• Author / Uploaded
• Anthony Bazan Rodriguez

Citation preview

PROBLEMA N° 01: SOLUCION: 90 L/s

34.89 l/s

67 l/s

30 L/s

19.42 l/s

DATOS:

A D= 10"

B D= 8"

D =12.01 I 1 0 " D= F 6"

D II = 6 " D= 8" E

37 l/s >Utilizaremos las formulas de wazen-wilians: wazen-wilians:

TRAMO

C

D 5.04= 6 "

AB BE EF FA BC CD DE EB

l/s

60 L/s D

L(m) 600 900 600 900 600 900 600 600

19.42 l/s n 1.8519 CH= 100

PRIMERA ITERACION:

I

AB BE EF FA

600 900 600 900

D(pulg) 0.254 0.152 0.152 0.254

II

BC CD DE EB

600 900 600 600

0.203 0.152 0.203 0.152

CIRCUITO

TRAMO

L(m)

CH 100 100 100 100

Q(supuestos) k 999.509 0.0349 17991.252 0.0120 11994.168 -0.0114 1498.498 -0.0669

100 100 100 100

2958.562 17991.252 2958.562 11994.168

Hp=KQ^n 2.0000 5.0000 -3.0000 -10.0000 ∑ -6.0000

Hp/Q 57.3269 416.1591 264.3137 149.5734 887.3731

ΔQ Otros circuitros 0.00365 0.00365 -0.00185 0.00365 0.00365

2.0000 1.0000 -2.0000 -3.3333 -2.3333

103.0048 198.4875 103.0048 277.4394 681.9364

0.00185 0.00185 0.00185 0.00185

Hp=KQ^n 2.4048

Hp/Q 62.3996

0.0194 0.0050 -0.0194 -0.0120 ∑

-0.00365

SEGUNDA ITERACION: CIRCUITO

TRAMO

L(m)

D(pulg)

CH

k

Q(supuestos)

ΔQ Otros circuitros 0.00099

468.8146 189.8985 142.5862 863.6989

0.00099 0.00099 0.00099

∑

6.4782 -1.4620 -9.0122 -1.5913

111.2978 259.0107 94.5939 312.5430 777.4454

0.00127 0.00127 0.00127 0.00127

∑

2.3667 1.7835 -1.6619 -4.3188 -1.8305

Hp=KQ^n 2.5210 6.2401 -1.1315 -8.7513 ∑ -1.1217

Hp/Q 63.7692 460.8098 168.7835 140.6721 834.0347

ΔQ Otros circuitros 0.00073 0.00073 -0.00035 0.00073 0.00073

2.6354 2.4409 -1.4461 -4.1601 -0.5299

116.9421 299.2302 88.7302 307.2065 812.1091

0.00035 0.00035 0.00035 0.00035

Hp=KQ^n 2.6075 6.5629 -0.9151 -8.5631 ∑ -0.3077

Hp/Q 64.7658 471.6264 153.0777 139.2720 828.7419

ΔQ Otros circuitros 0.00020 0.00020 -0.00027 0.00020 0.00020

I

II

-0.00127

-0.00099

TERCERA ITERACION: CIRCUITO

TRAMO

L(m)

D(pulg)

CH

k

Q(supuestos)

I

II ∑

-0.00073

CUARTA ITERACION: CIRCUITO

I

TRAMO

L(m)

D(pulg)

CH

k

Q(supuestos)

2.7122 2.6397 -1.3887 -4.3753 -0.4121

118.4978 310.2056 87.0934 314.4176 830.2144

0.00027 0.00027 0.00027 0.00027

Hp=KQ^n 2.6316 6.5041 -0.8590 -8.5114 ∑ -0.2348

Hp/Q 65.0405 469.6760 148.6928 138.8850 822.2942

ΔQ Otros circuitros 0.00015 0.00015 -0.00007 0.00015 0.00015

2.7713 2.7958 -1.3458 -4.3360 -0.1148

119.6790 318.5099 85.8447 313.1173 837.1509

0.00007 0.00007 0.00007 0.00007

Hp=KQ^n 2.6502 6.5740 -0.8171 -8.4718 ∑ -0.0647

Hp/Q 65.2516 471.9910 145.3052 138.5872 821.1350

ΔQ Otros circuitros 0.00004 0.00004 -0.00006 0.00004 0.00004

2.7877 2.8396 -1.3340

120.0049 320.7972 85.4992

0.00006 0.00006 0.00006

II ∑

-0.00020

QUINTA ITERACION: CIRCUITO

TRAMO

L(m)

D(pulg)

CH

k

Q(supuestos)

I

II ∑

-0.00015

SEXTA ITERACION: CIRCUITO

I

II

TRAMO

L(m)

D(pulg)

CH

k

Q(supuestos)

-4.3826 -0.0894

314.6607 840.9619

0.00006

Hp=KQ^n 2.6553 6.5610 -0.8056 -8.4609 ∑ -0.0502

Hp/Q 65.3098 471.5630 144.3677 138.5050 819.7456

ΔQ Otros circuitros 0.00003 0.00003 -0.00002 0.00003 0.00003

2.8005 2.8738 -1.3250 -4.3740 -0.0247

120.2573 322.5680 85.2313 314.3753 842.4320

0.00002 0.00002 0.00002 0.00002

Hp=KQ^n 2.6593 6.5761 -0.7968 -8.4524 ∑ -0.0138

Hp/Q 65.3551 472.0603 143.6387 138.4412 819.4952

ΔQ Otros circuitros 0.00001 0.00001 -0.00001 0.00001 0.00001

2.8040 2.8832 -1.3225 -4.3840 -0.0192

120.3270 323.0565 85.1573 314.7068 843.2477

0.00001 0.00001 0.00001 0.00001

∑

-0.00004

SEPTIMA ITERACION: CIRCUITO

TRAMO

L(m)

D(pulg)

CH

k

Q(supuestos)

I

II ∑

-0.00003

OCTAVA ITERACION: CIRCUITO

TRAMO

L(m)

I

D(pulg)

CH

k

Q(supuestos)

II ∑ NOVENA ITERACION:

-0.00001

CIRCUITO

TRAMO

I

AB BE EF FA

II

BC CD DE EB

L(m)

D(pulg)

DATOS REALES AB TRAMO Q(L/s) 40.71

BE 13.93

EF

NUDO P(m)

B 47.34

C

A 50.00

CH

-5.53

FA -61.04

44.53

D 41.6422

k

BC 23.32 E

Q(supuestos)

Hp=KQ^n 2.6604 6.5733 -0.7944 -8.4501 ∑ -0.0108

Hp/Q 65.3675 471.9679 143.4375 138.4235 819.1964

ΔQ Otros circuitros 0.00001 0.00001 0.00000 0.00001 0.00001

120.3812 323.4366 85.0997 314.6452 843.5627

0.00000 0.00000 0.00000 0.00000

∑

2.8068 2.8906 -1.3205 -4.3822 -0.0053

8.94

DE -15.51

CD

F

NUDO A B C D E F

-0.00001

COTA 50 48 46 45 43 40

D(pulg) 10 6 6 10 8 6 8 6

Q(corregida) 0.03854 0.01382 -0.00770 -0.06321

0.02126 0.00689 -0.01757 -0.01382

Q(corregida) 0.03953

Q(supuestos) 0.0254 0.0254 0.0254 0.0254 0.0254 0.0254 0.0254 0.0254

34.89 12.01 11.35 66.86 19.42 5.04 19.42 NUDO A B C D E F

COTA 50 48 46 45 43 40

0.01354 -0.00670 -0.06221

0.02254 0.00816 -0.01630 -0.01354

Q(corregida) 0.04026 0.01392 -0.00598 -0.06148

0.02289 0.00851 -0.01595 -0.01392

Q(corregida) 0.04046 0.01385 -0.00578 -0.06128

0.02316 0.00878 -0.01568 -0.01385

Q(corregida) 0.04061 0.01393 -0.00562 -0.06113

0.02323 0.00885 -0.01560 -0.01393

Q(corregida) 0.04066 0.01391 -0.00558 -0.06109

0.02329 0.00891 -0.01555

-0.01391

Q(corregida) 0.04069 0.01393 -0.00555 -0.06105

0.02330 0.00892 -0.01553 -0.01393

Q(corregida) 0.04070 0.01393 -0.00554 -0.06104

0.02332 0.00894 -0.01552 -0.01393

Q(corregida) 0.04071 0.01393 -0.00553 -0.06104

0.02332 0.00894 -0.01551 -0.01393

PROBLEMA N° 02: SOLUCION: 400 L/s 133.33 l/s

100 l/s 1

2

D= 8"

I

II 166.67

D=6" 50.00 l/s

50.00 l/s

292.86

l/s

D=8"

D=8" 76.19 l/s

8

7

l/s

57.14

III

l/s

IV

D=6"

D=10"

D=6" 50.00 l/s

4

133.33

l/s D=10"

D=8" 3

TRAMO

9

D= 6"

100 l/s

DATOS:

D=6" 57.14 l/s

5

D=6" 6

1-2 2-3 3-8 8-1 1-9 9-7 7-8 8-1 3-4 4-5 5-8 8-3 8-5 5-6 6-7 7-8

L(m) 400 900 600 900 600 900 600 600 400 900 600 900 600 900 600 600

400 L/s >Utilizaremos las formulas de wazen-wilians: wazen-wilians: n 1.8519 CH= 130 tubo de acero:

hallar la districbucion de los caudales en cada tuberia?

PRIMERA ITERACION: CIRCUITO

I

TRAMO

1-2 2-3 3-8 8-1

L(m)

400 900 600 900

D(pulg) 0.152 0.203 0.152 0.254

CH 130 130 130 130

Q(supuestos) k 4933.7231 -0.1000 2734.3831 -0.1000 7400.5846 0.0500 922.2989 0.1667

Hp=KQ^n -69.3942 -2734.3831 7400.5846 922.2989

Hp/Q 693.9416 27343.8315 148011.6929 5533.7937

II

II I

V I  3-

1-9 9-7 7-8 8-1

3-4 4-5 5-8 8-3

8-5 5-6 6-7 7-8

4 SEGUNDA ITERACION: 4 TRAMO L(m) CIRCUITO 0

600 900 600 600

400 900 600 900

600 900 600 600

0.203 0.203 0.203 0.254

0.152 0.152 0.254 0.152

0.254 0.152 0.152 0.203

D(pulg)

130 130 130 130

130 130 130 130

130 130 130 130

CH

1822.9221 2734.3831 1822.9221 614.8660

4933.7231 11100.8770 614.8660 11100.8770

614.8660 11100.8770 7400.5846 1822.9221

k

∑

5519.1063

181583.2597

∑

1822.9221 2734.3831 -15.4958 -22.2720 4519.5374

13671.9157 20507.8736 203.3823 133.6321 34516.8037

∑

-19.2247 -43.2556 614.8660 -43.2556 509.1300

384.4943 865.1123 2099.5423 865.1123 4214.2612

∑

-63.2566 11100.8770 7400.5846 1822.9221 20261.1271

215.9982 194265.3470 129510.2313 23925.8525 347917.4291

∑

Hp=KQ^n -91.9491 -2734.3831 7400.5846 922.2989 5496.5513

Hp/Q 789.8530 23488.6504 220340.4340 4174.0565 248792.9939

∑

1822.9221 2734.3831 -15.4958 -37.5445 4504.2650

29107.5205 43661.2807 203.3823 169.9153 73142.0988

0.1333 0.1333 -0.0762 -0.1667

-0.0500 -0.0500 0.2929 -0.0500

-0.2929 0.0571 0.0571 0.0762

Q(supuestos)

0 0, 1I 5 2 1 4 0 II 4 3 0 1, 0 4 0 1 4

4 3 0 1, 0 4

∑

-98.3272 -221.2362 614.8660 -221.2362 74.0664

814.5997 1832.8493 2099.5423 1832.8493 6579.8407

∑

-63.2566 -3.8617 -2.5744 1822.9221 1753.2294

215.9982 284.7141 189.8094 23925.8525 24616.3743

∑

Hp=KQ^n -110.1572 -2734.3831 7400.5846 922.2989 5478.3433

Hp/Q 858.3023 21305.2599 341719.5185 3806.6822 367689.7628

∑

1822.9221 2734.3831 -15.4958 -44.5289 4497.2806

62061.7873 93092.6809 203.3823 183.7878 155541.6382

∑

-154.3043 -347.1846 614.8660 -347.1846 -233.8075

1002.2319 2255.0217 2099.5423 2255.0217 7611.8177

-63.2566 -38.2961

215.9982 817.9830

II 0 I1 4 1, 6 6 6

V 7 I4 

33 4 0 TERCERA ITERACION: 1, 4 TRAMO L(m) CIRCUITO 0 4 0 0 0, 2I 1 3 5 0, 2 3 1 6 4 0 0 3 II 4 -1 3 4, 0 5 1, 0 0 9 4 0 II 0 1 I 1  4 1 1, 2 6 7, 6 1 6 V 5 7 I74  6 33 6 4 0 1, 4

D(pulg)

CH

k

Q(supuestos)

1 1, 2 6 7, 6 1 6 V 5 7 I74  6 33 6 4 0 CUARTA ITERACION: 1, 4   TRAMO CIRCUITO 0 44 0 5 0 0, 9I 2 1 0 3 5 0 0, 2 0, 3 1 1 6 4 5 0 0 2 3 II 4 1 -1 3 4 4, 0 5 0 1, 0 9 0 9 6 4 0 7 II 0 7, 1 I13  4 4 1 1, 1 2 6 1 7, 6 4 1 6 V 1, 5 7 6 I74  6 33 6 6 4 0 7 CUARTA ITERACION: 1, 4   9 TRAMO CIRCUITO 0 46 4 1-2 0 5 7 0 2-3 0, 7, 9 I123 3-8 0 3 5 4 0 0, 0 2 0, 3 1 5 1 6 4 6 5 0

-25.5308 1822.9221 1695.8386

545.3220 23925.8525 25505.1558

∑

Hp=KQ^n -123.2857 -2734.3831 7400.5846 922.2989 5465.2147

Hp/Q 903.9290 20048.4496 543711.2095 3691.3821 568354.9702

∑

1822.9221 2734.3831 -15.4958 -47.1387 4494.6707

132486.4258 198729.6387 203.3823 188.6667 331608.1135

∑

-184.5281 -415.1881 614.8660 -415.1881 -400.0383

1088.1859 2448.4182 2099.5423 2448.4182 8084.5646

∑

-63.2566 -65.2558 -43.5039 1822.9221 1650.9058

215.9982 1045.2442 696.8295 23925.8525 25883.9245

Hp=KQ^n -132.1185 -2734.3831 7400.5846

Hp/Q 933.1632 19313.1638 879066.6869

∑ L(m)

L(m)

D(pulg)

D(pulg)

CH

CH

k

k

Q(supuestos)

Q(supuestos)

9 0 46 4 0 5 7 0 0, 7, 9 2 1 3 0 3 5 4 0 0, 0 2 0, 3 1 5 1 6 4 6 5 0 8, 0 2 3 II 3 4 1 -1 1 3 4 4, 0 0 5 0 1, 6 0 9 0 -1 9 6 4 4, 0 7 II 5 0 7, 1 0 I3 1  9 4 4 0 1 1, 1 2 6 1 1 7, 6  6 4 1 V 1 1, 5 7 2 6 7 I4  7, 6 33 1 6 6 4 0 5 7 1, 4  7 9 0 6 46 4 0 6 5 7 0 0, 7, 9  1 2 3 0 53 5 4 0 0, 8 0 2 0, 3 6 1 5 1 6 0 4 6 5 0 0 8, 0 2 3 0, 3 4 1 -1 2 1 3 4 4, 5 0 0 5 0 1, 4 6 0 9 0 1 -1 9 6 4 4, 0 7 5 0 7, 1 0 1

8-1 ∑

922.2989 5456.3820

3660.2270 902973.2409

∑

1822.9221 2734.3831 -15.4958 -47.8845 4493.9250

283059.6355 424589.4533 203.3823 190.0339 708042.5049

∑

-199.5481 -448.9832 614.8660 -448.9832 -482.6485

1128.0705 2538.1587 2099.5423 2538.1587 8303.9303

∑

-63.2566 -80.1267 -53.4178 1822.9221 1626.1210

215.9982 1148.7631 765.8421 23925.8525 26056.4559

1-9 9-7 7-8 8-1

3-4 4-5 5-8 8-3

8-5 5-6 6-7 7-8

DATOS REALES TRAMO

Q(L/S) TRAMO

Q(L/S)

1-2 -144.84

2-3 -144.84

3-8 5.16

8-1 252.14

1-9 3.01

3.01

7-8 -76.19

3-4

4-5 3.01

5-8 -76.19

8-3 -180.32

8-5 -292.86

5-6 -73.18

6-7 -73.18

3.01

9-7

0 8, 0 2 3 0, 3 4 1 -1 2 1 3 4 4, 5 0 0 5 0 1, 4 6 0 9 0 1 -1 9 6 4 4, 0 7 5 0 7, 1 0 1 5 3  9 4 3 4 0 1 1, 6, 1 2 6 0 1 1 7, 6 1  6 4 1 8 1 1, 5 7 8 2 6 7 4 0, 7, 6 3 5 1 6 6 0 5 7 1, 5  7 9 0 6 46 6 4 5 6 5 7 0 3 7, 9  2 6, 3 0 53 0 4 0 0, 8 1 0 0, 3 7 6 5 1 6 0 8 6 5 0 0 6, 8, 2 3 6 0, 3 1 -1 5 2 1 4 4, 4 5 0 5 0 0 4 6 0 9 -1 1 -1 9 6 4, 4 4, 0 7 5 5 0 7, 1 0 0 5 3 9  9 3 4 0 0 1 6, 1 2 1 0 1 1 7, 1   4 1 8 6 1 1, 5 6, 8 2 6 7 0 0, 7, 6 4 5 1 6 6

3 9  9 3 4 0 0 1 6, 1 2 1 0 1 1 7, 1   1 4 8 6 1 1, 5 6, 8 2 6 7 0 0, 7, 6 4 5 1 6 6 6 5 7 5  7 9 6 45 6 6 5 6 5 7   3 7, 9 8  6, 3 0 53 0 4 0 9 8 1 0 0, 0 7 6 5 1 0 8 6 5 0, 0 6, 8, 2 1 6 0, 3 1 5 2 1 4 4 5 2 0 0 1 0 4 6 9 4 -1 1 -1 6 4, 4 0 4, 7 5 5 9 0 7, 0 0 6 5 3 9 9 7 3 4 0 0 7, 6, 1 3 1 0 1 1 4 1   4 1 8 6 1 1, 4 6, 8 2 6 1, 0 0, 7, 6 6 4 5 1 6 6 5 7 6 5 7 9 7 6 5 6 6 9 5 6 7   6 3 7, 8 7 6, 3 53 7, 0 4 3 9 8 1 0 4 0 7 6 5

5 7 6 5 7 9 7 6 5 6 6 9 5 6 7   6 3 7, 8 7 6, 3 53 7, 0 4 3 9 8 1 0 4 0 7 6 5 0 0 8 6 5 0, 0 6, 8, 2 1 6 0, 3 3 5 2 1 2, 4 5 2 0 2 1 0 4 6 5 4 -1 1 -1 6 4, 4 0 4, 2 5 5 9 0 -1 0 0 6 5 4, 9 9 7 3 5 0 0 7, 6, 0 3 1 0 1 9 4 1  0   1 8 6 1 4 6, 8 2 1 1, 0 0, 7, 4, 6 4 5 1 5 6 5 0 6 5 7 9 7 6 0 5 6 9 5 6  1 6 3 4  87 6, 1, 53 7, 0 6 3 9 8 1 6 4 0 7 6 6 0 0 6 8 5 0, 0 6, 7 2 1 6 0, ∑ 3 5 2 2 2, 4 5 2 4 2 1 0 4 1 5 4 -1 1 9 6 4, 4 0 1, 2 5

0 6 8 5 0, 0 6, 7 2 1 6 0, ∑ 3 5 2 2 2, 4 5 2 4 2 1 0 4 1 5 4 -1 1 9 6 4, 4 0 1, 2 5 7 9 0 -1 0 3 6 5 4, 9 9 7 3 5 0 7, 6, 1 0 3 1 0 3 9 4 1 3  0 1 7, 8 6 1 5 4 6, 8 1 8 1, 0 0, 4, 1 6 4 5 5 6 5 1 0 6 5 9 7 0 5 6 9 5 1   6 3 4 87 6, 1, 3 7, 0 6 3 9 1 6 4 0 7 6 0 0 6 8 5 0, 6, 7 2 1 6 ∑ 3 5 2 2, 4 2 4 2 1 0 1 5 4 -1 9 6 4, 0 1, 2 5 7 9 -1 0 3 6 4, 9 9 7 5 0 7, 1 0 3 1 3 9 4 3  0 1 7, 6 1 5 4 6, 1 8 1, 0 4,

7 9 -1 0 3 6 4, 9 9 7 5 0 7, 1 0 3 1 3 9 4 3  0 1 7, 6 1 5 4 6, 1 8 1, 0 4, 1 6 4 5 6 1 0 6 5 9 7 0 5 9 1   6 4 87 1, 3 7, 6 3 9 6 4 0 6 0 0 6 5 0, 7 2 1 ∑ 3 5 2 2, 2 4 2 1 1 5 4 9 6 0 1, 2 7 9 -1 3 6 4, 9 7 5 7, 1 0 3 3 9 4 3 0 1 7, 1 5 4 1 8 1, 4, 1 6 5 6 1 0 6 9 7 0 9 1 6 4 7 1, 7, 6 3 6

6 5 6 0 6 9 7 0 9 1 6 4 7 1, 7, 6 3 6 4 6 0 6 5 7 2 ∑ 3 2 2, 4 2 1 5 9 6 1, 2 7 -1 3 4, 9 5 1 0 3 9 3 0 7, 1 5 1 8 4, 1 5 1 0 9 0 1 4 1, 6 6 6 6 7 ∑ 2 4 1 9

6 6 7 ∑ 2 4 1 9 1, 7 3 9 1 3 3 7, 5 8 1 1

ASUMIDOS D(pulg) 6 8 6 10 8 8 8 10 6 6 10 6 10 6 6 8

Q(supuestos) 100.00 100.00 50.00 166.67 133.33 133.33 76.19 166.67 50.00 50.00 292.86 50.00 292.86 57.14 57.14 76.19

ΔQ Otros circuitrQ(corregida) -0.0164 -0.1164 -0.0164 -0.1164 -0.0164 0.0336 -0.0164 0.0707 0.2210

Hp=KQ^n -137.8126 -2734.3831 7400.5846 922.2989

Hp/Q 951.4528 18878.0774 1435436.2139 3657.8417

ΔQ -0.0020 -0.0020 -0.0020 -0.0020

-0.0707 -0.0707 -0.0707 -0.0707

-0.0707 -0.0707 -0.0707 -0.0707

-0.0707 -0.0707 -0.0707 -0.0707

0.0707 0.0164

0.0707

0.0707

0.0707

5450.6879

1458923.5859

0.0626 0.0626 -0.0762 -0.2210

1822.9221 2734.3831 -15.4958 -47.9423 4493.8671

605079.2749 907618.9124 203.3823 190.1394 1513091.7090

-0.0016 -0.0016 -0.0016 -0.0016

-0.1207 -0.1207 0.2929 -0.1207

-206.7669 -465.2256 614.8660 -465.2256 -522.3522

1146.6627 2579.9911 2099.5423 2579.9911 8406.1872

-0.0016 -0.0016 -0.0016 -0.0016

-0.2929 -0.0136 -0.0136 0.0762

-63.2566 -87.5701 -58.3801 1822.9221 1613.7153

215.9982 1196.6761 797.7841 23925.8525 26136.3109

-0.0016 -0.0016 -0.0016 -0.0016

ΔQ Otros circuitrQ(corregida) -0.0119 -0.1283 -0.0119 -0.1283 -0.0119 0.0217 -0.0119 0.0333 0.2423

-0.0333 -0.0333 -0.0333 -0.0333

0.0333 0.0119

0.0294 0.0294 -0.0762 -0.2423

-0.0333 -0.0333 -0.0333 -0.0333

-0.0333 -0.0333 -0.0333 -0.0333

0.0333

0.0333

0.0333

-0.1540 -0.1540 0.2929 -0.1540

-0.2929 -0.0468 -0.0468 0.0762

ΔQ Otros circuitrQ(corregida) -0.0080 -0.1364 -0.0080 -0.1364 -0.0080 0.0136 -0.0080 0.0156 0.2499

-0.0156 -0.0156 -0.0156 -0.0156

-0.0156 -0.0156 -0.0156 -0.0156

-0.0156 -0.0156

0.0156 0.0080

0.0156

0.0156

0.0138 0.0138 -0.0762 -0.2499

-0.1696 -0.1696 0.2929 -0.1696

-0.2929 -0.0624

-0.0156 -0.0156

0.0156

-0.0624 0.0762

ΔQ Otros circuitrQ(corregida) -0.0052 -0.1416 -0.0052 -0.1416 -0.0052 0.0084 -0.0052 0.0073 0.2520

-0.0073 -0.0073 -0.0073 -0.0073

-0.0073 -0.0073 -0.0073 -0.0073

-0.0073 -0.0073 -0.0073 -0.0073

0.0073 0.0052

0.0073

0.0073

0.0073

0.0064 0.0064 -0.0762 -0.2520

-0.1769 -0.1769 0.2929 -0.1769

-0.2929 -0.0698 -0.0698 0.0762

ΔQ Otros circuitrQ(corregida) -0.0033 -0.1448 -0.0033 -0.1448 -0.0033 0.0052

-0.0033

-0.0034 -0.0034 -0.0034 -0.0034

-0.0034 -0.0034 -0.0034 -0.0034

-0.0034 -0.0034 -0.0034 -0.0034

8-1 -252.14 7-8 76.19

0.0034

0.2521

0.0034 0.0033

0.0030 0.0030 -0.0762 -0.2521

0.0034

0.0034

0.0034

-0.1803 -0.1803 0.2929 -0.1803

-0.2929 -0.0732 -0.0732 0.0762

Otros circuitrQ(corregida) -0.1469 -0.1469 0.0031 0.0016 0.2517

Hp=KQ^n -141.3884 -2734.3831 7400.5846 922.2989

Hp/Q 962.7304 18618.7424 ### 3663.8531

ΔQ Otros circuitrQ(corregida) -0.0012 -0.1481 -0.0012 -0.1481 -0.0012 0.0019 -0.0012 0.0008 0.2512

Hp=KQ^n -143.5983 -2734.3831 7400.5846 922.2989

0.0016 0.0020

0.0016

0.0016

0.0016

5447.1121

###

5444.9022

0.0014 0.0014 -0.0762 -0.2517

1822.9221 2734.3831 -15.4958 -47.7967 4494.0127

### ### 203.3823 189.8736 ###

-0.0008 -0.0008 -0.0008 -0.0008

-0.1819 -0.1819 0.2929 -0.1819

-210.1854 -472.9172 614.8660 -472.9172 -541.1538

1155.3447 2599.5255 2099.5423 2599.5255 8453.9380

-0.0008 -0.0008 -0.0008 -0.0008

-0.2929 -0.0748 -0.0748 0.0762

-63.2566 -91.1574 -60.7716 1822.9221 1607.7365

215.9982 1218.9815 812.6543 23925.8525 26173.4866

-0.0008 -0.0008 -0.0008 -0.0008

0.0008 0.0012

0.0008

0.0008

0.0008

0.0007 0.0007 -0.0762 -0.2512

1822.9221 2734.3831 -15.4958 -47.6264 4494.1831

-0.1827 -0.1827 0.2929 -0.1827

-211.7932 -476.5347 614.8660 -476.5347 -549.9967

-0.2929 -0.0755 -0.0755 0.0762

-63.2566 -92.8580 -61.9053 1822.9221 1604.9022

Hp/Q 969.6232 18463.4641 ### 3670.9252

ΔQ Otros circuitrQ(corregida) -0.0008 -0.1488 -0.0008 -0.1488 -0.0008 0.0012 -0.0008 0.0004 0.2508

Hp=KQ^n -144.9508 -2734.3831 7400.5846 922.2989

Hp/Q 973.8135 18370.2335 ### 3676.7911

ΔQ Otros circuitr -0.0005 -0.0005 -0.0005 -0.0005 0.0002

### ### ### 203.3823 189.5620 ###

-0.0004 -0.0004 -0.0004 -0.0004

1159.4016 2608.6537 2099.5423 2608.6537 8476.2513

-0.0004 -0.0004 -0.0004 -0.0004

215.9982 1229.3902 819.5934 23925.8525 26190.8344

-0.0004 -0.0004 -0.0004 -0.0004

0.0004 0.0008

0.0004

0.0004

0.0004

5443.5497

###

0.0003 0.0003 -0.0762 -0.2508

1822.9221 2734.3831 -15.4958 -47.4858 4494.3237

### ### 203.3823 189.3043 ###

-0.0002 -0.0002 -0.0002 -0.0002

-0.1830 -0.1830 0.2929 -0.1830

-212.5470 -478.2307 614.8660 -478.2307 -554.1423

1161.2979 2612.9202 2099.5423 2612.9202 8486.6806

-0.0002 -0.0002 -0.0002 -0.0002

-0.2929 -0.0759 -0.0759 0.0762

-63.2566 -93.6581 -62.4388 1822.9221 1603.5686

215.9982 1234.2521 822.8347 23925.8525 26198.9376

-0.0002 -0.0002 -0.0002 -0.0002

0.0002 0.0005

0.0002

0.0002

0.0002

Q(corregida) -0.1493 -0.1493 0.0007 0.2506

0.0001 0.0001 -0.0762 -0.2506

-0.1832 -0.1832 0.2929 -0.1832

-0.2929 -0.0760 -0.0760 0.0762

PROBLEMA N° 03: 80L/s

200L/s 75L/s

B

D II 75L/s

125L/s

230L/s I

A 400L/s

C

170L/s

120L/s

SOLUCION: PRIMERA ITERACION: CIRCUITO I

II

TRAMO

D(m)

L(m)

CH

Q (m3/s)

AB

0.203

320

90

0.2300

BC

0.152

1200

120

0.0750

CA

0.152

810

120

-0.170

BD

0.152

1000

120

0.075

DC

0.152

300

110

-0.125

CB

0.152

1200

120

-0.075

TRAMO

D(m)

L(m)

CH

Q (m3/s)

AB

0.203

320

90

0.2481

BC

0.152

1200

120

0.0767

CA

0.152

810

120

-0.1519

BD

0.152

1000

120

0.091

DC

0.152

300

110

-0.109

CB

0.152

1200

120

-0.077

SEGUNDA ITERACION: CIRCUITO I

II

TERCERA ITERACION: CIRCUITO

TRAMO

D(m)

L(m)

CH

Q (m3/s)

AB

0.203

320

90

0.2548

BC

0.152

1200

120

0.0763

CA

0.152

810

120

-0.1452

BD

0.152

1000

120

0.099

DC

0.152

300

110

-0.101

CB

0.152

1200

120

-0.076

TRAMO

D(m)

L(m)

CH

Q (m3/s)

AB

0.203

320

90

0.2578

BC

0.152

1200

120

0.0765

CA

0.152

810

120

-0.1422

BD

0.152

1000

120

0.101

DC

0.152

300

110

-0.099

CB

0.152

1200

120

-0.077

TRAMO

D(m)

L(m)

CH

Q (m3/s)

AB

0.203

320

90

0.2589

BC

0.152

1200

120

0.0764

CA

0.152

810

120

-0.1411

BD

0.152

1000

120

0.102

DC

0.152

300

110

-0.098

CB

0.152

1200

120

-0.076

TRAMO

D(m)

L(m)

CH

Q (m3/s)

AB

0.203

320

90

0.2594

I

II

CUARTA

ITERACION:

CIRCUITO I

II

QUINTA

ITERACION:

CIRCUITO I

II

SEXTA

ITERACION:

CIRCUITO I

II

BC

0.152

1200

120

0.0765

CA

0.152

810

120

-0.1406

BD

0.152

1000

120

0.103

DC

0.152

300

110

-0.097

CB

0.152

1200

120

-0.076

SETIMA ITERACION: CIRCUITO I

II

OCTAVA

TRAMO

D(m)

L(m)

CH

Q (m3/s)

AB

0.203

320

90

0.2596

BC

0.152

1200

120

0.0764

CA

0.152

810

120

-0.1404

BD

0.152

1000

120

0.103

DC

0.152

300

110

-0.097

CB

0.152

1200

120

-0.076

TRAMO

D(m)

L(m)

CH

Q (m3/s)

AB

0.203

320

90

0.2597

BC

0.152

1200

120

0.0764

CA

0.152

810

120

-0.1403

BD

0.152

1000

120

0.103

DC

0.152

300

110

-0.097

CB

0.152

1200

120

-0.076

TRAMO

D(m)

L(m)

CH

Q (m3/s)

AB

0.203

320

90

0.2597

ITERACION:

CIRCUITO I

II

NOVENA ITERACION: CIRCUITO I

II

BC

0.152

1200

120

0.0764

CA

0.152

810

120

-0.1403

BD

0.152

1000

120

0.103

DC

0.152

300

110

-0.097

CB

0.152

1200

120

-0.076

AB

BC

CA

BD

DC

DATOS REALES TRAMO

Q(L/s)

259.68

76.44

-140.32

103.24

-96.76

Calcular el caudal en cada unas de las tuberias se sabe que: En los puntos B, C y D las descargas son de 80, 120, 200L/s. resprectivamnete . TRAMO AB CA BC BD DC CB

L(m) 320 810 1200 1000 300 1200

D(pulg) 8 6 6 6 6 6

CH 90 120 120 120 110 120

Q( supuestos) 0.230 -0.170 0.075 0.075 -0.125 -0.075

ΔQ

otros circuitos

0.01806

-0.01635

n= 1.851 1m= 0.0254

k

Hp

Hp/Q

1919.34

126.389

549.517

17145.05

141.866

1891.542

11572.91

-435.515

2561.855

-167.2607

5002.914

14287.54

118.221

1576.285

5035.30

-107.252

858.017

∑

17145.05

-141.866

1891.542

-130.8964

4325.8432

k

Hp

Hp/Q

∑

1919.34

145.372

586.033

17145.05

147.927

1928.277

11572.91

-353.759

2328.310

∑

-60.4597

4842.619

14287.54

170.297

1864.276

5035.30

-82.744

761.545

17145.05

-147.927

1928.277

0.01635 -0.01806

ΔQ

otros circuitos

0.00674

-0.00716

0.00716 -0.00674

∑

-60.3736

4554.0976

k

Hp

Hp/Q

ΔQ

1919.34

152.773

599.566

0.00295

17145.05

146.441

1919.351

0.00295

11572.91

-325.240

2240.054

0.00295

∑

-26.0255

4758.971

14287.54

195.833

1987.959

0.00275

otros circuitos -0.00275

5035.30

-72.932

718.610

0.00275

17145.05

-146.441

1919.351

0.00275

-0.00295

∑

-23.5406

4625.9207 otros circuitos

k

Hp

Hp/Q

ΔQ

1919.34

156.069

605.477

0.00113

17145.05

147.171

1923.744

0.00113

11572.91

-313.096

2201.205

0.00113

∑

-9.8564

4730.425

14287.54

206.069

2035.076

0.00121

5035.30

-69.317

702.011

0.00121

17145.05

-147.171

1923.744

0.00121

-0.00113

∑

-10.4195

4660.8307

k

Hp

Hp/Q

ΔQ

otros circuitos

-0.00121

1919.34

157.332

607.726

0.00049

17145.05

146.879

1921.987

0.00049

11572.91

-308.525

2186.371

0.00049

∑

-4.3136

4716.085

14287.54

210.642

2055.714

0.00046

5035.30

-67.756

694.697

0.00046

17145.05

-146.879

1921.987

0.00046

-0.00049

∑

-3.9936

4672.3985

k

Hp

Hp/Q

ΔQ

otros circuitos

1919.34

157.889

608.713

0.00019

17145.05

146.995

1922.680

0.00019

11572.91

-306.529

2179.854

0.00019

∑

-1.6453

4711.248

14287.54

212.402

2063.595

0.00020

5035.30

-67.164

691.897

0.00020

17145.05

-146.995

1922.680

0.00020

∑

-1.7558

4678.1726

-0.00046

-0.00020

-0.00019

k

Hp

Hp/Q

ΔQ

1919.34

158.101

609.090

0.00008

otros circuitos

17145.05

146.944

1922.379

0.00008

11572.91

-305.768

2177.365

0.00008

∑

-0.7220

4708.834

14287.54

213.177

2067.054

0.00008

5035.30

-66.904

690.667

0.00008

17145.05

-146.944

1922.379

0.00008

-0.00008

∑

-0.6710

4680.0998

k

Hp

Hp/Q

ΔQ

otros circuitos

-0.00008

1919.34

158.195

609.255

0.00003

17145.05

146.963

1922.494

0.00003

11572.91

-305.434

2176.272

0.00003

∑

-0.2757

4708.021

14287.54

213.474

2068.376

0.00003

5035.30

-66.805

690.197

0.00003

17145.05

-146.963

1922.494

0.00003

-0.00003

∑

-0.2947

4681.0659

k

Hp

Hp/Q

ΔQ

otros circuitos

1919.34

158.230

609.319

0.00001

17145.05

146.955

1922.443

0.00001

11572.91

-305.307

2175.855

0.00001

∑

-0.1210

4707.616

14287.54

213.604

2068.956

0.00001

5035.30

-66.762

689.990

0.00001

17145.05

-146.955

1922.443

0.00001

∑

-0.1126

4681.3887

CB

-76.44

-0.00003

-0.00003

-0.00001

PROBLEMA N° 04: SOLUCION: 320 L/s 106.67 l/s

89.60 l/s 1

2

9

D= 6"

D= 8"

I

II

89.60 l/s

123.73

l/s D=10"

D=8" D=6" 44.80 l/s

3

44.80 l/s

D=8" 60.95 l/s

8

229.49

D=8" 7

l/s

45.71

III

IV

D=6"

D=12"

D=6" 44.80 l/s

4

106.67

D=6" D=6" 45.71 l/s

5

6

320L/s >Utilizaremos las formulas de wazen-wilians: wazen-wilians: n 1.852 CH= 140 tubo de acero:

hallar la districbucion de los cauda

PRIMERA ITERACION:

I

1-2 2-3 3-8 8-1

400 900 600 900

D(m) 0.178 0.203 0.152 0.254

II

1-9 9-7 7-8 8-1

600 900 600 600

0.203 0.203 0.203 0.254

140 140 140 140

1589.1571 2383.7357 1589.1571 536.0178

II I

3-4 4-5 5-8 8-3

400 900 600 900

0.152 0.152 0.305 0.152

140 140 140 140

4301.0402 9677.3405 220.5653 9677.3405

CIRCUITO

TRAMO

L(m)

CH 140 140 140 140

k 2030.1019 2383.7357 6451.5604 804.0267

V I  3-

8-5 5-6 6-7 7-8

4 SEGUNDA ITERACION: 4 TRAMO CIRCUITO 0

600 900 600 600

0.305 0.152 0.152 0.203

140 140 140 140

220.5653 9677.3405 6451.5604 1589.1571

L(m)

D(m)

CH

k

L(m)

D(m)

CH

k

0 0, 1I 5 2 1 4 0 II 4 3 0 1, 0 4

II 0 I 1 4 1, 6 6 6

V 7 I4 

33 4 0 TERCERA ITERACION: 1, 4 TRAMO CIRCUITO 0 4 0 0 0, 2I 1 3 5 0, 2 3 1 6 4 0 0 3 II 4 -1 3 4, 0 5 1, 0 0 9 4 0 0 1 1

0 3 4 -1 3 4, 0 5 1, 0 0 9 4 0 II 0 1 I 1   4 1 1, 2 6 7, 6 1 6 V 5 7 7 I4  6 33 6 4 0 CUARTA ITERACION: 1, 4   TRAMO CIRCUITO 0 44 0 5 0 0, 9I 2 1 0 3 5 0 0, 2 0, 3 1 1 6 4 5 0 0 2 3 II 4 1 -1 3 4 4, 0 5 0 1, 0 9 0 9 6 4 0 7 II 0 7, 1 I13   4 4 1 1, 1 2 6 1 7, 6 4 1 6 V 1, 5 7 6 7 I4  6 33 6 6 4 0 7 CUARTA ITERACION: 1, 4   9 TRAMO CIRCUITO 0 46 4 1-2 0 5 7 0 2-3 0, 7, 9 I123 3-8 0 3 5 8-1 4 0 0, 0 2 0, 3 1 5 1 6 4 6 5 0 8, 0 2 3 3 4 1 -1 1 3 4 4,

L(m)

D(m)

CH

k

L(m)

D(m) 0.178 0.203 0.152 0.254

CH

k

2 1 3 0 3 5 4 0 0, 0 2 0, 3 1 5 1 6 4 6 5 0 8, 0 2 3 II 3 4 1 -1 1 3 4 4, 0 0 5 0 1, 6 0 9 0 -1 9 6 4 4, 0 7 II 5 0 7, 1 0 I3 1  9 4 4 0 1 1, 1 2 6 1 1 7, 6  6 4 1 V 1 1, 5 7 I7624  7, 6 33 1 6 6 4 0 5 7 1, 4  7 9 0 6 46 4 0 6 5 7 0 0, 7, 9  1 2 3 0 53 5 4 0 0, 8 0 2 0, 3 6 1 5 1 6 0 4 6 5 0 0 8, 0 2 3 0, 3 4 1 -1 2 1 3 4 4, 5 0 0 5 0 1, 4 6 0 9 0 1 -1 9 6 4 4, 0 7 5 0 7, 1 0 1 5 3  9 4 3 4 0 1 1, 6, 1 2 6 0 1 1 7, 6 1  6 4 1 8 1 1, 5 7 8 2 6 7 4 0, 7, 6 3 5 1 6 6 0 5 7 1, 5  7 9 0 6 46 6 4 5 6 5 7 0 3 7, 9  2 6, 3 0 53 0 4 0 0, 8 1 0

1-9 9-7 7-8 8-1

0.203 0.203 0.203 0.254

3-4 4-5 5-8 8-3

0.152 0.152 0.305 0.152

8-5 5-6 6-7 7-8

0.305 0.152 0.152 0.203

DATOS REALES TRAMO

Q(L/S) TRAMO

Q(L/S)

1-2 -45.14

2-3 -45.14

3-8 -0.34

8-1 274.08

3-4 0.78

4-5 0.78

5-8 60.95

8-3 -61.09

5 1 6 6 0 5 7 1, 5  7 9 0 6 46 6 4 5 6 5 7 0 3 7, 9  2 6, 3 0 53 0 4 0 0, 8 1 0 0, 3 7 6 5 1 6 0 8 6 5 0 0 6, 8, 2 3 6 0, 3 1 -1 5 2 1 4 4, 4 5 0 5 0 0 4 6 0 9 -1 1 -1 9 6 4, 4 4, 0 7 5 5 0 7, 1 0 0 5 3 9  9 3 4 0 0 1 6, 1 2 1 0 1 1 7, 1  4  1 8 6 1 1, 5 6, 8 2 6 7 0 0, 7, 6 4 5 1 6 6 6 5 7 5  7 9 6 45 6 6 5 6 5 7   3 7, 9 8  6, 3 0 53 0 4 0 9 8 1 0 0, 0 7 6 5 1 0 8 6 5 0, 0 6, 8, 2 1 6 0, 3 1 5 2 1 4 4 5 2 0 0 1 0 4 6 9 4 -1 1 -1 6 4, 4 0 4, 7 5 5 9 0 7, 0 0 6 5 3 9 9 7 3 4 0 0 7, 6, 1 3 1 0 1 1 4 1  4   1 8 6 1 1, 4 6, 8 2 6 1, 0 0, 7, 6 6 4 5 1 6 6 5 7 6 5 7 9

1 3 1 0 1 1 4 1   4 1 8 6 1 1, 4 6, 8 2 6 1, 0 0, 7, 6 6 4 5 1 6 6 5 7 6 5 7 9 7 6 5 6 6 9 5 6 7   6 3 7,  87 6, 3 53 7, 0 4 3 9 8 1 0 4 0 7 6 5 0 0 8 6 5 0, 0 6, 8, 2 1 6 0, 3 3 5 2 1 2, 4 5 2 0 2 1 0 4 6 5 4 -1 1 -1 6 4, 4 0 4, 2 5 5 9 0 -1 0 0 6 5 4, 9 9 7 3 5 0 0 7, 6, 0 3 1 0 1 9 4 1  0   1 8 6 1 4 6, 8 2 1 1, 0 0, 7, 4, 6 4 5 1 5 6 5 0 6 5 7 9 7 6 0 5 6 9 5 6 1   6 3 4 8 7 6, 1, 53 7, 0 6 3 9 8 1 6 4 0 7 6 6 0 0 6 8 5 0, 0 6, 7 2 1 6 0, ∑ 3 5 2 2 2, 4 5 2 4 2 1 0 4 1 5 4 -1 1 9 6 4, 4 0 1, 2 5 7 9 0 -1 0 3 6 5 4, 9 9 7 3 5 0 7, 6, 1 0 3 1 0 3 9 4 1 3  0 1 7, 8 6

-1 1 9 6 4, 4 0 1, 2 5 7 9 0 -1 0 3 6 5 4, 9 9 7 3 5 0 7, 6, 1 0 3 1 0 3 9 4 1 3  0 1 7, 8 6 1 5 4 6, 8 1 8 1, 0 0, 4, 1 6 4 5 5 6 5 1 0 6 5 9 7 0 5 6 9 5 1   6 3 4 87 6, 1, 3 7, 0 6 3 9 1 6 4 0 7 6 0 0 6 8 5 0, 6, 7 2 1 6 ∑ 3 5 2 2, 4 2 4 2 1 0 1 5 4 -1 9 6 4, 0 1, 2 5 7 9 -1 0 3 6 4, 9 9 7 5 0 7, 1 0 3 1 3 9 4 3 0   1 7, 6 1 5 4 6, 1 8 1, 0 4, 1 6 4 5 6 1 0 6 5 9 7 0 5 9 1   6 4 87 1, 3 7, 6 3 9 6 4 0 6 0 0 6 5 0, 7 2 1 ∑ 3 5 2 2, 2 4 2 1 1 5 4 9 6 0 1, 2 7 9 -1

5 0, 7 2 1 ∑ 3 5 2 2, 2 4 2 1 1 5 4 9 6 0 1, 2 7 9 -1 3 6 4, 9 7 5 7, 1 0 3 3 9 4 3 0 1 7, 1 5 4 1 8 1, 4, 1 6 5 6 1 0 6 9 7 0 9 1 6 4 7 1, 7, 6 3 6 4 6 0 6 5 7 2 ∑ 3 2 2, 4 2 1 5 9 6 1, 2 7 -1 3 4, 9 5 1 0 3 9 3 0 7, 1 5 1 8 4, 1 5 1 0 9 0 1 4 1, 6 6 6 6 7 ∑

4 1, 6 6 6 6 7 ∑ 2 4 1 9 1, 7 3 9 1 3 3 7, 5 8 1 1

DATOS: TRAMO

1-2 2-3 3-8 8-1 1-9 9-7 7-8 8-1 3-4 4-5 5-8 8-3 8-5 5-6 6-7 7-8

l/s

l/s

L(m) 400 900 600 900 600 900 600 600 400 900 600 900 600 900 600 600

ASUMIDOS D(pulg) 7 8 6 10 8 8 8 10 6 6 12 6 12 6 6 8

Q(supuestos) 89.60 89.60 44.80 123.73 106.67 106.67 60.95 123.73 44.80 44.80 229.49 44.80 229.49 45.71 45.71 60.95

ar la districbucion de los caudales en cada tuberia?

Q(supuestos) -0.0896 -0.0896 -0.0448 0.1237

Hp/Q 260.0396 26604.1932 144008.0438 6498.0603 177370.3368

1589.1571 2383.7357 1589.1571 -11.1840 5550.8659

14898.3482 22347.5223 26072.1094 90.3883 63408.3682

-0.0473 -0.0473 -0.0473 -0.0473

-13.6754 -30.7697 220.5653 9677.3405

305.2546 686.8228 961.1287 216012.0656

-0.0473 -0.0473 -0.0473 -0.0473

0.1067 0.1067 0.0610 -0.1237 ∑ -0.0448 -0.0448 0.2295 0.0448

ΔQ Otros circui Q(corregida) 0.0245 -0.0651 0.0245 -0.0651 0.0245 -0.0203 0.0245 0.0473 0.1955

Hp=KQ^n -23.2995 -2383.7357 -6451.5604 804.0267 ∑ -8054.5690

0.0473 -0.0245

0.0473

0.0594 0.0594 0.0610 -0.1955

-0.0921 -0.0921 0.2295 -0.0025

∑ -0.2295 0.0457 0.0457 -0.0610

Q(supuestos)

Q(supuestos)

9853.4608

217965.2717

-14.4461 9677.3405 6451.5604 -8.9361 ∑ 16105.5186

62.9500 211691.8243 141127.8829 146.6084 353029.2656

-0.0473 -0.0473 -0.0473 -0.0473

Hp=KQ^n -12.8877 -2383.7357 -6451.5604 804.0267 ∑ -8044.1571

Hp/Q 198.0340 36628.8765 318154.9327 4112.0853 359093.9287

ΔQ Otros circui Q(corregida) 0.0121 -0.0530 0.0121 -0.0530 0.0121 -0.0082 0.0121 0.0321 0.2397

26756.0830 40134.1245 26072.1094 133.4731 93095.7900

-0.0321 -0.0321 -0.0321 -0.0321

∑

1589.1571 2383.7357 1589.1571 -26.0977 5535.9523

563.8523 1268.6678 961.1287 58.2216 2851.8704

-0.0321 -0.0321 -0.0321 -0.0321

∑

-51.9153 -116.8093 220.5653 -0.1439 51.6968

62.9500 39.2892 26.1928 146.6084 275.0405

-0.0321 -0.0321 -0.0321 -0.0321

∑

-14.4461 -0.0612 -0.0408 -8.9361 -23.4843

Hp=KQ^n -8.8061 -2383.7357 -6451.5604 804.0267 ∑ -8040.0755

Hp/Q 166.2110 44991.9652 788567.7550 3353.8064 837079.7375

ΔQ Otros circui Q(corregida) 0.0052 -0.0478 0.0052 -0.0478 0.0052 -0.0030 0.0052 0.0174 0.2623

1589.1571 2383.7357 1589.1571 -38.0659 5523.9841

58247.0007 87370.5010 26072.1094 158.7827 171848.3937

-0.0174 -0.0174 -0.0174 -0.0174

∑

0.0473

0.0473

0.0321 -0.0121

0.0321

0.0321

0.0321

0.0174 -0.0052

-0.2295 -0.0016 -0.0016 -0.0610

0.0273 0.0273 0.0610 -0.2397

-0.1242 -0.1242 0.2295 -0.0346

-0.2295 -0.0337 -0.0337 -0.0610

0.0099 0.0099 0.0610 -0.2623

Q(supuestos)

Q(supuestos)

727.5292 1636.9407 961.1287 550.9216 3876.5203

-0.0174 -0.0174 -0.0174 -0.0174

∑

-90.3472 -203.2812 220.5653 -19.0529 -92.1159

62.9500 538.4901 358.9934 146.6084 1107.0420

-0.0174 -0.0174 -0.0174 -0.0174

∑

-14.4461 -18.1306 -12.0871 -8.9361 -53.5999

Hp=KQ^n Hp/Q -7.2765 152.2457 -2383.7357 49874.4641 -6451.5604 2154316.5415 804.0267 3065.5249 ∑ -8038.5460 2207408.7762

0.0174

0.0174

-0.2295 -0.0510 -0.0510 -0.0610

ΔQ Otros circui Q(corregida) 0.0020 -0.0458 0.0020 -0.0458 0.0020 -0.0010 0.0020 0.0070 0.2712

160116.0779 240174.1168 26072.1094 171.4169 426533.7209

-0.0070 -0.0070 -0.0070 -0.0070

∑

1589.1571 2383.7357 1589.1571 -44.9593 5517.0907

813.3035 1829.9329 961.1287 779.0505 4383.4156

-0.0070 -0.0070 -0.0070 -0.0070

∑

-115.1163 -259.0117 220.5653 -40.4652 -194.0279

62.9500 767.3538 511.5692 146.6084 1488.4813

-0.0070 -0.0070 -0.0070 -0.0070

∑

-14.4461 -39.1560 -26.1040 -8.9361 -88.6423

Hp=KQ^n Hp/Q -6.7319 146.8932 -2383.7357 52014.5617 -6451.5604 6274384.3568 804.0267 2964.3560 ∑ -8038.0013 6329510.1678

0.0174

-0.1415 -0.1415 0.2295 -0.0519

0.0070 -0.0020

0.0070

0.0070

0.0070

0.0029 0.0029 0.0610 -0.2712

-0.1485 -0.1485 0.2295 -0.0589

-0.2295 -0.0580 -0.0580 -0.0610

ΔQ Otros circui Q(corregida) 0.0007 -0.0451 0.0007 -0.0451 0.0007 -0.0003 0.0007 0.0022 0.2741

-0.0022 -0.0022 -0.0022 -0.0022

∑

1589.1571 540476.8221 2383.7357 810715.2332 1589.1571 26072.1094 -47.8420 176.3879 5514.2080 1377440.5526 847.3696 1906.5815 961.1287 867.4453 4582.5251

-0.0022 -0.0022 -0.0022 -0.0022

∑

-125.8567 -283.1777 220.5653 -51.1154 -239.5845

62.9500 855.9670 570.6446 146.6084 1636.1700

-0.0022 -0.0022 -0.0022 -0.0022

∑

-14.4461 -49.6564 -33.1043 -8.9361 -106.1430

1-9 0.78

9-7 0.78

7-8 60.95

8-1 -274.08

8-5 -229.49

5-6 -60.17

6-7 -60.17

7-8 -60.95

0.0022 -0.0007

0.0022

0.0022

0.0022

0.0008 0.0008 0.0610 -0.2741

-0.1507 -0.1507 0.2295 -0.0611

-0.2295 -0.0602 -0.0602 -0.0610

v 1.81815536 1.3920252 0.01877469 5.40900514

0.0240074 0.0240074 1.87954345 5.40900514

8.26072548 8.26072548 3.14510271 3.34885193

3.14510271 3.29873077 3.29873077 1.87954345