REDES ABIERTASEjemplo
DATOS DE ENTRADASTUBO LONGITUD DIAMETRO
1 De A-U1 13002 De U1-B 7603 De U1-C 5404 De U1-U2 2360
5 De U2-D 11506 De U2-E 1350
Calculo del diametro del tubo A-U1Al asunir alturas entonces se obtien dh, y usar frmula de velocidadHT Longitud Dimetro
30 1300 0.3530 1300 0.430 1300 0.4530 1300 0.530 1300 0.5530 1300 0.630 1300 0.630 1300 0.630 1300 0.6
DATOS DE ENTRADASTUBO LONGITUD DIAMETRODe A-U1 1300De U1-B 760De U1-C 540De U1-U2 2360
De U2-D 1150De U2-E 1350
Calculo del diametro del tubo U1-BAl asunir alturas entonces se obtien dh, y usar frmula de velocidad
HT Longitud Dimetro30 760 0.1530 760 0.230 760 0.2530 760 0.330 760 0.330 760 0.330 760 0.3
Calculo del diametro del tubo U1-cAl asunir alturas entonces se obtien dh, y usar frmula de velocidadHT Longitud Dimetro
50 760 0.1550 1300 0.250 1300 0.250 1300 0.2
Tener cuidado con los caudales que salende los nudos
caudales COTAS que salen Ks viscosidA= 150 m 0.31 0.0003 0.00000114B= 90 m 0.31 0.0003 0.00000114C= 70 m 120 0.0003 0.00000114U1 120 0.0003 0.00000114U2 75 0.0003D= 12 m 330 0.0003 0.00000114E= 0 m 255 0.0003 0.00000114
Asumiendos cotas para los nudosU1= 120U2= 75Altura Dh 2g Ks/3.7D VELOC Q =caudal suma(hm)
30 19.62 0.00023166 2.86480432 0.27474977 1.547720930 19.62 0.0002027 3.11391284 0.39006118 1.8285869930 19.62 0.00018018 3.35070284 0.53121121 2.1172617330 19.62 0.00016216 3.57703437 0.70011505 2.4129534730 19.62 0.00014742 3.7943321 0.89860124 2.7150223
27.2849777 19.62 0.00013514 3.81692386 1.07577709 2.7474494727.2525505 19.62 0.00013514 3.81463804 1.07513284 2.7441597527.2558402 19.62 0.00013514 3.81486999 1.07519822 2.7444934927.2555065 19.62 0.00013514 3.81484646 1.07519159 2.74445964
caudales COTAS que salen Ks viscosidA= 150 m 0.31 0.0003 0.00000114B= 90 m 0.31 0.0003 0.00000114C= 70 m 120 0.0003 0.00000114U1 120 0.0003 0.00000114U2 75 0.0003D= 12 m 330 0.0003 0.00000114E= 0 m 255 0.0003 0.00000114
Asumiendos cotas para los nudosU1= 120U2= 75
Altura Dh 2g Ks/3.7D VELOC Q =caudal suma(hm)30 19.62 0.00054054 2.19798965 0.03871814 0.9110747530 19.62 0.00040541 2.64068764 0.08269577 1.3150334130 19.62 0.00032432 3.04099827 0.14879985 1.7439541730 19.62 0.00027027 3.41029765 0.24029298 2.1932457430 19.62 0.00027027 3.41029765 0.24029298 2.19324574
27.8067543 19.62 0.00027027 3.28220912 0.23126774 2.0315860327.968414 19.62 0.00027027 3.29181885 0.23194485 2.0434997
Asumiendos cotas para los nudosU1= 120U2= 75Altura Dh 2g Ks/3.7D VELOC Q =caudal suma(hm)
50 19.62 0.00054054 2.84576209 0.05012881 1.5272140150 19.62 0.00040541 2.60625002 0.08161733 1.2809579550 19.62 0.00040541 2.60625002 0.08161733 1.2809579550 19.62 0.00040541 2.60625002 0.08161733 1.28095795
Tener cuidado con los caudales que salen
Km3.72.52.24.5
4.25
Km3.72.52.24.5
4.25
Problema de diseo de Tubera en sLa tubera de descarga de la Planta de Tratamiento de aguas residuales del Municipio de San Migueltiene una longitud de L=150mts, y por ella debe pasar un caudal mximo de 120 lts/seg. La altura mnima de operacin es 2.2 m y en la tubera se tienen prdidas menores por entrada Km1=0.5, por un codo, K=0.8por uniones Km3=10x0.8, por salida Kms=1.0Calcular el dametro de la tubera comercial de PVC requerida si la temperatura del agua es 14CDATOS DE I Longitud 150 Mts L
caudal 120 m3/seg QDifrencia de aZ2 2.2 mts Z2Viscosidad deViscosidad 0.00000117 m2/seg ver tablaRugosidad absKs= 0.00015Prdidas de CKm 9.4Gravedad g= 9.81Densidad 998.20 Kg/m3
ProcesoSuponer un dimetro inicia 0.15Suma de Prdida Menores 3.30
H Dametro Ks/d hf Vam m
m variable variable2.2 1.50E-01 1.00E-03 2.2000 -0.4155192.2 2.00E-01 7.50E-04 2.2000 -0.4798002.2 2.50E-01 6.00E-04 2.2000 -0.5364332.2 3.00E-01 5.00E-04 2.2000 -0.5876332.2 3.00E-01 5.00E-04 1.3730 -0.4642212.2 3.00E-01 5.00E-04 1.6899 -0.5150272.2 3.00E-01 5.00E-04 1.5687 -0.4962132.2 3.00E-01 5.00E-04 1.6151 -0.5034982.2 3.00E-01 5.00E-04 1.5974 -0.5007232.2 3.00E-01 5.00E-04 1.6042 -0.5017872.2 3.00E-01 5.00E-04 1.6016 -0.5013802.2 3.00E-01 5.00E-04 1.6026 -0.5015362.2 3.00E-01 5.00E-04 1.6022 -0.501476
DATOS DE I Longitud 45caudal 0.00049
Difrencia de aZ2 25Viscosidad deViscosidad 0.00000114Rugosidad absKs= 0.00015Prdidas de CKm 0Gravedad g= 9.81Densidad 0.00
ProcesoSuponer un dimetro inicia 0.01Suma de Prdida Menores 0.00
H Dametro Ks/dm
m25 1.27E-02 1.18E-0225 2.52E-02 5.95E-0325 3.77E-02 3.98E-0325 5.02E-02 2.99E-0325 6.27E-02 2.39E-0325 7.52E-02 1.99E-0325 8.77E-02 1.71E-0325 1.00E-01 1.50E-0325 1.13E-01 1.33E-0325 1.25E-01 1.20E-0325 1.38E-01 1.09E-0325 1.50E-01 9.99E-0425 1.63E-01 9.22E-04
La tubera de descarga de la Planta de Tratamiento de aguas residuales del Municipio de San Migueltiene una longitud de L=150mts, y por ella debe pasar un caudal mximo de 120 lts/seg. La altura mnima de operacin es 2.2 m y en la tubera se tienen prdidas menores por entrada Km1=0.5, por un codo, K=0.8
0.00049Calcular el dametro de la tubera comercial de PVC requerida si la temperatura del agua es 14C
H= Suma hf- suma (Km)V2/2GVb-1 Vb-2 Velocidad Area Caudal Q>= Qd suma
m/seg Hmvariable variable 3.14 D2/4 variable
0.000270 0.000094 1.429 0.0177 0.0252 no 0.34330.000203 0.000061 1.717 0.0314 0.0539 no 0.49580.000162 0.000044 1.977 0.0491 0.0971 no 0.6577
0.000135 0.000033 2.217 0.0707 0.1567 si 0.82700.000135 0.000042 1.741 0.0707 0.1231 si 0.51010.000135 0.000038 1.937 0.0707 0.1369 si 0.63130.000135 0.000039 1.865 0.0707 0.1318 no 0.58490.000135 0.000039 1.893 0.0707 0.1338 no 0.60260.000135 0.000039 1.882 0.0707 0.1330 no 0.59580.000135 0.000039 1.886 0.0707 0.1333 no 0.59840.000135 0.000039 1.885 0.0707 0.1332 no 0.59740.000135 0.000039 1.885 0.0707 0.1333 no 0.5978
0.000135 0.000039 1.885 0.0707 0.1332 no 0.5977
Mts L 0.0254m3/seg Q 0.00049mts Z2m2/seg ver tabla
Kg/m3
H= Suma hf- suma (Km)V2/2Ghf Va Vb-1 Vb-2 Velocidad Area Caudalm m/segvariable variable variable variable 3.14 D2/4
25.0000 -0.744124 0.003192 0.000606 1.801 0.0001 0.000225.0000 -1.048198 0.001609 0.028507 1.595 0.0005 0.000825.0000 -1.282076 0.001075 0.000000 3.806 0.0011 0.0042
25.0000 -0.810318 0.000808 0.000144 2.448 0.0020 0.004825.0000 -0.905603 0.000647 0.000103 2.830 0.0031 0.008725.0000 -0.991774 0.000539 0.000079 3.183 0.0044 0.014125.0000 -1.071035 0.000462 0.000063 3.513 0.0060 0.021225.0000 -1.144821 0.000405 0.000051 3.825 0.0079 0.030225.0000 -1.214132 0.000360 0.000043 4.122 0.0100 0.041125.0000 -1.279694 0.000324 0.000037 4.406 0.0123 0.054225.0000 -1.342057 0.000294 0.000032 4.679 0.0149 0.069725.0000 -1.401648 0.000270 0.000028 4.942 0.0177 0.0876
25.0000 -1.458806 0.000249 0.000025 5.197 0.0208 0.1080
0.0381
1er AproOjo
2da aprox
Q>= QsumaHmvariable
nononosi 1er Aprosi Ojosinonononononono 2da aprox
Caudal 2.1 ltscota capt 2500 msnmcota Rese 2450 msnm 50Longit. 380 msnm
Pendiente 0.13157895 m/mS(0.57) 0.31472863
2.839*HF 0.90135133Q/2.8639*hF 6.67241488
D= 2.01829538
Usando Monograma Hazen - Williams
se Tiene = 0 1 1/2" 25002450
Q= 2.1Hf 0.13157895hf(0.21) 0.65317439Q(0.38) 1.23089612
0.873936241.33798303
TUBERIAS EN SERIE
Datos de IngresoH1= 2540H2= 2511.5Diferencia de cotas 28.5
Dimetro Longitud Km Material Ksm m
Tubera I 0.6 423 4.2 concreto 0.0003Tubera II 0.5 174 3.4 PVC 0.000015Tubera III 0.3 373 5.3 PVCTubera IV 0.25 121 7.5 PVCViscosidad 1.14E-006Prdida por friccion PRIMERA ITERACIONPRIMERA TUBERAL1/D1(5) 5439.8148L2/D2(5) 5568L3/D3(5) 153497.94L4/D4(5) 123904
288409.76hf1= 0.5375502 m para la frmula
Dametro Ks/d hf Va Vb-1m
m variable variable variable6.00E-01 5.00E-04 0.5376 -0.244621 0.000135
Velocidad V1-1 9.20E-01Cuadal en la Tuber 1 2.60E-01 m3/sCaudal que sale 0.06Caudal que Pasa 2.00E-01Dametro 5.00E-01Velocidad V2-1 1.02E+00Dametro
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 446,753 7.47781403 7.477814030.01788342 0.000015 446,753 8.67007418 8.67007418
0.01330315 0.000015 446,753 8.55211496 8.552114960.01367266 0.000015 446,753 8.56309691 8.563096910.01363761 0.000015 446,753 8.56206861 8.562068610.01364089 0.000010 446,753 8.58488083 8.584880830.01356849 0.000010 446,753 8.58269202 8.582692020.01357541 0.000010 446,753 8.5829018 8.58290180.01357475 0.000010 446,753 8.58288169 8.58288169
Hf2-1 2.50E-01 0.250000 mHm2-1 1.80E-01 0.180000 m
Cuadal en la Tuber 1 2.60E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074Caudal que Pasa T3-1 1.26E-01Dametro 3.00E-01Velocidad V3-1 1.78E+00
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 469,087 7.51922149 7.519221490.017687 0.000015 469,087 8.70428902 8.70428902
0.01319877 0.000015 469,087 8.58802164 8.588021640.01355857 0.000015 469,087 8.59876432 8.598764320.01352471 0.000015 469,087 8.59776615 8.597766150.01352785 0.000010 469,087 8.62154088 8.621540880.01345334 0.000010 469,087 8.61927478 8.619274780.01346042 0.000010 469,087 8.61949052 8.619490520.01345974 0.000010 469,087 8.61946998 8.61946998
Hf3-1= 2.71E+00 2.700000 mHm3-1 8.58E-01 0.858000 m
Cuadal en la Tuber 1 2.60E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074caudal que sale 3 0.06Caudal que Pasa T4 6.60E-02Dametro 2.50E-01Velocidad V4-1 1.34E+00
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 294,855 7.12348302 7.123483020.01970676 0.000015 294,855 8.375036 8.3750360.01425695 0.000015 294,855 8.24258918 8.242589180.01471881 0.000015 294,855 8.25568743 8.255687430.01467214 0.000015 294,855 8.25438325 8.254383250.01467678 0.000010 294,855 8.27039127 8.270391270.01462002 0.000010 294,855 8.26877045 8.268770450.01462575 0.000010 294,855 8.26893442 8.268934420.01462517 0.000010 294,855 8.26891783 8.26891783
Hf4-1= 6.52E-01 0.652000 mHm4-1= 6.91E-01 0.690000 m
Perdida Total H1= 6.0600 M enor que H=28.5
SEGUNDA ITERACIONDatos de IngresoH1= 2540H2= 2511.5Diferencia de cotas 28.5
Dimetro Longitud Km Material Ksm m
Tubera I 0.6 423 4.2 concreto 0.0003Tubera II 0.5 174 3.4 PVC 0.000015Tubera III 0.3 373 5.3 PVCTubera IV 0.25 121 7.5 PVCViscosidad 1.14E-006Prdida por friccionPRIMERA TUBERAL1/D1(5) 5439.8148L2/D2(5) 5568L3/D3(5) 153497.94L4/D4(5) 123904
288409.76hf2= 0.4232505 m
0.5375502 0.4232505 0.96080073 para la frmula
Dametro Ks/d hf Va Vb-1m
m variable variable variable6.00E-01 5.00E-04 0.9608 -0.327041 0.000135
Velocidad V1-2 1.24E+00Cuadal en la Tuber 1 3.50E-01 m3/sCaudal que sale-1 0.06Caudal que Pasa T2 2.90E-01Dametro 5.00E-01Velocidad V2-2 1.48E+00
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 446,753 7.47781403 7.477814030.01788342 0.000015 446,753 8.67007418 8.670074180.01330315 0.000015 446,753 8.55211496 8.552114960.01367266 0.000015 446,753 8.56309691 8.563096910.01363761 0.000015 446,753 8.56206861 8.562068610.01364089 0.000010 446,753 8.58488083 8.584880830.01356849 0.000010 446,753 8.58269202 8.582692020.01357541 0.000010 446,753 8.5829018 8.58290180.01357475 0.000010 446,753 8.58288169 8.58288169
Hf2-2= 5.25E-01 mHm2-2 3.78E-01 m
Cuadal en la Tuber 1 3.50E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074Caudal que Pasa T3 2.16E-01Dametro 3.00E-01Velocidad v3-2 3.05E+00Dametro
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 803,909 7.97279653 7.972796530.01573181 0.000015 803,909 9.07381973 9.073819730.01214562 0.000015 803,909 8.97629703 8.976297030.01241097 0.000015 803,909 8.98450647 8.98450647
0.0123883 0.000015 803,909 8.9838124 8.98381240.01239021 0.000010 803,909 9.02109224 9.021092240.01228802 0.000010 803,909 9.01780972 9.017809720.01229696 0.000010 803,909 9.01809825 9.018098250.01229618 0.000010 803,909 9.01807289 9.01807289
Hf3-2= 7.27E+00 m
Hm3-2 2.52E+00 m
Cuadal en la Tuber 1 3.50E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074caudal que sale 3 0.06Caudal que Pasa T4 1.56E-01Dametro 2.50E-01Velocidad v4-2 3.18E+00Dametrohf2
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 696,641 7.85296637 7.852966370.01621558 0.000015 696,641 8.97727458 8.977274580.01240826 0.000015 696,641 8.87474611 8.874746110.01269662 0.000015 696,641 8.88361027 8.88361027
0.0126713 0.000015 696,641 8.88284033 8.882840330.01267349 0.000010 696,641 8.91596502 8.91596502
0.0125795 0.000010 696,641 8.91298242 8.912982420.01258792 0.000010 696,641 8.91325056 8.913250560.01258716 0.000010 696,641 8.91322645 8.91322645
Hf2= 3.13E+00 mHm2 3.86E+00 m
Perdida Total H= 18.4377 todava es menor a 28.5
TERCERA ITERACIONDatos de IngresoH1= 2540H2= 2511.5Diferencia de cotas 28.5
Dimetro Longitud Km Material Ksm m
Tubera I 0.6 423 4.2 concreto 0.0003Tubera II 0.5 174 3.4 PVC 0.000015Tubera III 0.3 373 5.3 PVCTubera IV 0.25 121 7.5 PVCViscosidad 1.14E-006Prdida por friccionPRIMERA TUBERA
L1/D1(5) 5439.8148L2/D2(5) 5568L3/D3(5) 153497.94L4/D4(5) 123904
288409.76hf= 0.1897893 mnuevo hf 0.5375502 0.4232505 0.18978934 1.1505901 prar la formula
Dametro Ks/d hf Va Vb-1m
m variable variable variable6.00E-01 5.00E-04 1.1506 -0.357886 0.000135
Cuadal en la Tuber 1 3.84E-01 m3/sCaudal que sale 0.06Caudal que Pasa T2-3 3.24E-01Dametro 5.00E-01Velocidad v2-3 1.65E+00Dametro
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 446,753 7.47781403 7.477814030.01788342 0.000015 446,753 8.67007418 8.670074180.01330315 0.000015 446,753 8.55211496 8.552114960.01367266 0.000015 446,753 8.56309691 8.563096910.01363761 0.000015 446,753 8.56206861 8.562068610.01364089 0.000010 446,753 8.58488083 8.584880830.01356849 0.000010 446,753 8.58269202 8.582692020.01357541 0.000010 446,753 8.5829018 8.58290180.01357475 0.000010 446,753 8.58288169 8.58288169
Hf2--3= 6.54E-01 mHm2-3 4.71E-01 m
Cuadal en la Tuber 1 3.84E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074Caudal que Pasa 3-3 2.50E-01Dametro 3.00E-01Velocidad v4-3 3.53E+00
Dametrof Nmero de Denomin denomina
dato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 929,307 8.09339437 8.093394370.01526647 0.000015 929,307 9.17002338 9.170023380.01189212 0.000015 929,307 9.07759175 9.077591750.01213553 0.000015 929,307 9.08515243 9.085152430.01211534 0.000015 929,307 9.08453151 9.084531510.01211699 0.000010 929,307 9.12649165 9.126491650.01200583 0.000010 929,307 9.12288391 9.122883910.01201533 0.000010 929,307 9.12319351 9.123193510.01201451 0.000010 929,307 9.12316694 9.12316694
Hf3-3= 9.49E+00 mHm3-3= 3.37E+00 m
Cuadal en la Tuber 1 3.84E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074caudal que sale 3 0.06Caudal que Pasa T4-3 1.90E-01Dametro 2.50E-01Velocidad v4-3 3.86E+00Dametro
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 847,119 8.01643911 8.016439110.01556098 0.000015 847,119 9.10875183 9.108751830.01205264 0.000015 847,119 9.01306498 9.013064980.01230991 0.000015 847,119 9.02103845 9.021038450.01228816 0.000015 847,119 9.02037123 9.020371230.01228998 0.000010 847,119 9.05928449 9.059284490.01218463 0.000010 847,119 9.05588698 9.055886980.01219377 0.000010 847,119 9.05618309 9.056183090.01219297 0.000010 847,119 9.05615727 9.05615727
Hf2= 4.49E+00 mHm2 5.70E+00 m
Perdida Total H= 24.7643
CUARTA ITERACIONDatos de IngresoH1= 2540H2= 2511.5Diferencia de cotas 28.5
Dimetro Longitud Km Material Ksm m
Tubera I 0.6 423 4.2 concreto 0.0003Tubera II 0.5 174 3.4 PVC 0.000015Tubera III 0.3 373 5.3 PVCTubera IV 0.25 121 7.5 PVCViscosidad 1.14E-006Prdida por friccionPRIMERA TUBERAL1/D1(5) 5439.8148L2/D2(5) 5568L3/D3(5) 153497.94L4/D4(5) 123904
288409.76 0.425 0.538hf= 0.0704597 m
0.5375502 0.4232505 0.18978934 0.0704597 1.2210497
Dametro Ks/d hf Va Vb-1m
m variable variable variable6.00E-01 5.00E-04 1.2210 -0.368682 0.000135
Cuadal en la Tuber 1 3.95E-01 m3/sCaudal que sale 0.06Caudal que Pasa 3.35E-01Dametro 5.00E-01Velocidad v2 1.71E+00Dametrohf2
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 446,753 7.47781403 7.477814030.01788342 0.000015 446,753 8.67007418 8.670074180.01330315 0.000015 446,753 8.55211496 8.552114960.01367266 0.000015 446,753 8.56309691 8.56309691
0.01363761 0.000015 446,753 8.56206861 8.562068610.01364089 0.000010 446,753 8.58488083 8.584880830.01356849 0.000010 446,753 8.58269202 8.582692020.01357541 0.000010 446,753 8.5829018 8.58290180.01357475 0.000010 446,753 8.58288169 8.58288169
Hf2= 7.03E-01 mHm2 5.06E-01 m
Cuadal en la Tuber 1 3.95E-01 m3/sCaudal que sale1 0.06Caudal que sale1 0.074Caudal que Pasa 2.61E-01Dametro 3.00E-01Velocidad v2 3.70E+00Dametrohf2
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 973,201 8.13163138 8.131631380.01512323 0.000015 973,201 9.20030538 9.200305380.01181396 0.000015 973,201 9.10950013 9.109500130.01205066 0.000015 973,201 9.11685731 9.116857310.01203122 0.000015 973,201 9.11625889 9.11625889
0.0120328 0.000010 973,201 9.15981543 9.159815430.01191864 0.000010 973,201 9.1560997 9.15609970.01192831 0.000010 973,201 9.15641607 9.156416070.01192749 0.000010 973,201 9.15638913 9.15638913
Hf2= 1.03E+01 mHm2 3.69E+00 m
Cuadal en la Tuber 1 3.95E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074caudal que sale 3 0.06Caudal que Pasa 2.01E-01Dametro 2.50E-01Velocidad v2 4.10E+00Dametrohf2
f Nmero de Denomin denomina
dato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 899,792 8.06660638 8.066606380.01536803 0.000015 899,792 9.14874332 9.14874332
0.0119475 0.000015 899,792 9.05517587 9.055175870.01219569 0.000015 899,792 9.06287976 9.062879760.01217496 0.000015 899,792 9.06224287 9.062242870.01217667 0.000010 899,792 9.10311766 9.103117660.01206757 0.000010 899,792 9.09958417 9.099584170.01207694 0.000010 899,792 9.09988906 9.099889060.01207613 0.000010 899,792 9.09986275 9.09986275
Hf2= 5.02E+00 mHm2 6.44E+00 m
Perdida Total H= 27.1799
QUINTA ITERACIONDatos de IngresoH1= 2540H2= 2511.5Diferencia de cotas 28.5
Dimetro Longitud Km Material Ksm m
Tubera I 0.6 423 4.2 concreto 0.0003Tubera II 0.5 174 3.4 PVC 0.000015Tubera III 0.3 373 5.3 PVCTubera IV 0.25 121 7.5 PVCViscosidad 1.14E-006Prdida por friccionPRIMERA TUBERAL1/D1(5) 5439.8148L2/D2(5) 5568L3/D3(5) 153497.94L4/D4(5) 123904
288409.76 0.425 0.538hf= 0.0248991 m
0.5375502 0.4232505 0.18978934 0.0704597 0.0248991
Dametro Ks/d hf Va Vb-1
mm variable variable variable
6.00E-01 5.00E-04 1.2459 -0.372422 0.000135Cuadal en la Tuber 1 3.99E-01 m3/sCaudal que sale 0.06Caudal que Pasa 3.39E-01Dametro 5.00E-01Velocidad v2 1.73E+00Dametrohf2
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 446,753 7.47781403 7.477814030.01788342 0.000015 446,753 8.67007418 8.670074180.01330315 0.000015 446,753 8.55211496 8.552114960.01367266 0.000015 446,753 8.56309691 8.563096910.01363761 0.000015 446,753 8.56206861 8.562068610.01364089 0.000010 446,753 8.58488083 8.584880830.01356849 0.000010 446,753 8.58269202 8.582692020.01357541 0.000010 446,753 8.5829018 8.58290180.01357475 0.000010 446,753 8.58288169 8.58288169
Hf2= 7.20E-01 mHm2 5.18E-01 m
Cuadal en la Tuber 1 3.99E-01 m3/sCaudal que sale1 0.06Caudal que sale1 0.074Caudal que Pasa 2.65E-01Dametro 3.00E-01Velocidad v2 3.76E+00Dametrohf2
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 988,410 8.14445971 8.144459710.01507563 0.000015 988,410 9.21043972 9.210439720.01178798 0.000015 988,410 9.12018148 9.120181480.01202245 0.000015 988,410 9.12747062 9.127470620.01200326 0.000015 988,410 9.12687968 9.126879680.01200481 0.000010 988,410 9.17098449 9.17098449
0.01188962 0.000010 988,410 9.16723202 9.167232020.01189936 0.000010 988,410 9.16755065 9.167550650.01189853 0.000010 988,410 9.16752359 9.16752359
Hf2= 1.06E+01 mHm2 3.81E+00 m
Cuadal en la Tuber 1 3.99E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074caudal que sale 3 0.06Caudal que Pasa 2.05E-01Dametro 2.50E-01Velocidad v2 4.19E+00Dametrohf2
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 918,042 8.08327624 8.083276240.01530471 0.000015 918,042 9.16199187 9.161991870.01191297 0.000015 918,042 9.06913089 9.069130890.01215818 0.000015 918,042 9.0767456 9.07674560.01213779 0.000015 918,042 9.07611867 9.076118670.01213947 0.000010 918,042 9.1176657 9.11766570.01202909 0.000010 918,042 9.11408613 9.114086130.01203854 0.000010 918,042 9.11439396 9.114393960.01203772 0.000010 918,042 9.11436748 9.11436748
Hf2= 5.20E+00 0.652000 mHm2 6.70E+00 0.690000 m
Perdida Total H= 28.0413
SEXTA ITERACIONDatos de IngresoH1= 2540H2= 2511.5Diferencia de cotas 28.5
Dimetro Longitud Km Material Ksm m
Tubera I 0.6 423 4.2 concreto 0.0003
0.5 174 3.4 PVC 0.000015Tubera III 0.3 373 5.3 PVCTubera IV 0.25 121 7.5 PVCViscosidad 1.14E-006Prdida por friccionPRIMERA TUBERAL1/D1(5) 5439.8148L2/D2(5) 5568L3/D3(5) 153497.94L4/D4(5) 123904
288409.76 0.425 0.538hf= 0.0086513 m
0.5375502 0.4232505 0.18978934 0.0704597 0.0248991
Dametro Ks/d hf Va Vb-1m
m variable variable variable6.00E-01 5.00E-04 1.2546 -0.373712 0.000135
Cuadal en la Tuber 1 4.01E-01 m3/sCaudal que sale 0.06Caudal que Pasa T2-6 3.41E-01Dametro 5.00E-01Velocidad v2 1.74E+00Dametro
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 446,753 7.47781403 7.477814030.01788342 0.000015 446,753 8.67007418 8.670074180.01330315 0.000015 446,753 8.55211496 8.552114960.01367266 0.000015 446,753 8.56309691 8.563096910.01363761 0.000015 446,753 8.56206861 8.562068610.01364089 0.000010 446,753 8.58488083 8.584880830.01356849 0.000010 446,753 8.58269202 8.582692020.01357541 0.000010 446,753 8.5829018 8.58290180.01357475 0.000010 446,753 8.58288169 8.58288169
hf-6 7.26E-01 mHm6 5.22E-01 m
Cuadal en la Tuber 1 4.01E-01 m3/sCaudal que sale1 0.06Caudal que sale1 0.074Caudal que Pasa T3 2.67E-01Dametro 3.00E-01Velocidad v2 3.78E+00Dametrohf2
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 993,658 8.14883907 8.148839070.01505943 0.000015 993,658 9.21389645 9.213896450.01177913 0.000015 993,658 9.12382511 9.123825110.01201285 0.000015 993,658 9.13109106 9.131091060.01199374 0.000015 993,658 9.13050266 9.130502660.01199529 0.000010 993,658 9.17479611 9.174796110.01187975 0.000010 993,658 9.17103104 9.17103104
0.0118895 0.000010 993,658 9.17135045 9.171350450.01188867 0.000010 993,658 9.17132335 9.17132335
Hf2= 1.07E+01 mHm2 3.85E+00 m
Cuadal en la Tuber 1 4.01E-01 m3/sCaudal que sale1 0.06Caudal que sale2 0.074caudal que sale 3 0.06Caudal que Pasa T4 2.07E-01Dametro 2.50E-01Velocidad v3 4.21E+00Dametrohf2
f Nmero de Denomin denominadato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000015 924,340 8.08894911 8.088949110.01528325 0.000015 924,340 9.16649578 9.166495780.01190127 0.000015 924,340 9.07387547 9.073875470.01214547 0.000015 924,340 9.08145988 9.081459880.01212519 0.000015 924,340 9.08083632 9.080836320.01212686 0.000010 924,340 9.12261449 9.12261449
0.01201604 0.000010 924,340 9.11901915 9.119019150.01202552 0.000010 924,340 9.11932797 9.11932797
0.0120247 0.000010 924,340 9.11930144 9.11930144
Hf2= 5.27E+00 mHm2 6.79E+00 m
Perdida Total H= 28.3415 aproximadamente a 28.528.5
Error 0.55606667 %
Salidas en la Red
0.060.740.06
Vb-2 Velocidad Area Caudal Hmm/segvariable 3.14 D2/4
0.000039 0.920 0.2827 0.2600 0.1810
G(f)1/f
0.017883420.01330315
0.013672660.013637610.013640890.013568490.013575410.013574750.0135748
G(f)1/f
0.0176870.013198770.013558570.013524710.013527850.013453340.013460420.013459740.0134598
G(f)1/f
0.019706760.014256950.014718810.014672140.014676780.014620020.014625750.014625170.0146252
Salidas en la Red
0.060.740.06
Vb-2 Velocidad Area Caudal Hmm/segvariable 3.14 D2/4
0.000029 1.238 0.2827 0.3499 0.3279
G(f)1/f
0.017883420.013303150.013672660.013637610.013640890.013568490.013575410.013574750.0135748
G(f)1/f
0.015731810.012145620.01241097
0.01238830.012390210.012288020.012296960.012296180.0122962
G(f)1/f
0.016215580.012408260.01269662
0.01267130.01267349
0.01257950.012587920.012587160.0125872
Salidas en la Red
0.060.740.06
prar la formula
Vb-2 Velocidad Area Caudal Hmm/segvariable 3.14 D2/4
0.000027 1.357 0.2827 0.3836 0.3941
G(f)1/f
0.017883420.013303150.013672660.013637610.013640890.013568490.013575410.013574750.0135748
G(f)1/f
0.015266470.011892120.012135530.012115340.012116990.012005830.012015330.012014510.0120146
G(f)1/f
0.015560980.012052640.012309910.012288160.012289980.012184630.012193770.01219297
0.012193
Salidas en la Red
0.060.740.06
0.189
0.113
para la formula
Vb-2 Velocidad Area Caudal Hmm/segvariable 3.14 D2/4
0.000026 1.398 0.2827 0.3954 0.4187
G(f)1/f
0.017883420.013303150.013672660.01363761
0.013640890.013568490.013575410.013574750.0135748
G(f)1/f
0.015123230.011813960.012050660.01203122
0.01203280.011918640.011928310.011927490.0119276
G(f)
1/f
0.015368030.0119475
0.012195690.012174960.012176670.012067570.012076940.012076130.0120762
Salidas en la Red
0.060.740.06
0.189
0.113
1.2459489 para la frmula
Vb-2 Velocidad Area Caudal Hm
m/segvariable 3.14 D2/4
0.000026 1.413 0.2827 0.3995 0.4273
G(f)1/f
0.017883420.013303150.013672660.013637610.013640890.013568490.013575410.013574750.0135748
G(f)1/f
0.015075630.011787980.012022450.012003260.012004810.01188962
0.011899360.011898530.0118986
G(f)1/f
0.015304710.011912970.012158180.012137790.012139470.012029090.012038540.012037720.0120378
Salidas en la Red
0.06
0.740.06
0.189
0.113
0.0086513 1.2546 para la frmula
Vb-2 Velocidad Area Caudal Hmm/segvariable 3.14 D2/4
0.000026 1.418 0.2827 0.4009 0.4304
G(f)1/f
0.017883420.013303150.013672660.013637610.013640890.013568490.013575410.013574750.0135748
G(f)1/f
0.015059430.011779130.012012850.011993740.011995290.01187975
0.01188950.011888670.0118887
G(f)1/f
0.015283250.011901270.012145470.012125190.012126860.01201604
0.012025520.0120247
0.0120248
METODO DE LA TUBERIA EQUIVALENTEDiferencia de cotas 28.5
Dimetro Longitud Km Materialm m
Tubera I 0.6 423 4.2 concretoTubera II 0.5 174 3.4 PVCTubera III 0.3 373 5.3 PVCTubera IV 0.25 121 7.5 PVCViscosidad 1.14E-006Asumir
Dametro equivale 0.3375fe equival 0.014f(fi/fe) 1.0714286 1.0714286 0.92857143 0.92857143(de/d1)(5) 0.0563135 0.140126 1.80203247 4.48403344(fi/fe)*(de/di)(5)*Li 25.522089 26.123498 624.146818 503.813186Desnivel 28.5 fe*(Le/de)*Ve(2)/2*9.81
V(2) 11.427541Ve 3.3804646Qe 0.302423Ht 1890.3061Qe 0.302423Tubera 4Q1= 0.1659386Diametro 4 0.25Velocidad 4 3.3804646hf4 5.97587 5.97586998Hm4 4.368326 4.36832601Ht4 10.344196Tubera 3Q1= 0.1659386Q salida 0.06Q en latuberia 3 0.2259386Diametro 3 0.3Velocidad 3 3.1963692hf3 8.4167768 8.41677678Hm3 3.9054955 3.90549552Ht3 12.322272
Tubera 2Q2= 0.2259386
Q salida 0.134Q en latuberia 2 0.3599386Diametro 2 0.5Velocidad 1.8331477hf2 0.7748516 0.77485158Hm2 1.2845683 1.28456826Ht2 2.0594198
Tubera 1Q3= 0.3599386Q salida 0.194Q en latuberia 1 0.5539386Diametro 1 0.6Velocidad 1.9591523hf1 1.7929569 1.79295694Hm1 1.4672315 1.46723154Ht1 3.2601885
27.9860766
Ks Salidas en la red fi
0.0003 0.06 0.0150.000015 0.74 0.013
0.06 0.0130.013
0.3375
0.92857143
1179.60559
TUBERIAS EN PARALELO
Longitud de la tuberas= 627 mKs1 Rugosida Ks1= 0.0015 mm PVC Dametro !=Ks2 Rugosidad Ks2= 0.03 mm Asb-cem Dametro 2=Km Prdida menores= 10.6HT Diferencia de nivel= 26.4T Temperatura y otros= 20 densidad 998.2 viscosidad
Tubera IDametro Ks/d hf Va
HT mm variable variable
1 26.4 2.00E-01 7.50E-06 26.4000 -0.8129482 26.4 2.00E-01 7.50E-06 19.2340 -0.6938983 26.4 2.00E-01 7.50E-06 21.3292 -0.7307154 26.4 2.00E-01 7.50E-06 20.7226 -0.7202505 26.4 2.00E-01 7.50E-06 20.8988 -0.7233056 26.4 2.00E-01 7.50E-06 20.8477 -0.7224207 26.4 2.00E-01 7.50E-06 20.8625 -0.7226778 26.4 2.00E-01 7.50E-06 20.8582 -0.7226029 26.4 2.00E-01 7.50E-06 20.8595 -0.722624
10 26.4 2.00E-01 7.50E-06 20.8591 -0.722618Datos de QI= 0.1006salida Velocid I 3.202
hf1= 20.8591hm1= 5.5408HT= 26.3999
Tubera IIDametro Ks/d hf Va
HT mm variable variable
1 26.4 3.00E-01 1.00E-04 26.4000 -0.9956542 26.4 3.00E-01 1.00E-04 16.2327 -0.7807323 26.4 3.00E-01 1.00E-04 20.2733 -0.8725074 26.4 3.00E-01 1.00E-04 18.6744 -0.8373945 26.4 3.00E-01 1.00E-04 19.3084 -0.8514906 26.4 3.00E-01 1.00E-04 19.0572 -0.8459337 26.4 3.00E-01 1.00E-04 19.1568 -0.848140
8 26.4 3.00E-01 1.00E-04 19.1173 -0.8472669 26.4 3.00E-01 1.00E-04 19.1329 -0.847612
10 26.4 3.00E-01 1.00E-04 19.1267 -0.847475Datos de salida QII= 0.2593
Velocidad= 3.668hf2= 19.1267hm2= 7.2708HT= 26.3975
CONCLUSIONES Caudal total QT= 0.3599
0.2 m Ks1 0.00000750.3 m Ks2 0.0001
(la prdiad que se debe buscar)1.007*10(-6) 1.01E-006
Vb-1 Vb-2 Velocidad Area Caudal Hmm/seg
variable variable 3.14 D2/40.000002 0.000031 3.642 0.0314 0.1144 7.16600.000002 0.000036 3.064 0.0314 0.0962 5.07080.000002 0.000035 3.242 0.0314 0.1018 5.67740.000002 0.000035 3.191 0.0314 0.1002 5.50120.000002 0.000035 3.206 0.0314 0.1007 5.55230.000002 0.000035 3.201 0.0314 0.1006 5.53750.000002 0.000035 3.203 0.0314 0.1006 5.54180.000002 0.000035 3.202 0.0314 0.1006 5.54050.000002 0.000035 3.202 0.0314 0.1006 5.54090.000002 0.000035 3.202 0.0314 0.1006 5.5408
lts
Vb-1 Vb-2 Velocidad Area Caudal Hmm/seg
variable variable 3.14 D2/40.000027 0.000017 4.338 0.0707 0.3066 10.16730.000027 0.000022 3.368 0.0707 0.2380 6.12670.000027 0.000019 3.781 0.0707 0.2673 7.72560.000027 0.000020 3.623 0.0707 0.2561 7.09160.000027 0.000020 3.687 0.0707 0.2606 7.34280.000027 0.000020 3.662 0.0707 0.2588 7.24320.000027 0.000020 3.671 0.0707 0.2595 7.2827
0.000027 0.000020 3.668 0.0707 0.2592 7.26710.000027 0.000020 3.669 0.0707 0.2594 7.27330.000027 0.000020 3.668 0.0707 0.2593 7.2708
lts
m3/seg
CALCULO DE POTENCIA PARA BOMBAS EN SERIEProblema- Ver grficoComo parte de un sistema de riego de una finca se utilizan dos tuberasen serie para conectar la bocatoma con el tanque de almacenamientoLos datos de muestran en la figura:
Tubera I Tubera IILongiud 184 mts Tubera II. 393Dimetro 0.2 mts 0.15Km 7.1 mts 11.2Rugosidades 0.000046 Acero 0.0000015Cuadal sale entre T-1 y T-2) 0.094 m3/segCuadal que llega la dpsito final 0.087 m3/segDatos ComplementariosT=Viscosida cinem 1.140E-006
SOLUCIONPARA LA PRIMERA TUBERAI) Hallas el caudal Q1= 0.094 0.087 0.1812.- Calculamos veloci V1= 5.76139553.- Hallamos las prdidas para ello se necesita el coeficiente de friccin4.- Se calcula Reynolds 1010771.13
f Nmero de Denomindato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000230 1,010,771 7.703476610.016851 0.000230 1,010,771 8.17990609
0.0149453 0.000230 1,010,771 8.167356040.0149912 0.000230 1,010,771 8.16768432
0.01499 0.000230 1,010,771 8.16767573f= 0.01499Perdidas por friccin1 23.331745 mtsPrdidas menores1 12.011983 mtsHT1 35.344 mts
PARA LA SEGUNDA TUBERAI) Hallas el caudal Q1= 0.087 0.0872.- Calculamos veloci V1= 4.9233.- Hallamos las prdidas para ello se necesita el coeficiente de friccin4.- Se calcula Reynolds 647787.025
f Nmero de Denomindato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000010 647,787 7.80456637
0.0164173 0.000010 647,787 8.9644660.0124437 0.000010 647,787 8.85338422
0.012758 0.000010 647,787 8.863428050.0127291 0.000010 647,787 8.862515110.0127317 0.000010 647,787 8.862598050.0127315 0.000010 647,787 8.862590520.0127315 0.000010 647,787 8.8625912
f= 0.012731Perdidas por friccin2 41.207145 mtsPrdidas menores2 13.836005 mtsHT2 55.043 mts
total de perdidas HT 90.387 mtsDiferencia de altura 31.7 mts (Z2-Z1)Altura total Requerida 122.087 mts Para el clculo de la Potencia
Potencia RequeridaCaudal Q 0.181 m3/segAltura 122.087 mDensidad 999.1 Kg/m3Gravedad 9.81 m/seg2Eficiencia 0.75Potencia Requerida 288778.4
288.78 KW solucion final
CALCULO DE POTENCIA PARA BOMBAS EN SERIE
mmmPVC
m3/seg (el total)m/s
denomina G(f)1/f
7.70347661 0.016851038.17990609 0.014945268.16735604 0.014991228.16768432 0.014990028.16767573 0.01499
m3/seg (el total)m/s
denomina G(f)1/f
7.80456637 0.01641733
8.964466 0.012443758.85338422 0.012757968.86342805 0.012729078.86251511 0.012731698.86259805 0.012731458.86259052 0.01273147
8.8625912 0.0127315
Para el clculo de la Potencia
CALCULO DE POTENCIA PARA TUBERIAS EN PARALELO
Con el fin de disminuir la vulnerabilidad del cruce subacuatico de un oleoductoal atravesar un ro, se decide colocar dos tuberas en paraleo a la existentever grficoDatos
Tubera Diametro Longitud Prdidas mI 0.45 278 7.7II 0.3 312 9.5III 0.3 312 9.5
Caudal total a bombear 0.46 m3/segPresin al inicio 875 mtsKPa
Densidad 860 Kg/m3Viscosid dinamica 0.00719 m2/seg
Calcular que pasa por cada Tubera , la altura y La Potencia
I) Como se conoce las caractersticas de la Tubera ICaudal 0.46 m3/segVelocidad 2.892290474 m/sViscosidad cinemtica 8.36047E-006Reynolds 1 155676.8308Rugosidad relativa 0.0001022222Para Hallar Hf1, se requeire de f
f Nmero dedato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000102 155,6770.0233852534 0.000102 155,6770.0166411739 0.000102 155,6770.0171644559 0.000102 155,6770.0171151056 0.000102 155,6770.0171196802 0.000102 155,6770.0171192555 0.000102 155,6770.0171192949 0.000102 155,6770.0171192913 0.000102 155,6770.017119292
Perdidas por friccin1 4.509235141 mtsPrdidas menores1 3.28303518 mtsHT1 7.792 mtsDiferencia de altura 96Altura total para la bomba 103.792 mtsPotencia Requerida
Caudal Q 0.46 m3/segAltura 103.792 mDensidad 860 Kg/m3Gravedad 9.81 m/seg2Eficiencia 0.85Potencia Requerida 473883.26963
473.88 KW
Suposicim inicial para la tubera existenteCaudal ini D1(5/2)
I 0.46 0.1358411296II 0.0492950302III 0.0492950302
Q1= 0.273 m3/seg
I) Como se conoce las caractersticas de la Tubera ICaudal 0.273 m3/segVelocidad 1.7164022773 m/sViscosidad cinemtica 8.36047E-006Reynolds 1 92384.934813Rugosidad relativa 0.0001022222Para Hallar Hf1, se requeire de f
f Nmero dedato Ks/d Rreynoldsasumido DATO CALCULADO
0.001 0.000102 92,3850.0268360881 0.000102 92,3850.0181302266 0.000102 92,3850.0188747321 0.000102 92,3850.0187953542 0.000102 92,3850.0188036342 0.000102 92,3850.0188027685 0.000102 92,385
0.018802859 0.000102 92,3850.0188028495 0.000102 92,3850.018802851
Perdidas por friccin1 1.7441954005 mtsPrdidas menores1 1.1561918036 mtsHT1 2.900 mts
Dametro Ks/d hfm
m variable2.9000000 3.00E-01 1.53E-04 2.90002.9000000 3.00E-01 1.53E-04 1.62572.9000000 3.00E-01 1.53E-04 2.23112.9000000 3.00E-01 1.53E-04 1.94792.9000000 3.00E-01 1.53E-04 2.08152.9000000 3.00E-01 1.53E-04 2.01872.9000000 3.00E-01 1.53E-04 2.04832.9000000 3.00E-01 1.53E-04 2.03442.9000000 3.00E-01 1.53E-04 2.04092.9000000 3.00E-01 1.53E-04 2.03782.9000000 3.00E-01 1.53E-04 2.03932.9000000 3.00E-01 1.53E-04 2.03862.9000000 3.00E-01 1.53E-04 2.03892.9000000 3.00E-01 1.53E-04 2.03882.9000000 3.00E-01 1.53E-04 2.0389
Caudal 9.43E-02 0.094 m3/seg
Caudal Total 0.273 0.094Prdidas Hf1 1.7442
Hf1 1.1562HT 2.9004
Altura Total96 2.9 98.9
Caudal Q 0.460Altura 98.900Densidad 860Gravedad 9.81Eficiencia 0.85Potencia Requerida 451546.68282
451.55
CALCULO DE POTENCIA PARA TUBERIAS EN PARALELO
Con el fin de disminuir la vulnerabilidad del cruce subacuatico de un oleoducto
Ks Material0.046 mm Acero0.046 mm Acero0.046 mm Acero
opcional
Denomin denomina G(f)1/f
6.53926534 6.539265337 0.02338525347.75189748 7.751897481 0.01664117397.63281928 7.63281928 0.01716445597.64381572 7.643815722 0.01711510567.64279439 7.642794385 0.0171196802
7.6428892 7.642889195 0.01711925557.64288039 7.642880394 0.01711929497.64288121 7.642881211 0.01711929137.64288113 7.642881135 0.0171192916
Raiz(L1)16.673332 0.00814721
17.6635217 0.00279078217.6635217 0.002790782
Denomin denomina G(f)1/f
6.10436363 6.104363626 0.02683608817.42674281 7.426742805 0.0181302266
7.2787969 7.278796903 0.01887473217.29415089 7.294150888 0.01879535427.29254475 7.292544754 0.01880363427.29271263 7.292712628 0.01880276857.29269508 7.29269508 0.0188028597.29269691 7.292696914 0.01880284957.29269672 7.292696722 0.0188028505
Va Vb-1 Vb-2 Velocidad Area Caudal Hmm/seg
variable variable variable 3.14 D2/4-0.467802 0.000041 0.000299 1.622 0.071 0.115 1.2743-0.350252 0.000041 0.000399 1.175 0.071 0.083 0.6689-0.410321 0.000041 0.000341 1.402 0.071 0.099 0.9521-0.383394 0.000041 0.000365 1.300 0.071 0.092 0.8185-0.396328 0.000041 0.000353 1.349 0.071 0.095 0.8813-0.390301 0.000041 0.000358 1.326 0.071 0.094 0.8517-0.393151 0.000041 0.000356 1.337 0.071 0.095 0.8656-0.391812 0.000041 0.000357 1.332 0.071 0.094 0.8591-0.392443 0.000041 0.000356 1.334 0.071 0.094 0.8622-0.392146 0.000041 0.000357 1.333 0.071 0.094 0.8607-0.392286 0.000041 0.000357 1.334 0.071 0.094 0.8614-0.392220 0.000041 0.000357 1.334 0.071 0.094 0.8611-0.392251 0.000041 0.000357 1.334 0.071 0.094 0.8612-0.392237 0.000041 0.000357 1.334 0.071 0.094 0.8611-0.392243 0.000041 0.000357 1.334 0.071 0.094 0.8612
por cada TuberaReal
0.094 0.461 0.460hf2 2.039 hf3 2.039hf2 0.861 hm3 0.861
2.900 2.900
TUBERIAS EQUIVALENTES , PERDIDAS MENORES.
Problema N1Para una prdida de carga de 5m/1000m y utilizando un C1=100 para todaslas tuberas Cuntas tuberas de 20 cm son equivalentes a una de 40 cm,Y a una de 60 cm.Para la tubera de 20 cmhf 5 5C= 100 5035.0060879D= 0.2 0.0003944719L= 1000 1000Cte 10.672
Multiplicando y dividiendo 0.0009305512Q20= m3/seg 0.023034
Para la tubera de 40 cmhf 5 5C= 100 5035.0060879D= 0.4 0.0115353867L= 1000 1000cte 10.672
Multiplicando y dividiendo 0.0272117421Q40= m3/seg 0.1427
Para la tubera de 60 cmhf 5 5C= 100 5035.0060879D= 0.6 0.0830991515L= 1000 1000cte 10.672
Multiplicando y dividiendo 0.1960292043Q40= m3/seg 0.41464Equivalencias(De 40 por 20) 142/23 4.77563093 6 Tuberas 20 cm equivalen a una de 40 cm(De 60 por 20) 414/23 18.0017353 18 Tuberas 20 cm equivalen a una de 60 cm(De 60 por 40) 414/142 2.90602392 2.90 Tuberas 40 cm equivalen a una de 60 cm
Qu producen la misma perdida: hf 5mts
Problema N2
Un sistema de tuberas en serie est constituido por un tramo de 1800mts de tubera de 50 cm de dimetro, otro de 1200 m de dametro de 40 cm, y 600 m de dimetro de 30 cmTodas las tuberas son nuevas de fierro fundido C=130, Hallar a partir del sistemaa) La longitud equivalente de una tubera de 40 cmb) El dimetro equivalente a la longitud si la lomgitu de tubera fuera de 3600 m.Solucin1.- Como la magnitud hidrulica comn para un sistema en serie es el caudal se tieneo se asume un caudal Q= 100 lts/seg
solucin hallamos los hfihallamos hf1Longitud 1 1800 1800D1 0.5 0.03419668C1 130 8182.93582constante 10.672 10.672Caudal supuesto 0.13 0.02290388Hf 1.572 mts o
hallamos hf2Longitud 2 1200 1200D2 0.4 0.01153539C2 130 8182.93582constante 10.672 10.672Caudal supuesto 0.13 0.02290388Hf 3.107 mts o
hallamos h3Longitud 3 600 600D3 0.3 0.00284171C3 130 8182.93582constante 10.672 10.672Caudal supuesto 0.13 0.02290388Hf 6.307 mts o
Suma total de prdidas hf1+hf2+hf3) Htt 10.987 mts
Para una tubera equivalente de 40 cm de dametro y con una prdida total de Hf= 10.987 mts se tiene:Proceso :hf 10.987 10.987C= 130 8182.9358232D= 0.4 0.0115353867Q= 0.13 0.0229038845
L= por determinarCte 10.987Despejar L de la ecuacion dada
Longitud equivalente 4121.28
Otros Mtodos de tubera equivalente y de los porcentajesPara el problema anterior hallar Q=? SiLongitud equivalente Le= 4121.28Perdidas de carga hf= 21Datos: De la frmula de Hf despejar Q=?
Longitud equivale 4121.28 mts 4121.28Prdidas 21 mts 21C= 130 8182.9358232Dimetro 0.4 0.0115353867constante 10.672 10.672
multiplic y divid 0.0450694879Q40= m3/seg 0.20952
mediante porcentajeshallamos hf1Longitud 1 1800 1800D1 0.5 0.03419668C1 130 8182.93582constante 10.672 10.672Caudal supuesto 0.13 0.02290388Hf 1.572 mts o
hallamos hf2Longitud 2 1200 1200D2 0.4 0.01153539C2 130 8182.93582constante 10.672 10.672Caudal supuesto 0.13 0.02290388Hf 3.107 mts o
hallamos h3Longitud 3 600 600D3 0.3 0.00284171C3 130 8182.93582constante 10.672 10.672
Caudal supuesto 0.13 0.02290388Hf 6.307 mts o
Suma total de prdidas hf1+hf2+hf3) Htt 10.987 mts
Problema N3Determinar , usando la Ecuacin Darcy -Wiesbach, gasto de una tubera de PVC de 4 " de dametro, y250 mts de largo, si el sistema incluye una coladera con vlvula de pie, un orifio de medida de bordescuadrados, que reduce el dametro a 2", y confusor de 2" de dametro a la slida, La prdida totalde carga en el sistema es de 8.00 metros, se puede tomar la carga medida en el orificio de 0.05 mts
solucin Htt= Prdida por fricin +perdida carga menoresHf= no se conoceHm Hallamos la suma de los coeficientes de prdidas menores
K1= 10 Para la coladera con vlvula de pieK2= 2.06 Para valvula compuerta media cerradaK3= 1 Para vvula globo totalmente abiertaK4= 5.5 confusor d/D= 0.5 es decir (2"/4")ho= 0.05 para la prdida en el orificio con borde cuadrados
suma 18.61Rugosidad absoluta Ks= 0.0000015PVCDamtero D= 0.1Longitud L= 250Viscosidad 1.140E-006 m2/segSolucinDebemos hallar Velocidad y hf
Ht= 7.95
Dametro Ks/d hf VaHT m
m variable variable
7.95 1.00E-01 1.50E-05 7.9500 -0.3154497.95 1.00E-01 1.50E-05 7.1214 -0.2985587.95 1.00E-01 1.50E-05 6.5498 -0.2863267.95 1.00E-01 1.50E-05 6.6622 -0.2887727.95 1.00E-01 1.50E-05 6.6401 -0.2882937.95 1.00E-01 1.50E-05 6.6445 -0.2883877.95 1.00E-01 1.50E-05 6.6436 -0.2883687.95 1.00E-01 1.50E-05 6.6438 -0.2883727.95 1.00E-01 1.50E-05 6.6437 -0.288371
7.95 1.00E-01 1.50E-05 6.6437 -0.288371
TUBERIAS EQUIVALENTES , PERDIDAS MENORES.
UsandoHazen-WilMono C=100 C=130
1.3*Q10023.03 18 23.4
142.68 110 143
414.64 305 396.5
6 Tuberas 20 cm equivalen a una de 40 cm18 Tuberas 20 cm equivalen a una de 60 cm2.90 Tuberas 40 cm equivalen a una de 60 cm
Un sistema de tuberas en serie est constituido por un tramo de 1800mts de tubera de 50 cm de dimetro, otro de 1200 m de dametro de 40 cm, y 600 m de dimetro de 30 cmTodas las tuberas son nuevas de fierro fundido C=130, Hallar a partir del sistema
b) El dimetro equivalente a la longitud si la lomgitu de tubera fuera de 3600 m.
1.- Como la magnitud hidrulica comn para un sistema en serie es el caudal se tiene
140
tamben con elmonogra S= Hf/L
S hf0.84m/1000m 0.93 1.674
1.67m/1000m 2.62 3.144
3.383m/1000 m 10.06 6.036
10.854
usando monogramamts Le= 4260
Otros Mtodos de tubera equivalente y de los porcentajes
206 lts/seg
Hallamos hi Ht Ordenamos los datos y calculamos el cuadal paraen % 21 cada tubera
Longitud eq 1800.00 mts 1800.00hallamos Prdidas 3.0053206 mts 3.00532064
los nuevos Damet 0.5 0.03419668hi para 21 C 130 8182.93582
0.14733*21 constante 10.672 10.67214.311 3.00532064 multiplic y divid 0.04377897
Q40= m3/seg 0.20647
Longitud eq 1200.00 mts 1200.00Prdidas 5.9395196 mts 5.93951959Damet 0.4 0.01153539C 130 8182.93582constante 10.672 10.672
28.283 5.93951959 multiplic y divid 0.04377897Q40= m3/seg 0.20647
Longitud eq 600.00 mts 600.00Prdidas 12.05516 mts 12.0551598Damet 0.3 0.00284171C 130 8182.93582
constante 10.672 10.67257.406 12.0551598 multiplic y divid 0.04377897
Q40= m3/seg 0.20647100.0
Determinar , usando la Ecuacin Darcy -Wiesbach, gasto de una tubera de PVC de 4 " de dametro, y250 mts de largo, si el sistema incluye una coladera con vlvula de pie, un orifio de medida de bordescuadrados, que reduce el dametro a 2", y confusor de 2" de dametro a la slida, La prdida totalde carga en el sistema es de 8.00 metros, se puede tomar la carga medida en el orificio de 0.05 mts
Prdida por fricin +perdida carga menores 8.00 mts
Hallamos la suma de los coeficientes de prdidas menoresPara la coladera con vlvula de pie 0.05Para valvula compuerta media cerradaPara vvula globo totalmente abiertaconfusor d/D= 0.5 es decir (2"/4")para la prdida en el orificio con borde cuadrados
Vb-1 Vb-2 Velocidad Area Caudal Hmm/seg
variable variable 3.14 D2/4
0.000004 0.000115 1.238 0.0079 0.0097 0.82860.000004 0.000000 1.610 0.0079 0.0126 1.40020.000004 0.000000 1.544 0.0079 0.0121 1.28780.000004 0.000000 1.557 0.0079 0.0122 1.30990.000004 0.000000 1.555 0.0079 0.0122 1.30550.000004 0.000000 1.555 0.0079 0.0122 1.30640.000004 0.000000 1.555 0.0079 0.0122 1.30620.000004 0.000000 1.555 0.0079 0.0122 1.30630.000004 0.000000 1.555 0.0079 0.0122 1.3063
0.000004 0.000000 1.555 0.0079 0.0122 1.3063
METODO DE LA TEORA LINEAL
Elaboracin de Circuitossistema de Ecuaciones
PRIMERA ITERACION
1.1. Cculo de coeficientes de friccin DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.03717851 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f dato
asumido DATO CALCULADO asumido0.001 0.000400 446,750 7.0879478 7.087948 0.01990485 0.001
0.019905 0.000400 446,750 7.6598831 7.659883 0.01704338 0.01990490.017043 0.000400 446,750 7.6412177 7.641218 0.01712675 0.01704340.017127 0.000400 446,750 7.6418206 7.641821 0.01712404 0.01712670.017124 0.000400 446,750 7.6418011 7.641801 0.01712413 0.017124
Tubera (3-4)Longitud= 200 Caudal 0.1 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 12.7323657 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 1,116,874 6.933632 6.933632 0.02080072 0.0010.020801 0.001000 1,116,874 7.0877159 7.087716 0.01990616 0.0199220.019906 0.001000 1,116,874 7.0866644 7.086664 0.01991206 0.01835830.019912 0.001000 1,116,874 7.0866715 7.086672 0.01991202 0.01837930.019912 0.001000 1,116,874 7.0866715 7.086671 0.01991202 0.018379
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.1 2.03717851 0.0171241(1-6) 300 0.25 0.1 2.03717851 0.0171241(2-3) 400 0.15 0.1 5.65882919 0.0183791(3-4) 200 0.1 0.1 12.7323657 0.019912(4-5) 400 0.15 0.1 5.65882919 0.0183791(2-5) 200 0.1 0.1 12.7323657 0.019912(5-6) 600 0.2 0.1 3.18309142 0.017571ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0072.44 -43.47 0.00 0.00 0.00 3290.52
0 0 816.24 3290.52 -799.919 -3290.52
-0.018435213 0.9508394 0.811871 0.251645 0.115 0.0004241-0.981564787 -0.950839 -0.811871 -0.251645 -0.115 -0.000424-0.007400264 -0.019734 0.8249057 0.1986 0.046 0.0001703-0.007400264 -0.019734 -0.175094 0.1986 0.046 0.00017030.007400264 0.019734 0.1750943 0.8014 -0.04634627 -0.00017-0.011034949 -0.029427 -0.013035 0.053046 0.06910952 0.0002539
0.018435213 0.0491606 0.188129 0.748355 0.88454421 -0.000424
SEGUNDO TRAMITE DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1021126 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.08021682 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 456,188 7.0991927 7.099193 0.01984185 0.0010.019842 0.000400 456,188 7.664369 7.664369 0.01702343 0.019970.017023 0.000400 456,188 7.646207 7.646207 0.0171044 0.01706410.017104 0.000400 456,188 7.6467848 7.646785 0.01710182 0.01714990.017102 0.000400 456,188 7.6467664 7.646766 0.0171019 0.0171471
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal 0.0503203 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 6.40696634 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 562,015 6.7712603 6.77126 0.02181027 0.0010.02181 0.001000 562,015 7.0442786 7.044279 0.02015241 0.0208564
0.020152 0.001000 562,015 7.0407614 7.040761 0.02017255 0.01861190.020173 0.001000 562,015 7.0408066 7.040807 0.02017229 0.01865490.020172 0.001000 562,015 7.0408061 7.040806 0.02017229 0.018654
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.102113 2.08021682 0.0171019(1-6) 300 0.25 0.097887 1.9941402 0.0171472(2-3) 400 0.15 0.07032 3.97930643 0.0185929(3-4) 200 0.1 0.05032 6.40696634 0.0201723(4-5) 400 0.15 0.06468 3.66011297 0.018654(2-5) 200 0.1 0.051792 6.59438876 0.0201577
(5-6) 600 0.2 0.077887 2.47922578 0.017791ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0073.88 -42.60 0.00 0.00 0.00 1725.27
0 0 577.12 1677.44 -525.125 -1725.266
-0.030525884 0.9165418 0.7581839 0.297905 0.154 0.0007165-0.969474116 -0.916542 -0.758184 -0.297905 -0.154 -0.000716-0.011690521 -0.031962 0.7792836 0.230655 0.059 0.0002744-0.011690521 -0.031962 -0.220716 0.230655 0.059 0.00027440.011690521 0.031962 0.2207164 0.769345 -0.05890625 -0.000274-0.018835363 -0.051496 -0.0211 0.06725 0.09490771 0.00044210.030525884 0.0834582 0.2418161 0.702095 0.84618603 -0.000716
TERCERA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1035446 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.10938884 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 462,585 7.1066333 7.106633 0.01980032 0.0010.0198 0.000400 462,585 7.667324 7.667324 0.01701032 0.0200155
0.01701 0.000400 462,585 7.6494913 7.649491 0.01708972 0.01707850.01709 0.000400 462,585 7.6500529 7.650053 0.01708721 0.0171662
0.017087 0.000400 462,585 7.6500352 7.650035 0.01708729 0.0171633
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal 0.0252994 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=
Ks 0.000100 Velocidad 3.22121718 Ksf Nmero deDenomin denomina G(f) f
dato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 282,563 6.5174215 6.517421 0.02354227 0.0010.023542 0.001000 282,563 6.9678171 6.967817 0.02059712 0.02173550.020597 0.001000 282,563 6.9572917 6.957292 0.02065949 0.01885940.020659 0.001000 282,563 6.9575362 6.957536 0.02065804 0.01892910.020658 0.001000 282,563 6.9575305 6.95753 0.02065807 0.0189273
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.103545 2.10938884 0.0170873(1-6) 300 0.25 0.096455 1.96496818 0.0171634(2-3) 400 0.15 0.055299 3.12930084 0.018781(3-4) 200 0.1 0.025299 3.22121718 0.0206581(4-5) 400 0.15 0.047201 2.67099908 0.0189273(2-5) 200 0.1 0.028245 3.59628022 0.0205594(5-6) 600 0.2 0.066455 2.11533535 0.0179555ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0074.85 -42.02 0.00 0.00 0.00 959.63
0 0 457.02 863.67 -388.829 -959.6317
-0.045857163 0.8724605 0.6931521 0.354293 0.202 0.0010913-0.954142837 -0.872461 -0.693152 -0.354293 -0.202 -0.001091-0.016486887 -0.045854 0.7184586 0.273053 0.073 0.0003923-0.016486887 -0.045854 -0.281541 0.273053 0.073 0.00039230.016486887 0.0458539 0.2815414 0.726947 -0.07252985 -0.000392-0.029370276 -0.081686 -0.025306 0.08124 0.12920703 0.00069890.045857163 0.1275395 0.3068479 0.645707 0.79826312 -0.001091
CUARTA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1047353 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.13364565 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 467,905 7.1127124 7.112712 0.01976649 0.0010.019766 0.000400 467,905 7.6697304 7.66973 0.01699964 0.0200542
0.017 0.000400 467,905 7.6521646 7.652165 0.01707778 0.01709080.017078 0.000400 467,905 7.6527132 7.652713 0.01707533 0.017180.017075 0.000400 467,905 7.6526961 7.652696 0.01707541 0.017177
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal 0.0124757 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 1.58845283 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 139,338 6.1515291 6.151529 0.02642615 0.0010.026426 0.001000 139,338 6.8379622 6.837962 0.02138684 0.0223850.021387 0.001000 139,338 6.8102261 6.810226 0.0215614 0.01904710.021561 0.001000 139,338 6.8113298 6.81133 0.02155441 0.01914010.021554 0.001000 139,338 6.8112859 6.811286 0.02155469 0.0191372
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.104735 2.13364565 0.0170754(1-6) 300 0.25 0.095265 1.94071137 0.0171771(2-3) 400 0.15 0.047476 2.68656925 0.0189216(3-4) 200 0.1 0.012476 1.58845283 0.0215547(4-5) 400 0.15 0.038774 2.19417092 0.0191373(2-5) 200 0.1 0.01726 2.19755821 0.0210802(5-6) 600 0.2 0.060265 1.91827952 0.0180674ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0075.66 -41.54 0.00 0.00 0.00 601.25
0 0 394.66 444.38 -322.959 -601.2509
-0.06089314 0.8281895 0.6308982 0.408749 0.247 0.001466-0.93910686 -0.828189 -0.630898 -0.408749 -0.247 -0.001466
-0.020763984 -0.058586 0.6503161 0.322541 0.084 0.0004999-0.020763984 -0.058586 -0.349684 0.322541 0.084 0.00049990.020763984 0.0585858 0.3496839 0.677459 -0.08432693 -0.0005-0.040129157 -0.113225 -0.019418 0.086208 0.16297299 0.00096610.06089314 0.1718105 0.3691018 0.591251 0.75270008 -0.001466
QUINTA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1057614 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.15454771 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 472,489 7.1178743 7.117874 0.01973783 0.0010.019738 0.000400 472,489 7.6717681 7.671768 0.01699061 0.02008810.016991 0.000400 472,489 7.6544275 7.654427 0.01706768 0.01710170.017068 0.000400 472,489 7.6549651 7.654965 0.01706529 0.01719220.017065 0.000400 472,489 7.6549485 7.654948 0.01706536 0.0171891
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal 0.005666 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 0.72141804 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 63,282 5.6337213 5.633721 0.03150716 0.0010.031507 0.001000 63,282 6.6130321 6.613032 0.02286645 0.02276110.022866 0.001000 63,282 6.5472522 6.547252 0.02332823 0.01915750.023328 0.001000 63,282 6.5515179 6.551518 0.02329787 0.01926520.023298 0.001000 63,282 6.5512406 6.551241 0.02329984 0.0192616
Tramo Longitud Dimet Caudal Velocidad f
(1-2) 500 0.25 0.105761 2.15454771 0.0170654(1-6) 300 0.25 0.094239 1.9198093 0.0171892(2-3) 400 0.15 0.043166 2.44269119 0.0190186(3-4) 200 0.1 0.005666 0.72141804 0.0232998(4-5) 400 0.15 0.034959 1.97826912 0.0192617(2-5) 200 0.1 0.012595 1.60368519 0.021539(5-6) 600 0.2 0.056739 1.80604276 0.0181406ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0076.35 -41.12 0.00 0.00 0.00 448.32
0 0 360.35 218.16 -293.074 -448.3164
-0.071761379 0.7949794 0.5813636 0.452037 0.278 0.0017453-0.928238621 -0.794979 -0.581364 -0.452037 -0.278 -0.001745-0.024374366 -0.069637 0.5847938 0.37558 0.095 0.0005928-0.024374366 -0.069637 -0.415206 0.37558 0.095 0.00059280.024374366 0.069637 0.4152062 0.62442 -0.09452786 -0.000593-0.047387013 -0.135384 -0.00343 0.076457 0.18377475 0.00115250.071761379 0.2050206 0.4186364 0.547963 0.72169739 -0.001745
SEXTA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1064886 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.16936211 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 475,737 7.1214908 7.121491 0.01971779 0.0010.019718 0.000400 475,737 7.6731927 7.673193 0.01698431 0.02011250.016984 0.000400 475,737 7.6560089 7.656009 0.01706063 0.01710940.017061 0.000400 475,737 7.6565391 7.656539 0.01705827 0.0172009
0.017058 0.000400 475,737 7.6565227 7.656523 0.01705834 0.0171978
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal 0.0019288 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 0.24558579 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 21,543 4.8057635 4.805763 0.04329874 0.0010.043299 0.001000 21,543 6.1616289 6.161629 0.02633958 0.0229365
0.02634 0.001000 21,543 6.0103264 6.010326 0.02768241 0.01920940.027682 0.001000 21,543 6.0259615 6.025962 0.02753894 0.01932430.027539 0.001000 21,543 6.0243327 6.024333 0.02755384 0.0193203
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.106489 2.16936211 0.0170583(1-6) 300 0.25 0.093511 1.90499491 0.0171979(2-3) 400 0.15 0.040679 2.30194555 0.019083(3-4) 200 0.1 0.001929 0.24558579 0.0275538(4-5) 400 0.15 0.033384 1.88912482 0.0193204(2-5) 200 0.1 0.01081 1.37633458 0.0218044(5-6) 600 0.2 0.054761 1.74310662 0.0181853ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0076.85 -40.82 0.00 0.00 0.00 389.50
0 0 340.56 87.83 -280.720 -389.4999
-0.077997849 0.7751667 0.5444589 0.484962 0.295 0.0019107-0.922002151 -0.775167 -0.544459 -0.484962 -0.295 -0.001911-0.027653302 -0.079712 0.5284989 0.427462 0.105 0.0006774-0.027653302 -0.079712 -0.471501 0.427462 0.105 0.00067740.027653302 0.0797122 0.4715011 0.572538 -0.10451582 -0.000677-0.050344547 -0.145121 0.01596 0.057501 0.19027751 0.00123330.077997849 0.2248333 0.4555411 0.515038 0.70520667 -0.001911
SETIMA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500
(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1068846 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.17742975 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 477,507 7.1234459 7.123446 0.01970696 0.0010.019707 0.000400 477,507 7.6739618 7.673962 0.0169809 0.02012590.016981 0.000400 477,507 7.6568625 7.656863 0.01705683 0.01711370.017057 0.000400 477,507 7.6573886 7.657389 0.01705449 0.01720570.017054 0.000400 477,507 7.6573724 7.657372 0.01705456 0.0172026
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal -0.000112 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 0.01425784 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 1,251 2.3912589 2.391259 0.17488267 0.0010.174883 0.001000 1,251 4.5901076 4.590108 0.0474629 0.02300870.047463 0.001000 1,251 4.0461872 4.046187 0.06108127 0.01923080.061081 0.001000 1,251 4.1524193 4.152419 0.05799594 0.01934870.057996 0.001000 1,251 4.1306249 4.130625 0.05860956 0.0193446
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.106885 2.17742975 0.0170546(1-6) 300 0.25 0.093115 1.89692726 0.0172027(2-3) 400 0.15 0.039263 2.22182718 0.0191229(3-4) 200 0.1 -0.000112 0.01425784 0.0586096(4-5) 400 0.15 0.032768 1.85429822 0.0193447(2-5) 200 0.1 0.010122 1.28871454 0.021928(5-6) 600 0.2 0.05374 1.7106066 0.0182095ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.00
0.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0077.12 -40.66 0.00 0.00 0.00 366.77
0 0 329.30 -10.85 -275.891 -366.7716
-0.081942741 0.762641 0.5093832 0.517725 0.306 0.0020154-0.918057259 -0.762641 -0.509383 -0.517725 -0.306 -0.002015-0.031270145 -0.090578 0.4701538 0.484622 0.117 0.0007691-0.031270145 -0.090578 -0.529846 0.484622 0.117 0.00076910.031270145 0.0905785 0.5298462 0.515378 -0.11659787 -0.000769-0.050672596 -0.146781 0.0392294 0.033103 0.18894433 0.00124630.081942741 0.237359 0.4906168 0.482275 0.6944578 -0.002015
OCTVA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1070525 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.18084973 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 478,257 7.1242716 7.124272 0.0197024 0.0010.019702 0.000400 478,257 7.6742864 7.674286 0.01697946 0.02013160.016979 0.000400 478,257 7.6572228 7.657223 0.01705522 0.01711560.017055 0.000400 478,257 7.6577472 7.657747 0.01705289 0.01720780.017053 0.000400 478,257 7.657731 7.657731 0.01705296 0.0172046
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal -0.001225 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 0.15596689 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 13,681 4.4333581 4.433358 0.05087851 0.001
0.050879 0.001000 13,681 5.9302435 5.930244 0.02843511 0.02303440.028435 0.001000 13,681 5.734044 5.734044 0.03041431 0.01923850.030414 0.001000 13,681 5.7573732 5.757373 0.03016833 0.01935750.030168 0.001000 13,681 5.7545661 5.754566 0.03019777 0.0193532
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.107052 2.18084973 0.017053(1-6) 300 0.25 0.092948 1.89350728 0.0172047(2-3) 400 0.15 0.038463 2.17652922 0.0191466(3-4) 200 0.1 -0.001225 0.15596689 0.0301978(4-5) 400 0.15 0.032553 1.8421237 0.0193534(2-5) 200 0.1 0.00984 1.25285526 0.0219829(5-6) 600 0.2 0.05326 1.69531572 0.0182212ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0077.23 -40.59 0.00 0.00 0.00 357.46
0 0 322.93 -61.13 -274.203 -357.458
-0.084105819 0.7558702 0.4881634 0.538838 0.312 0.002072-0.915894181 -0.75587 -0.488163 -0.538838 -0.312 -0.002072-0.033649111 -0.097672 0.4337851 0.522477 0.125 0.000829-0.033649111 -0.097672 -0.566215 0.522477 0.125 0.0008290.033649111 0.0976716 0.5662149 0.477523 -0.12463641 -0.000829-0.050456709 -0.146458 0.0543782 0.016361 0.1868918 0.00124310.084105819 0.2441298 0.5118366 0.461162 0.68847179 -0.002072
NOVENA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1071317 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.1824637 Ks
f Nmero deDenomin denomina G(f) f
dato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 478,610 7.1246607 7.124661 0.01970025 0.0010.0197 0.000400 478,610 7.6744393 7.674439 0.01697879 0.0201343
0.016979 0.000400 478,610 7.6573925 7.657392 0.01705447 0.01711640.017054 0.000400 478,610 7.657916 7.657916 0.01705214 0.01720880.017052 0.000400 478,610 7.6578999 7.6579 0.01705221 0.0172056
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal -0.0017953 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 0.22858575 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 20,051 4.7475741 4.747574 0.04436664 0.0010.044367 0.001000 20,051 6.1264057 6.126406 0.02664333 0.02304570.026643 0.001000 20,051 5.9683051 5.968305 0.02807359 0.01924180.028074 0.001000 20,051 5.9850394 5.985039 0.02791682 0.01936130.027917 0.001000 20,051 5.9832528 5.983253 0.0279335 0.019357
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.107132 2.1824637 0.0170522(1-6) 300 0.25 0.092868 1.89189332 0.0172057(2-3) 400 0.15 0.038048 2.15309609 0.0191592(3-4) 200 0.1 -0.001795 0.22858575 0.0279335(4-5) 400 0.15 0.032459 1.83682058 0.0193572(2-5) 200 0.1 0.009708 1.23608979 0.0220094(5-6) 600 0.2 0.053025 1.68782032 0.0182269ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0077.28 -40.56 0.00 0.00 0.00 353.10
0 0 319.64 -82.87 -273.467 -353.1011
-0.085160746 0.7525662 0.4780682 0.549238 0.314 0.0020997-0.914839254 -0.752566 -0.478068 -0.549238 -0.314 -0.0021-0.03483047 -0.1012 0.4162934 0.541393 0.129 0.0008588-0.03483047 -0.1012 -0.583707 0.541393 0.129 0.00085880.03483047 0.1011996 0.5837066 0.458607 -0.12858493 -0.000859
-0.050330276 -0.146234 0.0617748 0.007844 0.18580613 0.00124090.085160746 0.2474338 0.5219318 0.450762 0.68560894 -0.0021
METODO DE LA
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.1071 2.1824637 0.0170522(1-6) 300 0.25 0.0929 1.89189332 0.0172057(2-3) 400 0.15 0.0380 2.15309609 0.0191592(3-4) 200 0.1 -0.0018 0.22858575 0.0279335(4-5) 400 0.15 0.0325 1.83682058 0.0193572(2-5) 200 0.1 0.0097 1.23608979 0.0220094(5-6) 600 0.2 0.0530 1.68782032 0.0182269
HARDY CROSSCIRCUITO TUBERA LONGIT DIAMETRO CAUDAL
I (1-2) 500 0.25 0.10733I (2-5) 200 0.1 0.00956I (5-6) 600 0.2 -0.05267I (6-1) 300 0.25 -0.09267
CIRCUITO TUBERA LONGIT DIAMETRO CAUDAL
II (2-3) Dimet Caudal 0.03777II (3-4) 0.25 0.107132 -0.00223II (4-5) 0.25 0.092868 -0.03223II (2-5) 0.15 0.038048 -0.00956
otro problema
PRIMERA ITERACION
1.1. Cculo de coeficientes de friccin DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200
(5-6) 600Tubera (1-2)
Longitud= 500 Caudal 0.15 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 3.05576776 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 670,125 7.2896584 7.289658 0.01881853 0.0010.018819 0.000400 670,125 7.7366854 7.736685 0.01670668 0.01881850.016707 0.000400 670,125 7.7260111 7.726011 0.01675287 0.01670670.016753 0.000400 670,125 7.7262645 7.726264 0.01675178 0.01675290.016752 0.000400 670,125 7.7262584 7.726258 0.0167518 0.0167518
Tubera (3-4)Longitud= 200 Caudal 0.15 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 19.0985485 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 1,675,311 6.9961066 6.996107 0.02043088 0.0010.020431 0.001000 1,675,311 7.1033542 7.103354 0.0198186 0.01929120.019819 0.001000 1,675,311 7.1028572 7.102857 0.01982138 0.01819310.019821 0.001000 1,675,311 7.1028595 7.102859 0.01982136 0.01820360.019821 0.001000 1,675,311 7.1028595 7.102859 0.01982136 0.0182035
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.15 3.05576776 0.0167518(1-6) 300 0.25 0.15 3.05576776 0.0167518(2-3) 400 0.15 0.15 8.48824378 0.0182035(3-4) 200 0.1 0.15 19.0985485 0.0198214(4-5) 400 0.15 0.15 8.48824378 0.0182035(2-5) 200 0.1 0.15 19.0985485 0.0198214(5-6) 600 0.2 0.15 4.77463713 0.0172987ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.00
106.30 -66.16 0.00 0.00 0.00 5006.260 0 1225.14 5006.26 -1206.777 -5006.263
-0.018519135 0.9517258 0.8137691 0.250039 0.114 0.0002799-0.981480865 -0.951726 -0.813769 -0.250039 -0.114 -0.00028-0.007450046 -0.01942 0.8266327 0.197561 0.046 0.0001126-0.007450046 -0.01942 -0.173367 0.197561 0.046 0.00011260.007450046 0.0194202 0.1733673 0.802439 -0.04592137 -0.000113-0.011069089 -0.028854 -0.012864 0.052478 0.0682288 0.00016730.018519135 0.0482742 0.1862309 0.749961 0.88584983 -0.00028
SEGUNDO TRAMITE DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1289938 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.62783446 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 576,279 7.2186881 7.218688 0.01919037 0.0010.01919 0.000400 576,279 7.7105447 7.710545 0.01682015 0.01802020.01682 0.000400 576,279 7.6973119 7.697312 0.01687803 0.01647
0.016878 0.000400 576,279 7.6976653 7.697665 0.01687648 0.01649510.016876 0.000400 576,279 7.6976558 7.697656 0.01687652 0.0164947
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal 0.0760923 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 9.68834944 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 849,855 6.8785937 6.878594 0.02113492 0.0010.021135 0.001000 849,855 7.0734512 7.073451 0.01998652 0.02014530.019987 0.001000 849,855 7.0717327 7.071733 0.01999624 0.01841790.019996 0.001000 849,855 7.0717478 7.071748 0.01999615 0.01844360.019996 0.001000 849,855 7.0717477 7.071748 0.01999615 0.0184432
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.128994 2.62783446 0.0168765(1-6) 300 0.25 0.221006 4.50229031 0.0164947(2-3) 400 0.15 0.096092 5.43769892 0.0184001(3-4) 200 0.1 0.076092 9.68834944 0.0199962(4-5) 400 0.15 0.088908 5.03113508 0.0184432(2-5) 200 0.1 0.077902 9.91870737 0.019988(5-6) 600 0.2 0.101006 3.21511891 0.0175631ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0092.10 -97.70 0.00 0.00 0.00 2598.22
0 0 784.61 2538.33 -720.123 -2598.223
-0.047680405 0.9073727 0.7575645 0.272912 0.135 0.000488-0.952319595 -0.907373 -0.757564 -0.272912 -0.135 -0.000488-0.018653661 -0.036238 0.7870125 0.2152 0.053 0.0001909-0.018653661 -0.036238 -0.212987 0.2152 0.053 0.00019090.018653661 0.0362379 0.2129875 0.7848 -0.05297783 -0.000191-0.029026744 -0.056389 -0.029448 0.057711 0.08243819 0.00029710.047680405 0.0926273 0.2424355 0.727088 0.86458398 -0.000488
TERCERA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1225304 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.49616254 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 547,404 7.1933905 7.193391 0.01932559 0.0010.019326 0.000400 547,404 7.7009964 7.700996 0.01686189 0.01779290.016862 0.000400 547,404 7.6867847 7.686785 0.01692429 0.0164044
0.016924 0.000400 547,404 7.6871794 7.687179 0.01692256 0.01642460.016923 0.000400 547,404 7.6871685 7.687168 0.0169226 0.0164243
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal 0.0404527 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 5.1505816 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 451,805 6.7014272 6.701427 0.02226719 0.0010.022267 0.001000 451,805 7.0243098 7.02431 0.02026715 0.02118440.020267 0.001000 451,805 7.0192577 7.019258 0.02029634 0.01870330.020296 0.001000 451,805 7.0193365 7.019337 0.02029588 0.01875560.020296 0.001000 451,805 7.0193353 7.019335 0.02029589 0.0187544
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.12253 2.49616254 0.0169226(1-6) 300 0.25 0.25247 5.14325686 0.0164243(2-3) 400 0.15 0.070453 3.98679614 0.0185915(3-4) 200 0.1 0.040453 5.1505816 0.0202959(4-5) 400 0.15 0.057047 3.22821108 0.0187544(2-5) 200 0.1 0.044578 5.67579717 0.0202379(5-6) 600 0.2 0.07247 2.30677429 0.0178632ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0087.72 -111.99 0.00 0.00 0.00 1499.05
0 0 578.18 1363.52 -468.308 -1499.054
-0.084472121 0.8493649 0.6821317 0.287745 0.152 0.0007542-0.915527879 -0.849365 -0.682132 -0.287745 -0.152 -0.000754-0.032393466 -0.057766 0.7301959 0.230145 0.058 0.0002892-0.032393466 -0.057766 -0.269804 0.230145 0.058 0.00028920.032393466 0.0577657 0.2698041 0.769855 -0.05840099 -0.000289-0.052078655 -0.092869 -0.048064 0.0576 0.0938907 0.0004650.084472121 0.1506351 0.3178683 0.712255 0.84770831 -0.000754
CUARTA ITERACION DATOS DE IN GRESOTramo Longitud
(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1238837 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.52373311 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 553,450 7.1988436 7.198844 0.01929632 0.0010.019296 0.000400 553,450 7.7030649 7.703065 0.01685283 0.01772370.016853 0.000400 553,450 7.6890671 7.689067 0.01691425 0.01638470.016914 0.000400 553,450 7.6894527 7.689453 0.01691255 0.01640350.016913 0.000400 553,450 7.6894421 7.689442 0.0169126 0.0164032
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal 0.0239042 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 3.0435661 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 266,979 6.4919598 6.49196 0.0237273 0.0010.023727 0.001000 266,979 6.959546 6.959546 0.02064611 0.022290.020646 0.001000 266,979 6.9480967 6.948097 0.02071421 0.01901940.020714 0.001000 266,979 6.9483752 6.948375 0.02071255 0.01910880.020713 0.001000 266,979 6.9483685 6.948368 0.02071259 0.0191061
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.123884 2.52373311 0.0169126(1-6) 300 0.25 0.263616 5.37033361 0.0164032(2-3) 400 0.15 0.058904 3.33328626 0.0187278(3-4) 200 0.1 0.023904 3.0435661 0.0207126(4-5) 400 0.15 0.039846 2.25480757 0.0191062(2-5) 200 0.1 0.03123 3.97626443 0.0204772(5-6) 600 0.2 0.053616 1.70665429 0.0182125ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.00
1.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0088.64 -117.11 0.00 0.00 0.00 1060.81
0 0 485.79 820.56 -332.640 -1060.814
-0.116902655 0.7946168 0.6040753 0.282228 0.152 0.0009982-0.883097345 -0.794617 -0.604075 -0.282228 -0.152 -0.000998-0.045933775 -0.0807 0.6644967 0.234103 0.060 0.0003922-0.045933775 -0.0807 -0.335503 0.234103 0.060 0.00039220.045933775 0.0806998 0.3355033 0.765897 -0.05962849 -0.000392-0.07096888 -0.124683 -0.060421 0.048125 0.09212757 0.0006060.116902655 0.2053832 0.3959247 0.717772 0.84824394 -0.000998
QUINTA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1277522 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.60253979 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 570,732 7.2139713 7.213971 0.01921548 0.0010.019215 0.000400 570,732 7.7087736 7.708774 0.01682788 0.01770960.016828 0.000400 570,732 7.6953609 7.695361 0.01688659 0.01638070.016887 0.000400 570,732 7.6957218 7.695722 0.01688501 0.01639920.016885 0.000400 570,732 7.6957121 7.695712 0.01688505 0.0163989
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal 0.0164138 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 2.08985875 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 183,321 6.3057878 6.305788 0.02514903 0.0010.025149 0.001000 183,321 6.8956177 6.895618 0.0210307 0.02329990.021031 0.001000 183,321 6.8761668 6.876167 0.02114985 0.0193177
0.02115 0.001000 183,321 6.8768013 6.876801 0.02114594 0.0194480.021146 0.001000 183,321 6.8767806 6.876781 0.02114607 0.0194432
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.127752 2.60253979 0.0168851(1-6) 300 0.25 0.265998 5.41885058 0.0163989(2-3) 400 0.15 0.053914 3.05088705 0.0188032(3-4) 200 0.1 0.016414 2.08985875 0.0211461(4-5) 400 0.15 0.030461 1.72375007 0.0194433(2-5) 200 0.1 0.026963 3.4330814 0.0205999(5-6) 600 0.2 0.040998 1.30499835 0.0185968ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0091.26 -118.20 0.00 0.00 0.00 920.89
0 0 445.96 574.68 -258.533 -920.8905
-0.13689948 0.7574125 0.5412224 0.262632 0.137 0.0011582-0.86310052 -0.757412 -0.541222 -0.262632 -0.137 -0.001158
-0.057302494 -0.101541 0.6052641 0.227442 0.057 0.0004848-0.057302494 -0.101541 -0.394736 0.227442 0.057 0.00048480.057302494 0.1015407 0.3947359 0.772558 -0.05747114 -0.000485-0.079596986 -0.141047 -0.064042 0.03519 0.07983125 0.00067340.13689948 0.2425875 0.4587776 0.737368 0.8626976 -0.001158
SEXTA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1308018 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.66466654 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 584,357 7.2254407 7.225441 0.01915452 0.0010.019155 0.000400 584,357 7.7130729 7.713073 0.01680913 0.01770920.016809 0.000400 584,357 7.7000954 7.700095 0.01686583 0.01638050.016866 0.000400 584,357 7.7004383 7.700438 0.01686433 0.0163990.016864 0.000400 584,357 7.7004292 7.700429 0.01686437 0.0163988
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal 0.0130001 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 1.65522422 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 145,195 6.1756241 6.175624 0.02622034 0.0010.02622 0.001000 145,195 6.8472509 6.847251 0.02132885 0.024076
0.021329 0.001000 145,195 6.8209066 6.820907 0.02149393 0.01955220.021494 0.001000 145,195 6.8219251 6.821925 0.02148751 0.01971790.021488 0.001000 145,195 6.8218857 6.821886 0.02148776 0.0197109
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.130802 2.66466654 0.0168644(1-6) 300 0.25 0.266073 5.42038567 0.0163988(2-3) 400 0.15 0.05175 2.92845152 0.01884(3-4) 200 0.1 0.013 1.65522422 0.0214878(4-5) 400 0.15 0.025437 1.43945726 0.0197112(2-5) 200 0.1 0.025614 3.26129203 0.0206465(5-6) 600 0.2 0.033573 1.06866506 0.0189339ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0093.32 -118.24 0.00 0.00 0.00 876.64
0 0 428.71 462.32 -218.755 -876.641
-0.147781572 0.7355831 0.4991159 0.24411 0.123 0.0012498-0.852218428 -0.735583 -0.499116 -0.24411 -0.123 -0.00125-0.065218236 -0.116691 0.5631321 0.217854 0.054 0.0005516-0.065218236 -0.116691 -0.436868 0.217854 0.054 0.0005516
0.065218236 0.1166912 0.4368679 0.782146 -0.05448044 -0.000552-0.082563335 -0.147726 -0.064016 0.026256 0.06896977 0.00069830.147781572 0.2644169 0.5008841 0.75589 0.87654979 -0.00125
SETIMA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1325204 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.69967792 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 592,035 7.2317358 7.231736 0.01912119 0.0010.019121 0.000400 592,035 7.715422 7.715422 0.01679889 0.01771010.016799 0.000400 592,035 7.7026803 7.70268 0.01685451 0.01638080.016855 0.000400 592,035 7.7030136 7.703014 0.01685306 0.01639930.016853 0.000400 592,035 7.7030049 7.703005 0.01685309 0.016399
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal 0.0113906 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 1.45029748 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 127,219 6.0971505 6.09715 0.02689962 0.0010.0269 0.001000 127,219 6.8166123 6.816612 0.02152102 0.0245829
0.021521 0.001000 127,219 6.7856042 6.785604 0.02171816 0.01970750.021718 0.001000 127,219 6.786918 6.786918 0.02170975 0.0198979
0.02171 0.001000 127,219 6.7868623 6.786862 0.0217101 0.0198893
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.13252 2.69967792 0.0168531(1-6) 300 0.25 0.265917 5.41720519 0.016399(2-3) 400 0.15 0.050766 2.87274065 0.0188577(3-4) 200 0.1 0.011391 1.45029748 0.0217101
(4-5) 400 0.15 0.022828 1.29180396 0.0198897(2-5) 200 0.1 0.025036 3.18768189 0.0206679(5-6) 600 0.2 0.029667 0.94432964 0.0191665ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0094.48 -118.17 0.00 0.00 0.00 857.68
0 0 420.86 409.19 -198.041 -857.6801
-0.153751362 0.7233148 0.4742587 0.23211 0.115 0.0013011-0.846248638 -0.723315 -0.474259 -0.23211 -0.115 -0.001301-0.069928389 -0.125841 0.5377068 0.210585 0.052 0.0005918-0.069928389 -0.125841 -0.462293 0.210585 0.052 0.00059180.069928389 0.1258405 0.4622932 0.789415 -0.05226494 -0.000592-0.083822973 -0.150845 -0.063448 0.021525 0.06264984 0.00070940.153751362 0.2766852 0.5257413 0.76789 0.88508522 -0.001301
OCTVA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1334005 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.71760585 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 595,966 7.2349137 7.234914 0.01910439 0.0010.019104 0.000400 595,966 7.716605 7.716605 0.01679374 0.01771070.016794 0.000400 595,966 7.7039816 7.703982 0.01684882 0.0163810.016849 0.000400 595,966 7.7043101 7.70431 0.01684738 0.01639950.016847 0.000400 595,966 7.7043015 7.704302 0.01684742 0.0163992
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal 0.0106027 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 1.34996986 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 118,418 6.0532385 6.053238 0.02729131 0.0010.027291 0.001000 118,418 6.7989801 6.79898 0.02163279 0.02487590.021633 0.001000 118,418 6.765199 6.765199 0.02184937 0.0197980.021849 0.001000 118,418 6.7667011 6.766701 0.02183967 0.0200033
0.02184 0.001000 118,418 6.7666343 6.766634 0.0218401 0.0199936
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.1334 2.71760585 0.0168474(1-6) 300 0.25 0.265818 5.41519272 0.0163992(2-3) 400 0.15 0.05029 2.84583444 0.0188664(3-4) 200 0.1 0.010603 1.34996986 0.0218401(4-5) 400 0.15 0.021507 1.21702808 0.0199941(2-5) 200 0.1 0.024751 3.15138006 0.0206788(5-6) 600 0.2 0.027693 0.88150219 0.0193043ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0095.08 -118.12 0.00 0.00 0.00 848.33
0 0 417.08 383.13 -187.531 -848.3291
-0.156954218 0.7167116 0.460657 0.225443 0.110 0.0013287-0.843045782 -0.716712 -0.460657 -0.225443 -0.110 -0.001329-0.072518563 -0.13089 0.5236464 0.2063 0.051 0.0006139-0.072518563 -0.13089 -0.476354 0.2063 0.051 0.00061390.072518563 0.1308896 0.4763536 0.7937 -0.05096856 -0.000614-0.084435655 -0.152399 -0.062989 0.019143 0.05934431 0.00071480.156954218 0.2832884 0.539343 0.774557 0.88968713 -0.001329
NOVENA ITERACION DATOS DE IN GRESOTramo Longitud(1-2) 500(1-6) 300(2-3) 400(3-4) 200(4-5) 400
(2-5) 200(5-6) 600
Tubera (1-2)Longitud= 500 Caudal 0.1338419 Longitud=Viscosidad= 1.1E-006 Dimetro 0.25 Viscosida=Ks 0.000100 Velocidad 2.72659865 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.000400 597,938 7.2364964 7.236496 0.01909604 0.0010.019096 0.000400 597,938 7.7171935 7.717193 0.01679118 0.0177110.016791 0.000400 597,938 7.7046287 7.704629 0.01684599 0.0163810.016846 0.000400 597,938 7.7049548 7.704955 0.01684457 0.01639960.016845 0.000400 597,938 7.7049464 7.704946 0.0168446 0.0163993
CIRCUITO IITubera (3-4)
Longitud= 200 Caudal 0.0102103 Longitud=Viscosidad= 1.1E-006 Dimetro 0.1 Viscosida=Ks 0.000100 Velocidad 1.30001504 Ks
f Nmero deDenomin denomina G(f) fdato Ks/d Rreynolds 1/f datoasumido DATO CALCULADO asumido
0.001 0.001000 114,036 6.0297726 6.029773 0.02750414 0.0010.027504 0.001000 114,036 6.7894143 6.789414 0.02169379 0.02503370.021694 0.001000 114,036 6.7541039 6.754104 0.02192121 0.01984690.021921 0.001000 114,036 6.7557138 6.755714 0.02191076 0.02006030.021911 0.001000 114,036 6.7556404 6.75564 0.02191124 0.0200501
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.133842 2.72659865 0.0168446(1-6) 300 0.25 0.265767 5.41415765 0.0163993(2-3) 400 0.15 0.050054 2.83247422 0.0188708(3-4) 200 0.1 0.01021 1.30001504 0.0219112(4-5) 400 0.15 0.020844 1.17954726 0.0200506(2-5) 200 0.1 0.024608 3.13320034 0.0206844(5-6) 600 0.2 0.026705 0.85004341 0.0193795ELABORACION DE LA MATRIZ
-1.00 -1.00 0.00 0.00 0.00 0.001.00 0.00 -1.00 0.00 0.00 -1.000.00 0.00 1.00 -1.00 0.00 0.000.00 0.00 0.00 1.00 1.00 0.000.00 0.00 0.00 0.00 -1.00 1.0095.38 -118.10 0.00 0.00 0.00 843.65
0 0 415.19 370.14 -182.257 -843.6461
-0.158623039 0.7132731 0.4535215 0.22196 0.108 0.0013431-0.841376961 -0.713273 -0.453522 -0.22196 -0.108 -0.001343-0.073884288 -0.133553 0.5162252 0.204011 0.050 0.0006256-0.073884288 -0.133553 -0.483775 0.204011 0.050 0.00062560.073884288 0.1335532 0.4837748 0.795989 -0.05027557 -0.000626-0.084738751 -0.153174 -0.062704 0.017948 0.05766164 0.00071750.158623039 0.2867269 0.5464785 0.77804 0.8920628 -0.001343
METODO DE LA
Tramo Longitud Dimet Caudal Velocidad f(1-2) 500 0.25 0.1338 2.72659865 0.0168446(1-6) 300 0.25 0.2658 5.41415765 0.0163993(2-3) 400 0.15 0.0501 2.83247422 0.0188708(3-4) 200 0.1 0.0102 1.30001504 0.0219112(4-5) 400 0.15 0.0208 1.17954726 0.0200506(2-5) 200 0.1 0.0246 3.13320034 0.0206844(5-6) 600 0.2 0.0267 0.85004341 0.0193795
Dimetro Caudal0.25 0.10.25 0.10.15 0.1
0.1 0.10.15 0.1
0.1 0.10.2 0.1
Tubera (1-6)300 Caudal 0.1 Longitud=
Viscosida= 1.14E-006 Dimetro 0.25 Viscosida=0.000100 Velocidad 2.03717851 Ks
Nmero de Denomin denomina G(f) fKs/d Rreynolds 1/f dato Ks/d
DATO CALCULADO asumido DATO0.000400 446,750 7.0879478 7.0879478 0.01990485 0.001 0.0006670.000400 446,750 7.6598831 7.6598831 0.01704338 0.019922 0.0006670.000400 446,750 7.6412177 7.6412177 0.01712675 0.0183583 0.0006
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