV(i)=DV;DZ(i)=DZ;

%CONDICIONES GENERALES (t>0)

while abs(Z(i))>=0.0001

i=i+1;

t(i)=t(i-1)+Dt;

Z(i)=Z(i-1)+DZ(i-1);

V(i)=V(i-1)+DV(i-1);

DV(i)=-(2*pi/T)^2*(Z(i)+M*V(i)*abs(V(i)))*Dt;

DZ(i)=V(i)*Dt;

ID(i)=i-1;

end

RESUL=[ID' t' Z' V' DV' DZ']';%Tabla de Resultados

fprintf('Iter Tiempo(s) Nivel Z(m) Velocidad(m/s) DV(m/s)

DZ(m) \n')

fprintf('%3.0i %8.4f %9.4f %12.4f %12.4f %8.4f\n',RESUL)

plot(t,Z,tte,ZZe);grid;%Grafico de Resultados

title('Osciliación en la Chimenea de Equilibrio');

xlabel('Tiempo t (s)');ylabel('Nivel en Chimenea Equilibrio

Z(m)')

Documents

MNIRH_TP6