Saldarriaga(ejercicios)

(1)

D m L m ks m km H m Z m Densidad 999.1 kg/m3

Visco. Abso. 1.14E-03 Pa.s Visco. Cine. 1.141E-06 m2/s

g 9.81 m/s2 Solución 1º H hf ks/d V hm hfi 37.2 37.2 7.5000E-06 5.3312 11.4441 25.7559 37.2 25.7559 7.5000E-06 4.3640 7.6684 29.5316 37.2 29.5316 7.5000E-06 4.7018 8.9013 28.2987 Otros EJERCICIOS DATOS Caracteristicas de la tubería Accesorios Características topográficas

(2)

37.2 28.2987 7.5000E-06 4.5938 8.4972 28.7028 37.2 28.7028 7.5000E-06 4.6294 8.6295 28.5705 37.2 28.5705 7.5000E-06 4.6178 8.5861 28.6139 37.2 28.6139 7.5000E-06 4.6216 8.6003 28.5997 37.2 28.5997 7.5000E-06 4.6204 8.5957 28.6043 37.2 28.6043 7.5000E-06 4.6208 8.5972 28.6028 37.2 28.6028 7.5000E-06 4.6206 8.5967 28.6033 37.2 28.6033 7.5000E-06 4.6207 8.5969 28.6031 37.2 28.6031 7.5000E-06 4.6207 8.5968 28.6032 37.2 28.6032 7.5000E-06 4.6207 8.5968 28.6032 2º Velocidad 4.6207 Area 0.0314 Solución 1º H hf ks/d V hm hfi 37.2 37.2 7.5000E-04 3.4431 4.7734 32.4266 37.2 32.4266 7.5000E-04 3.2111 4.1518 33.0482 37.2 33.0482 7.5000E-04 3.2422 4.2327 32.9673 37.2 32.9673 7.5000E-04 3.2382 4.2221 32.9779 37.2 32.9779 7.5000E-04 3.2387 4.2235 32.9765 37.2 32.9765 7.5000E-04 3.2386 4.2233 32.9767 37.2 32.9767 7.5000E-04 3.2387 4.2234 32.9766 37.2 32.9766 7.5000E-04 3.2387 4.2234 32.9766 2º Velocidad 3.2387 Area 0.0314 Caudal Caudal

(3)

H hf ks/d V hm hfi 12 12 2.0000E-03 3.4297 5.7556 6.2444 12 6.2444 2.0000E-03 2.4662 2.9759 9.0241 12 9.0241 2.0000E-03 2.9704 4.3172 7.6828 12 7.6828 2.0000E-03 2.7386 3.6696 8.3304 12 8.3304 2.0000E-03 2.8528 3.9822 8.0178 12 8.0178 2.0000E-03 2.7982 3.8313 8.1687 12 8.1687 2.0000E-03 2.8247 3.9041 8.0959 12 8.0959 2.0000E-03 2.8120 3.8690 8.1310 12 8.1310 2.0000E-03 2.8181 3.8859 8.1141 12 8.1141 2.0000E-03 2.8152 3.8777 8.1223 12 8.1223 2.0000E-03 2.8166 3.8817 8.1183 12 8.1183 2.0000E-03 2.8159 3.8798 8.1202 12 8.1202 2.0000E-03 2.8162 3.8807 8.1193 12 8.1193 2.0000E-03 2.8161 3.8803 8.1197 12 8.1197 2.0000E-03 2.8162 3.8805 8.1195 12 8.1195 2.0000E-03 2.8161 3.8804 8.1196 12 8.1196 2.0000E-03 2.8161 3.8804 8.1196 Velocidad 2.8161 Area 0.0177 H hf ks/d V hm hfi 12 12 2.0000E-03 3.4497 5.8229 6.1771 12 6.1771 2.0000E-03 2.4724 2.9909 9.0091 12 9.0091 2.0000E-03 2.9878 4.3679 7.6321 12 7.6321 2.0000E-03 2.7492 3.6982 8.3018 Caudal

(4)

12 8.3018 2.0000E-03 2.8677 4.0239 7.9761 12 7.9761 2.0000E-03 2.8107 3.8655 8.1345 12 8.1345 2.0000E-03 2.8386 3.9425 8.0575 12 8.0575 2.0000E-03 2.8251 3.9051 8.0949 12 8.0949 2.0000E-03 2.8316 3.9233 8.0767 12 8.0767 2.0000E-03 2.8284 3.9144 8.0856 12 8.0856 2.0000E-03 2.8300 3.9187 8.0813 12 8.0813 2.0000E-03 2.8292 3.9166 8.0834 12 8.0834 2.0000E-03 2.8296 3.9176 8.0824 12 8.0824 2.0000E-03 2.8294 3.9172 8.0828 12 8.0828 2.0000E-03 2.8295 3.9174 8.0826 12 8.0826 2.0000E-03 2.8295 3.9173 8.0827 12 8.0827 2.0000E-03 2.8295 3.9173 8.0827 Velocidad 2.8295 Area 0.0177 PROBLEMA CAUDAL 2.6 0.0494 2.7 0.0500 Solución f Q D 0.020000 0.237 0.25 D 0.25 m 0.020108 0.237 0.25 L m 0.020108 0.237 0.25 ks 2.60E-07 m f 0.020108 km Comparando H m Z m Densidad 999.1 kg/m3

Caudal 0.237 m3/s Otros Caudal DATOS Caracteristicas de la tubería Accesorios Características topográficas

(5)

x F(x) F'(x) xi f ks 7.0711 7.9086 -0.0123 7.8984 0.02 4.60E-05 7.8984 7.8650 -0.0122 7.8654 0.02 4.60E-05 7.8654 7.8667 -0.0122 7.8667 0.02 4.60E-05 7.8667 7.8666 -0.0122 7.8666 0.02 4.60E-05 7.8666 7.8666 -0.0122 7.8666 0.02 4.60E-05 f 0.0159 comparando Problema f 2.10 0.0179 Conclusión 2.11 0.0159

(6)

Solución

Calculo de Hm

Caudal Diámetro Velocidad km

0.46 0.35 4.78114441 7.4 Calculo de Hf f Q D v ʯ

ᵨ

0.020000 0.46 0.35 4.7811 1.14E-03 999.1 0.013382 0.46 0.35 4.7811 1.14E-03 999.1 0.013532 0.46 0.35 4.7811 1.14E-03 999.1 0.013527 0.46 0.35 4.7811 1.14E-03 999.1 f L D V g 0.013527 370 0.35 4.7811 9.81 Calculo de H Z Hf Hm H 15 16.6611 8.6218 40.2829 Calculo de la potencia

ᵨ

Q g H 999.1 0.46 9.81 40.2829 Potencia 242.16 324.74 Calculo de H Z Hf Hm H 48 16.6611 8.6218 73.2829 Calculo de la potencia

ᵨ

Q g H 999.1 0.46 9.81 73.2829

(7)

Potencia 440.53 590.76

CONCLUSION

A mas altura, se requiere mayor potencia. Teniendo la misma eficiencia

Km n Caudal Ks Diametro L ᵞ

1.8 68% 0.045 1.50E-06 0.1 26.3 1.141E-06

Calculo de Hm

Caudal Diámetro Velocidad km Hm

0.045 0.1 5.7296 1.8 3.0117 Calculo de Hf f Q D v ʯ

ᵨ

ᵞ 0.020000 0.045 0.1 5.7296 1.14E-03 999.1 1.141E-06 0.012887 0.045 0.1 5.7296 1.14E-03 999.1 1.141E-06 0.013408 0.045 0.1 5.7296 1.14E-03 999.1 1.141E-06 0.013360 0.045 0.1 5.7296 1.14E-03 999.1 1.141E-06 0.013364 0.045 0.1 5.7296 1.14E-03 999.1 1.141E-06 f L D V g Hf 0.013364 26.3 0.1 5.7296 9.81 5.8809 Calculo de H Z Hf Hm H 0 5.8809 3.0117 8.8926 Calculo de la potencia

ᵨ

Q g H

(8)

999.1 0.09 9.81 8.8926 Potencia 11.54 15.47 Solución H hf D V A Q 4 0.4 1.2192 1.2267 1.1675 1.4321 4 2.6 0.8292 2.4614 0.5400 1.3292 4 0.3 0.9144 0.8125 0.6567 0.5336 4 3.6 0.9144 3.1204 0.6567 2.0491 Diámetro 0.9144 36"

(9)

Calculo de H

ᵨ

Q g H n 999.1 0.85 9.81 ? 0.68 H 96.0269 H Z-hf-hm H hf D V A Q Q>Qd 96.0269 96.0269 0.35 5.4502 0.0962 0.5244 SI 96.0269 85.7 0.35 5.1436 0.0962 0.4949 No 96.0269 96.0269 0.4280 6.1600 0.1439 0.8862 SI 96.0269 82.8756 0.4280 5.7146 0.1439 0.8222 SI 96.0269 84.7086 0.4280 5.7787 0.1439 0.8314 SI 96.0269 84.4533 0.4280 5.7698 0.1439 0.8301 SI 96.0269 84.4889 0.4280 5.7710 0.1439 0.8303 SI 96.0269 84.4839 0.4280 5.7709 0.1439 0.8303 SI 96.0269 84.4846 0.4280 5.7709 0.1439 0.8303 SI 96.0269 84.4845 0.4280 5.7709 0.1439 0.8303 SI Diámetro 0.428 18"

(10)

hf 0.0000 D L ks km H Z Densidad Visco. Abso. Visco. Cine. H hf D V A Q

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4.4294 7.0000 0.3000 0.2996 3.6821 0.0705 0.2596 4.3963 7.0000 0.4000 0.2376 3.7128 0.0443 0.1646 4.3510 7.0000 0.5351 0.2376 4.3510 0.0443 0.1929 Diámetro 0.2376 H hf D V A Q 2.3676 1.2000 0.2000 0.2996 2.9517 0.0705 0.2081 2.4367 1.2000 0.1408 0.2996 2.4367 0.0705 0.1718 Diámetro 0.2996

(12)

H hf ks/d V hm hfi 6.2 6.2 7.5000E-06 2.0009 1.6121 4.5879 6.2 4.5879 7.5000E-06 1.6953 1.1572 5.0428 6.2 5.0428 7.5000E-06 1.7859 1.2842 4.9158 6.2 4.9158 7.5000E-06 1.7610 1.2486 4.9514 6.2 4.9514 7.5000E-06 1.7680 1.2586 4.9414 6.2 4.9414 7.5000E-06 1.7660 1.2558 4.9442 6.2 4.9442 7.5000E-06 1.7666 1.2566 4.9434

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Pulgadas Metros 3/8" 0.009246 1/2" 0.012416 3/4" 0.018160 1" 0.023370 1 1/4" 0.028560 1 1/2" 0.033750 2" 0.044170 4" 0.103600 6" 0.152000 8" 0.190200 10" 0.237600 12" 0.299600 30" 0.762 14“ 0.337600 36" 0.9144 16“ 0.380400 42" 1.0668 18“ 0.428000 48" 1.2192 20“ 0.475400 60" 1.524 24“ 0.599200 72" 1.8288 D 0.2 m L 430 m ks 1.50E-06 m km 7.9 H 37.2 m Z 0 m Densidad 999.1 kg/m3

g 9.81 m/s2

D L g Visco. Abso. Densidad Visco. Cine. ks

0.2 430 9.81 1.1400E-03 999.1 1.1410E-06 1.5000E-06

DIAMETROS Agua Desague EJERCICIOS DATOS Caracteristicas de la tubería Accesorios Características topográficas

Características del fluido

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0.2 430 9.81 1.1400E-03 999.1 1.1410E-06 1.5000E-06

ᵨ

D L g ʯ

ᵨ

ᵞ ks

0.2 650 9.81 1.1400E-03 999.1 1.1410E-06 1.5000E-04

D 0.15 m L 126 m ks 3.00E-04 m km 9.6 H 12 m Características topográficas 0.1452 0.1017 DATOS Caracteristicas de la tubería Accesorios

(15)

Z 0 m

Densidad 999.1 kg/m3

g 9.81 m/s2

D L g ʯ

ᵨ

ᵞ ks

0.15 126 9.81 1.1400E-03 999.1 1.1410E-06 3.0000E-04

D L g ʯ

ᵨ

ᵞ ks

0.15 126 9.81 3.5400E-04 971.8 3.6427E-07 3.0000E-04

Otros

(16)

0.15 126 9.81 3.5400E-04 971.8 3.6427E-07 3.0000E-04

v ʯ

ᵨ

ᵞ RE Ks fi

4.8281 1.14E-03 999.1 1.14E-06 1.06E+06 2.60E-04 0.020108 4.8281 1.14E-03 999.1 1.14E-06 1.06E+06 2.60E-04 0.020108 4.8281 1.14E-03 999.1 1.14E-06 1.06E+06 2.60E-04 0.020108

Problema f

2.8 0.011675 2.9 0.020108 0.0500

(17)

D Q V ʯ

ᵨ

ᵞ RE

0.2 0.173 5.5068 2.92E-04 680 4.29E-07 2.56E+06

Por ser gasolina, el coeficiente de fricción es menor

D 0.35 m L 370 m ks 4.60E-05 m km 7.4 H ? m Z 15 m Densidad 999.1 kg/m3

g 9.81 m/s2

Caudal 0.46 m3/s

Eficiencia 75% %

Otros DATOS

Caracteristicas de la tubería

Accesorios

(18)

Hm 8.6218

ᵞ RE Ks fi

1.14E-06 1.47E+06 4.60E-05 0.013382 1.14E-06 1.47E+06 4.60E-05 0.013532 1.14E-06 1.47E+06 4.60E-05 0.013527 1.14E-06 1.47E+06 4.60E-05 0.013527

Hf 16.6611 n Pot 0.75 242155.7199 kw hp n Pot 0.75 440531.4210

(19)

kw hp

A mas altura, se requiere mayor potencia. Teniendo la misma eficiencia

RE Ks fi 5.02E+05 1.50E-06 0.012887 5.02E+05 1.50E-06 0.013408 5.02E+05 1.50E-06 0.013360 5.02E+05 1.50E-06 0.013364 5.02E+05 1.50E-06 0.013364 n Pot

(20)

0.68 11535.6467 kw hp D ? m L 390 m ks 5.00E-04 m km 12.3 H 4 m Z m Densidad 996 kg/m3 2 Tuberías 1.43

Visco. Abso. 7.99E-04 Pa.s 1 Tubería 1.44

Visco. Cine. 8.02E-07 m2/s

g 9.81 m/s2 4.30 Caudal 4.3 m3/s 1.43 Eficiencia % Q>Qd Hm hfi km L ks ʯ SI 0.9434 3.0566 12.3 390 5.00E-04 7.99E-04 SI 3.7981 0.2019 12.3 390 5.00E-04 7.99E-04 SI 0.4139 3.5861 12.3 390 5.00E-04 7.99E-04 SI 6.1041 -2.1041 12.3 390 5.00E-04 7.99E-04 D ? m L 1680 m ks 4.60E-02 m km 6.8 H m DATOS Caracteristicas de la tubería Accesorios Características topográficas Otros DATOS Caracteristicas de la tubería Accesorios Características topográficas

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Z 126 m

Densidad 996 kg/m3

g 9.81 m/s2 Caudal 0.85 m3/s Pot 800 Kw Pot 800000 Hm hfi km L ks ʯ

ᵨ

10.2951 85.7318 6.8 1680 4.60E-05 7.99E-04 996 9.1695 86.8574 6.8 1680 4.60E-05 7.99E-04 996 13.1513 82.8756 6.8 1680 4.60E-05 0.0008 996.0000 11.3183 84.7086 6.8 1680 4.60E-05 0.0008 996.0000 11.5736 84.4533 6.8 1680 4.60E-05 0.0008 996.0000 11.5380 84.4889 6.8 1680 4.60E-05 0.0008 996.0000 11.5430 84.4839 6.8 1680 4.60E-05 0.0008 996.0000 11.5423 84.4846 6.8 1680 4.60E-05 0.0008 996.0000 11.5424 84.4845 6.8 1680 4.60E-05 0.0008 996.0000 11.5424 84.4845 6.8 1680 4.60E-05 0.0008 996.0000 Vp H hf D D ? m 3.3972 7.0000 3.0000 0.2376 L 92 m 2.9195 7.0000 4.0459 0.2376 ks 1.20E-04 m 3.4082 7.0000 2.9742 0.2376 3.1903 7.0000 3.4724 0.2376 Otros DATOS Caracteristicas de la tubería Accesorios Características del fluido

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km 1.35 3.2174 7.0000 3.4124 0.2376 3.1897 7.0000 3.4738 0.2376 H 7 m 3.2180 7.0000 3.4109 0.2376 Z 0 m 3.1890 7.0000 3.4754 0.2376 3.2187 7.0000 3.4093 0.2376 Densidad 999.1 kg/m3 3.1882 7.0000 3.4770 0.2376

Visco. Abso. 1.14E-03 Pa.s 3.2195 7.0000 3.4076 0.2376

Visco. Cine. 1.14E-06 m2/s 3.1875 7.0000 3.4787 0.2376

3.2203 7.0000 3.4059 0.2376 g 9.81 m/s2 3.1867 7.0000 3.4805 0.2376 0.112 3.2211 7.0000 3.4041 0.2376 3.1858 7.0000 3.4823 0.2376 3.2219 7.0000 3.4022 0.2376 Diámetro 0.2376 3.1849 7.0000 3.4843 0.2376 3.2228 7.0000 3.4001 0.2376 3.1840 7.0000 3.4864 0.2376 3.1814 7.0000 3.4921 0.2376 D ? m L 11 m ks 1.50E-06 m km 6.7 H 7 m Z 3 m Densidad 996 kg/m3

g 9.81 m/s2

Caudal 0.19 m3/s

Q>Qd Hm hfi km L ks ʯ

Características topográficas

Otros

DATOS

Caracteristicas de la tubería

Accesorios

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SI 4.6298 2.3702 6.7 11 1.50E-06 1.14E-03 No 4.7075 2.2925 6.7 11 1.50E-06 1.14E-03 No 6.4648 0.5352 6.7 11 1.50E-06 1.14E-03 D ? m L 4.8 m ks 1.50E-06 m km 3.5 H 1.2 m Z m Densidad 996 kg/m3

g 9.81 m/s2 Caudal 0.137 m3/s Q>Qd Hm hfi km L ks ʯ SI 1.5542 -0.3542 3.5 11 1.50E-06 1.14E-03 No 1.0592 0.1408 3.5 11 1.50E-06 1.14E-03 hm Caudal 0.63 hf L 60 z z 6.2 km 2.4 Velocidad 3.9612 Accesorios Características topográficas

Otros DATOS

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D L g 0 Densidad 0 ks

0.2 430 9.81 1.1400E-03 999.1 1.1410E-06 1.5000E-06

(25)

km 7.9 7.9 7.9 EJERCICIOS

(26)

7.9 7.9 7.9 7.9 7.9 7.9 7.9 7.9 7.9 7.9 km 7.9 7.9 7.9 7.9 7.9 7.9 7.9 7.9

(27)

km 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 km 9.6 9.6 9.6 9.6

(28)

9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6 9.6

(29)

(30)

(31)

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Vp 2.5260

ᵨ

ᵞ g 996 8.02E-07 9.81 996 8.02E-07 9.81 996 8.02E-07 9.81 996 8.02E-07 9.81

(33)

ᵞ g 8.02E-07 9.81 8.02E-07 9.81 0.0000 9.8100 0.0000 9.8100 0.103600 0.0000 9.8100 0.152000 0.0000 9.8100 0.190200 0.0000 9.8100 0.237600 0.0000 9.8100 0.299600 0.0000 9.8100 0.337600 0.0000 9.8100 0.380400 0.428000 0.475400 0.599200 V A Q Q>Qd Hm hfi km 2.9441 0.0443 0.1305 SI 3.0041 3.9959 6.8 3.4293 0.0443 0.1520 si 4.0758 2.9242 6.8 2.9311 0.0443 0.1300 SI 2.9776 4.0224 6.8 3.1722 0.0443 0.1407 SI 3.4876 3.5124 6.8

(34)

3.1441 0.0443 0.1394 SI 3.4262 3.5738 6.8 3.1729 0.0443 0.1407 SI 3.4891 3.5109 6.8 3.1434 0.0443 0.1394 SI 3.4246 3.5754 6.8 3.1736 0.0443 0.1407 SI 3.4907 3.5093 6.8 3.1427 0.0443 0.1393 SI 3.4230 3.5770 6.8 3.1744 0.0443 0.1407 SI 3.4924 3.5076 6.8 3.1419 0.0443 0.1393 SI 3.4213 3.5787 6.8 3.1751 0.0443 0.1408 SI 3.4941 3.5059 6.8 3.1411 0.0443 0.1393 SI 3.4195 3.5805 6.8 3.1760 0.0443 0.1408 SI 3.4959 3.5041 6.8 3.1402 0.0443 0.1392 SI 3.4177 3.5823 6.8 3.1768 0.0443 0.1409 SI 3.4978 3.5022 6.8 3.1393 0.0443 0.1392 SI 3.4157 3.5843 6.8 3.1778 0.0443 0.1409 SI 3.4999 3.5001 6.8 3.1384 0.0443 0.1392 SI 3.4136 3.5864 6.8 3.1787 0.0443 0.1409 SI 3.5020 3.4980 6.8 3.1814 0.0443 0.1411 SI 3.5079 3.4921 6.8 q 0.12

ᵨ

ᵞ g

(35)

999.1 1.14E-06 9.81 999.1 1.14E-06 9.81 999.1 0.0000 9.81

ᵨ

ᵞ g 999.1 1.14E-06 9.81 999.1 1.14E-06 9.81

(36)

km 7.9 7.9 7.9 7.9 7.9 7.9 7.9

(37)

(38)

(39)

(40)

(41)

(42)

(43)

(44)

(45)

L ks ʯ

ᵨ

ᵞ g

92 1.20E-04 1.14E-03 991 1.15E-06 9.81

92 1.20E-04 1.14E-03 991 0.0000 9.8100

(46)

92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100 92 1.20E-04 1.14E-03 991 0.0000 9.8100