Tabla 1

Tubo N°4 tanque plano Modelo Ocon-Tojo

h(m) t(s)experimental(promedio)

velocidad experimental

(m/s)

velocidad (m/s)modelo

Ocon-tojo

Re f t (s)modelo

Ocon-tojo0.38 0 2.413 18995.9306 0.02691671 00.36 3.45 2.661934339 2.371 18663.0649 0.02703593 3.596515420.34 7.03 2.565271919 2.328 18324.5213 0.02715995 7.260535850.32 10.31 2.799900448 2.284 17979.9931 0.02728913 10.99589680.3 14.12 2.410412984 2.24 17629.1456 0.0274239 14.8068074

0.28 17.715 2.55456842 2.195 17271.6109 0.02756474 18.69790360.26 21.3 2.561694134 2.148 16906.9845 0.02771217 22.67431040.24 25.065 2.439222701 2.101 16534.8186 0.02786681 26.74171710.22 28.845 2.429543246 2.05 16154.6162 0.02802934 30.90646810.2 32.8 2.322041332 2.003 15765.8231 0.02820057 35.175672

0.18 36.83 2.278827164 1.953 15367.8177 0.02838141 39.55733740.16 40.965 2.220960936 1.901 14959.8993 0.02857294 44.06053870.14 45.165 2.186588921 1.85 14541.2733 0.0287764 48.69562530.12 49.525 2.106347126 1.794 14111.0323 0.02899328 53.47448540.1 53.82 2.138224323 1.74 13668.1321 0.02922535 58.4108839

0.08 58.185 2.103934357 1.68 13211.3615 0.02947475 63.52090240.06 63.055 1.885764573 1.619 12739.3017 0.02974409 68.82352030.04 68.12 1.813163568 1.557 12250.2726 0.03003659 74.34139610.02 73.22 1.800720288 1.493 11742.2603 0.03035632 80.1019421

0 78.455 1.754283375 1.43 11212.8154 0.03070849 86.1388357

Tubo N°4 tanque cono 45° Modelo Ocon-Tojo

h(m) t(s)experimental(promedio)

velocidad experimental

(m/s)

velocidad (m/s)modelo

Ocon-tojo

Re f t (s)modelo

Ocon-tojo0.38 0 - 2.6 19929.9922 0.02659563 00.36 3.385 2.71304977 2.56 19623.37694 0.02669892 3.541076440.34 6.69 2.77872117 2.514 19270.76938 0.02682022 7.142247960.32 9.975 2.7956388 2.472 18948.82336 0.02693342 10.80592320.3 13.235 2.81707775 2.43 18626.87733 0.02704905 14.5354742

0.28 16.82 2.56169413 2.385 18281.93516 0.02717575 18.3351260.26 20.22 2.70108043 2.341 17944.65837 0.02730255 22.2079510.24 23.645 2.68136452 2.295 17592.05081 0.02743835 26.1590520.22 27.35 2.47872428 2.25 17247.10864 0.02757452 30.19206180.2 30.99 2.52298722 2.202 16879.17032 0.02772358 34.3138753

0.18 34.805 2.40725386 2.154 16511.232 0.02787675 38.52896490.16 38.635 2.39782597 2.105 16135.6283 0.02803759 42.84422660.14 42.45 2.40725386 2.054 15744.69384 0.02821003 47.26763510.12 46.6 2.21293337 2.003 15353.75938 0.02838791 51.80581390.1 50.635 2.27600334 1.951 14955.15953 0.0285752 56.4685502

0.08 54.865 2.1710812 1.897 14541.22893 0.02877642 61.26727360.06 59.155 2.14071643 1.841 14111.96756 0.0289928 66.21416480.04 63.615 2.05911961 1.784 13675.0408 0.02922166 71.32187110.02 68.285 1.96652537 1.725 13222.78329 0.02946839 76.6077406

0 73.15 1.88770267 1.664 12755.19501 0.02973482 82.0908067

Tubo N° 4 tanque cono 60° modelo Ocon-tojo

h(m) t experimental(promedio)

velocidad experimental

velocidad(m/s)

ModeloOcon-Tojo

Re f t (s)modelo

Ocon-tojo

0.38 0 2.7279652 20910.8943 0.0262781 00.36 3.355 2.73730953 2.68731138 20599.2673 0.02637692 3.356525170.34 6.56 2.86542074 2.64607119 20283.1455 0.0264791 6.766345920.32 9.455 3.17225336 2.60421799 19962.3247 0.02658486 10.23200870.3 12.73 2.80417511 2.56172308 19636.585 0.02669443 13.7562675

0.28 15.955 2.84765069 2.51855547 19305.6888 0.02680808 17.34210790.26 19.535 2.56527192 2.47468156 18969.3785 0.02692612 20.99277530.24 22.99 2.65808205 2.43006486 18627.3745 0.02704887 24.71180750.22 26.485 2.62766051 2.38466559 18279.3718 0.0271767 28.5030730.2 29.82 2.75372518 2.33844029 17925.0372 0.02731002 32.370815

0.18 33.36 2.59425804 2.29134128 17564.0053 0.02744929 36.31970480.16 36.91 2.58695027 2.24331612 17195.8742 0.02759504 40.35490380.14 40.74 2.39782597 2.19430685 16820.1994 0.02774785 44.48213840.12 44.515 2.43276118 2.14424918 16436.4882 0.02790839 48.70779020.1 48.51 2.29879186 2.09307146 16044.1915 0.02807745 53.0390047

0.08 52.38 2.37304224 2.04069345 15642.6941 0.0282559 57.48382550.06 57.74 1.71337192 1.9870248 15231.3034 0.0284448 62.05135930.04 60.83 2.97206261 1.93196316 14809.2349 0.02864534 66.75198180.02 64.86 2.27882716 1.87539182 14375.594 0.02885896 71.5975989

0 69.435 2.00736032 1.8171767 13929.3529 0.02908736 76.6019789

Tubo N° 4 tanque plano modelo Bird Crosby

h(m) t(s)experimenta

l

velocidad experimental

(m/s)

v (m/s)modelo Birdasumiendo

laminar

Re v(m/s)modelo

BirdTurbulento

Re t(s)Bird Crosby

0.38 0 0 75.2110292 576521.241 5.30936623 40698.3183

0

0.36 3.45 2.68528464 72.68292738

557142.375 5.20663905 39910.8752

1.67876077

0.34 7.03 2.435987658 70.15482555

537763.51 5.10236868 39111.6031

3.39123084

0.32 10.31 2.869897959 67.62672373

518384.645 4.99647502 38299.8878

5.13933973

0.3 14.12 2.455527666 65.09862191

499005.78 4.88887066 37475.0593

6.92520454

0.28 17.715 2.594258042 62.57052009

479626.914 4.77945983 36636.3836

8.75115631

0.26 21.3 2.586950273 60.04241827

460248.049 4.66813731 35783.0539

10.6197712

0.24 25.065 2.536926373 57.51431644

440869.184 4.554787 34914.1805

12.533908

0.22 28.845 2.360841509 54.98621462

421490.319 4.43928026 34028.7773

14.496753

0.2 32.8 2.307455646 52.4581128 402111.454 4.32147396 33125.7471

16.5118743

0.18 36.83 2.273186502 49.93001098

382732.588 4.20120802 32203.8627

18.5832891

0.16 40.965 2.197051069 47.40190916

363353.723 4.07830242 31261.7444

20.7155457

0.14 45.165 2.197051069 44.87380734

343974.858 3.95255354 30297.8312

22.9138266

0.12 49.525 2.073063989 42.34570551

324595.993 3.82372952 29310.346 25.1840784

0.1 53.82 2.063746847 39.81760369

305217.127 3.69156439 28297.2498

27.5331777

0.08 58.185 2.348765593 37.28950187

285838.262 3.55575053 27256.1847

29.9691466

0.06 63.055 1.807809738 34.76140005

266459.397 3.41592883 26184.398 32.5014358

0.04 68.12 1.762701242 32.23329823

247080.532 3.27167559 25078.642 35.1413051

0.02 73.22 1.897453196 29.70519641

227701.666 3.12248484 23935.0379

37.9023427

0 78.455 1.726254412 27.17709458

208322.801 2.96774372 22748.8881

40.801194

Tubo N° 4 tanque 45° modelo Bird Crosby

h(m) t(s)experimental

velocidad experimental

(m/s)

v (m/s)modelo Birdasumiendo

laminar

Re v(m/s)modelo BirdTurbulento

Re t(s)Bird Crosby

0.38 0 0 83.250393 638146.032 5.62659173 43129.9728 00.36 3.385 2.7578599 80.7222912 618767.167 5.52830974 42376.6039 1.6346706450.34 6.69 2.64659178 78.1941893 599388.302 5.42869944 41613.0529 3.2988654370.32 9.975 2.76616671 75.6660875 580009.436 5.32769901 40838.846 4.9940988460.3 13.235 3.03091534 73.1379857 560630.571 5.22524161 40053.471 6.722016771

0.28 16.82 2.49556344 70.6098839 541251.706 5.12125472 39256.3718 8.4844129420.26 20.22 2.66193434 68.0817821 521872.841 5.01565949 38446.9441 10.283248020.24 23.645 2.63898663 65.5536802 502493.975 4.90836986 37624.5281 12.120672020.22 27.35 2.55812631 63.0255784 483115.11 4.79929168 36788.4022 13.999050630.2 30.99 2.55812631 60.4974766 463736.245 4.68832149 35937.7734 15.92099661

0.18 34.805 2.43598766 57.9693748 444357.38 4.57534528 35071.7676 17.889407010.16 38.635 2.33088159 55.441273 424978.514 4.46023682 34189.4173 19.907508160.14 42.45 2.404103 52.9131711 405599.649 4.34285573 33289.6465 21.978910010.12 46.6 2.1507432 50.3850693 386220.784 4.22304518 32371.2529 24.107672590.1 50.635 2.35478807 47.8569675 366841.919 4.10062901 31432.8862 26.29838793

0.08 54.865 2.15579189 45.3288657 347463.054 3.97540814 30473.0205 28.556282120.06 59.155 2.12585034 42.8007638 328084.188 3.84715619 29489.9204 30.887343870.04 63.615 2.10634713 40.272662 308705.323 3.71561384 28481.598 33.298488420.02 68.285 1.97074538 37.7445602 289326.458 3.58048161 27445.7579 35.7977695

0 73.15 1.95397308 35.2164584 269947.593 3.44141051 26379.7249 38.39465761

Tubo N° 4 tanque 60° modelo Bird Crosby

h(m) t(s)experimental

velocidad experimental

(m/s)

v (m/s)modelo Birdasumiendo

laminar

Re v(m/s)modelo BirdTurbulento

Re t(s)Bird Crosby

0.38 0 0 83.250393 638146.032 5.62659173 43129.9728 00.36 3.355 2.7578599 80.7222912 618767.167 5.52830974 42376.6039 1.628116680.34 6.56 2.86095747 78.1941893 599388.302 5.42869944 41613.0529 3.285639130.32 9.455 3.2451143 75.6660875 580009.436 5.32769901 40838.846 4.974075750.3 12.73 2.85207251 73.1379857 560630.571 5.22524161 40053.471 6.69506585

0.28 15.955 2.71706316 70.6098839 541251.706 5.12125472 39256.3718 8.450395950.26 19.535 2.60160722 68.0817821 521872.841 5.01565949 38446.9441 10.24201890.24 22.99 2.57968356 65.5536802 502493.975 4.90836986 37624.5281 12.0720760.22 26.485 2.53692637 63.0255784 483115.11 4.79929168 36788.4022 13.94292350.2 29.82 2.88794763 60.4974766 463736.245 4.68832149 35937.7734 15.8571637

0.18 33.36 2.65424089 57.9693748 444357.38 4.57534528 35071.7676 17.81768210.16 36.91 2.53692637 55.441273 424978.514 4.46023682 34189.4173 19.8276920.14 40.74 2.404103 52.9131711 405599.649 4.34285573 33289.6465 21.89078880.12 44.515 2.39158163 50.3850693 386220.784 4.22304518 32371.2529 24.01101650.1 48.51 2.37304224 47.8569675 366841.919 4.10062901 31432.8862 26.1929485

0.08 52.38 2.35478807 45.3288657 347463.054 3.97540814 30473.0205 28.441790.06 57.74 1.39995022 42.8007638 328084.188 3.84715619 29489.9204 30.76350570.04 60.83 4.61491129 40.272662 308705.323 3.71561384 28481.598 33.16498310.02 64.86 2.22364975 37.7445602 289326.458 3.58048161 27445.7579 35.6542437

0 69.435 2.04992711 35.2164584 269947.593 3.44141051 26379.7249 38.2407199

Porcentajes de error

Tanque plano tubo N°4

h(m) % errorOcon Tojo

% errorBird Crosby

0.38 0 00.36 7.03647988 51.34026760.34 6.04017133 51.76058550.32 9.50101004 50.1518940.3 7.660536 50.954642

0.28 8.35912158 50.60030310.26 9.28448605 50.14191910.24 9.52395788 49.99438250.22 9.99413188 49.74257940.2 10.0846478 49.6589198

0.18 10.2459165 49.54306510.16 10.3970223 49.43111010.14 10.6553761 49.26640840.12 10.8145268 49.14875630.1 11.3740421 48.8421075

0.08 12.029538 48.49334610.06 12.0026838 48.45541860.04 11.979663 48.41264670.02 12.2436643 48.2349867

0 12.6288801 47.9941444

Tanque 45° tubo N°4

h(m) % ErrorOcon Tojo

% ErrorBird

0.38 0 00.36 4.40759863 51.70840040.34 6.33201151 50.68960480.32 7.68951575 49.9338462

0.3 8.94689881 49.21030020.28 8.26351551 49.55759250.26 8.95152817 49.14318480.24 9.61063893 48.73896380.22 9.41327504 48.8151714

0.2 9.68668008 48.6253740.18 9.66536453 48.60104290.16 9.8244896 48.47286620.14 10.192249 48.22400470.12 10.0487059 48.266797

0.1 10.330618 48.06282630.08 10.4497445 47.95173220.06 10.6611098 47.78574280.04 10.8057612 47.65623140.02 10.8640987 47.5759398

0 10.8913618 47.5124298

Tanque 60° tubo N°4h(m) % error

Ocon-Tojo%error

Bird0.38 0 00.36 0.02108487 51.47193210.34 3.02930089 49.91403770.32 7.57475895 47.39211260.3 7.44304338 47.4071811

0.28 7.97744777 47.03606420.26 6.92430037 47.57092980.24 6.94819136 47.48988260.22 7.06035724 47.35539540.2 7.85868723 46.8237299

0.18 8.13038242 46.5896820.16 8.5179505 46.28097540.14 8.39411081 46.26708680.12 8.58947955 46.06084140.1 8.52019693 46.0050537

0.08 8.85007313 45.70105010.06 6.92891178 46.72063450.04 8.85281306 45.47923210.02 9.39073229 45.0289182

0 9.33254086 44.9258732

Graficas

1.Velocidades Modelo ocon Tojo

Velocidad vs tiempo tanque plano tubo 4

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5

3

t (s) experimentalt (s) ocon tojo

Velocidad vs tiempo tanque 45° tubo 4

Velocidad experimental

Velocidad Ocon tojo

0 10 20 30 40 50 60 70 80 900

0.5

1

1.5

2

2.5

3

velocidad experimentalvelocidad Ocon Tojo

Velocidad vs tiempo tanque 45° tubo 4

0 10 20 30 40 50 60 70 80 900

0.5

1

1.5

2

2.5

3

3.5

velocidad experimentalvelocidad ocon tojo (m/s)

2. Velocidades Modelo Bird Crosby

Velocidad vs tiempo tanque plano° tubo 4

0 5 10 15 20 25 30 35 40 450

1

2

3

4

5

6

velocidad exp (m/s)v(m/s) Bird Crosby

Velocidad vs tiempo tanque 45° tubo 4

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

velocidad exp (m/s)v(m/s) Bird Crosby

Velocidad vs tiempo tanque 60° tubo 4

0 10 20 30 40 50 60 70 800

1

2

3

4

5

6

velocidad exp (m/s)v(m/s)

Tiempos de escurrimiento para diferentes modelos

Tanque de base Plana tubo 4

Modelo Ocon Tojo

0 10 20 30 40 50 60 70 80 90 1000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

t (s) experimentalt (s) ocon tojo

Modelo Bird-Crosby

0 10 20 30 40 50 60 70 80 900

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

experimentalt(s) Bird Crosby

Tanque de cono 45 ° tubo 4

Modelo Ocon Tojo

0 10 20 30 40 50 60 70 80 900

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

t experimentalt (s) Ocon tojo

Modelo Bird-Crosby

0 10 20 30 40 50 60 70 800

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

T (s)experimentalt(s) Bird Crosby

Tanque de cono 60 ° tubo 4

Modelo Ocon Tojo

0 10 20 30 40 50 60 70 80 900

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

t experimentalt (s)OCON TOJO

Modelo Bird-Crosby

0 10 20 30 40 50 60 70 800

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

T (s)experimentalt(s) Bird Crosby

Historia

A través de los años se han propuesto algunos modelos que intentaban determinar el tiempo de escurrimiento de un tanque , cuya finalidad sería la de evaluar tiempos de drenado para la limpieza y mantenimiento de los mismos .

Los modelos tienen en común que hacen uso de balances globales de materia y energía, sin embargo la eficacia de los modelos va a depender de las simplifaciones establecidas.

Byron Bird y por su parte Crosby desarrollaron en la decada de 1960 un modelo matématico , que no consideraba la energía cinética a la salida del tubo conectado al tanque , sin embargo proporciona un valor preliminar que permite mostrar una idea en el estudio de drenado.Bird es considerado por ser uno de los primeros en desarrollar los

fenómenos de tranporte de manera científica, la cual es base del flujo de fluidos.

El modelo planteado por Ocon-Tojo , sugiere menos simplificaciones , ya que considera las perdidas generadas por cambios de diámetro entre el tanque y el tubo ( cambios bruscos y graduales), es por esta razón que se presenta mayor cercanía con los resultados experimentales, el estrechamiento que se presenta en los tanques, es por lo tanto un factor importante en el modelo matemático, en el caso de tanques planos la presencia de un cambio abrupto genera remolinos a los lados del tanque.

Para el desarrollo de correlaciones que permitan evaluar las perdidas por friccion generadas por cambios de diámetro en el flujo de fluidos , fue necesario la elaboración de experimentos , debido a la dificultad de generalizar los efectos de los accesorios y las contracciónes o ensanchamientos.

En el año 1935, Crane en el folleto “Flow of Fluids and Heat Transmission” propone una correlacion basada en sus experimentos en diferentes accesorios , entre ellos los estrechamientos . Crane se basó en las investigaciones de ensanchamientos llevadas anteriormente por A. H. Gibson quien introduce un factor de corrección “C” que se evalúa en la ecuación de resistencia brusca para convertirla a resistencias graduales.El coeficiente C involucra el ángulo interior.

Figura 1. Byron Bird

BIBLIOGRAFÍA

*Crane , Flujo de Fluidos en válvulas accesorios y tuberías” McGRAW-HILL capítulo 2 , p. 14

*E.J. Crosby Experimentos sobre fenómenos de transporte en las operaciones unitarias de la industria química.1968 Editorial Hispano Americana H.A.S.A. pp55-63

*Bird ,Byron ,Warren E. Stewart , Edwin N. Lightfoot. Fenómenos de transporte.Segunda edición .Editorial Limusa- Wisley .

* Ocon-Tojo Problemas de Ingenieria Quimica Vol 1 . Colecciones ciencia y tecnología.

*Valiente, Problemas de Flujo de Fluidos

Gráficas