HARDY CROSS PARA TUBERIA

100 C = HIERRO GALVANIZADO

CIR.No. TRAMO V(m/s) DIAM" LONG(m) Q1(l/s) HF(m) HF/Q

TEORICOCOMERCIAL
AaB 1.5 1.4374 1.5 300 -1.57 -33.37879 21.2604
BaC 1.5 1.4374 1.5 300 1.57 33.37879 21.2604
1 CaA 1.5 2.791186 3 300 5.92 13.2995 2.24654
13.2995 44.7673
dq -0.1606
DaC 1.5 2.890778 4 300 -6.35 -3.730095 0.58742
BaD 1.5 2.890778 4 300 6.35 3.730095 0.58742
2 CaB 1.5 1.4374 1.5 300 -1.57 -33.37879 21.2604
-33.3788 22.4352
dq 0.80421
DaB 1.5 2.890778 4 300 -6.35 -3.730095 0.58742
BaE 1.5 4.442972 4 300 15 18.29605 1.21974
3 EaD 1.5 3.244688 3 300 8 23.21436 2.90179
37.7803 4.70895
dq -4.3368
 dq Q2 HF(m) HF/Q dq Q3 HF(m) HF/Q dq

-0.16058 -1.73058 -39.968 23.09511 0.33613 -1.39445 -26.8043 19.222064 -0.0525

-0.96479 0.605207 5.72241 9.455286 0.46195 1.06716 16.34111 15.312696 -0.2847
-0.16058 5.759416 12.6398 2.194633 0.33613 6.09555 14.038263 2.3030365 -0.0525
-21.606 34.745 3.575073 36.8378
dq 0.33613 dq -0.05246
0.80421 -5.54579 -2.9035 0.523549 -0.12582 -5.67162 -3.026538 0.5336288 0.23222
5.14101 11.49101 11.1751 0.972508 0.51867 12.0097 12.126115 1.0096951 0.29603
0.96479 -0.60521 -5.7224 9.455286 -0.46195 -1.06716 -16.34111 15.312696 0.28468
2.5492 10.9513 -7.241532 16.85602
dq -0.1258 dq 0.232222
-5.14101 -11.491 -11.175 0.972508 -0.51867 -12.0097 -12.12612 1.0096951 -0.296
-4.33681 10.66319 9.73151 0.912626 -0.64449 10.0187 8.6714127 0.8655224 -0.0638
-4.33681 3.663195 5.47244 1.493899 -0.64449 3.0187 3.8256752 1.2673238 -0.0638
4.0288 3.37903 0.370973 3.142541
dq -0.6445 dq -0.06381

NOTA: ver que Vmax = 6 m/s y Vmin = 0.5

 Q4 VEL.FINAL
m/s
-1.44691 1.27
0.78248 0.69
6.043086 1.33

-5.43939 0.67
12.30571 1.52
-0.78248 0.69

-12.3057 1.52
9.954894 1.23
2.954894 0.65

= 6 m/s y Vmin = 0.5 m/s

HARDY CROSS PARA TUBERIA

32
32

47

57 100
25

47

59 81
73

HARDY CROSS PARA TUBERIA

90 C = HIERRO GALVANIZADO

CIR.No. TRAMO V(m/s) DIAM" LONG(m) Q1(l/s)

TEORICO COMERCIAL
KG 1.6 8.39 10 250 57
GC 1.6 7.61 8 250 47
CD 1.6 6.28 6 250 32
DH 1.6 5.55 6 250 -25
HL 1.6 11.11 12 250 -100
I LK 1.6 5.55 6 250 25

DA 1.6 6.28 6 250 32

AB 1.6 3.85 4 250 12
BE 1.6 2.48 3 250 5
EI 1.6 1.92 2 250 -3
IH 1.6 7.45 7 250 -45
II HD 1.6 5.55 6 250 25

IE 1.6 1.92 2 250 3

EF 1.6 2.22 3 250 -4
FJ 1.6 5.55 6 250 -25
JH 1.6 7.28 8 250 -43

III
 HM 1.6 8.60 8 250 -60
III MI 1.6 1.57 2 250 -2

RO 1.6 8.53 8 250 59

OK 1.6 7.61 8 250 47
KL 1.6 5.55 6 250 -25
LP 1.6 13.60 12 250 -150
PS 1.6 10.00 10 250 81
IV SR 1.6 9.49 10 250 73

MQ 1.6 9.36 10 250 -71

QP 1.6 9.93 10 250 -80
PL 1.6 13.60 12 250 150
LH 1.6 11.11 12 250 100
HI 1.6 7.45 8 250 45
V IM 1.6 1.57 2 250 2
 32 12
5
32
3 4 sentido (+) positivo de
47 25 25
45 caudal interno en
cada circuito
57 100 43
25 2

150 71 60
47
80

59 81
331
73

HF(m) HF/Q dq Q2 HF(m) HF/Q dq

2.5262 0.04432 -7.930 49.070 1.9147 0.03902 -2.095

5.2411 0.11151 -7.930 39.070 3.7235 0.09530 -2.095
10.4477 0.32649 -7.930 24.070 6.1691 0.25630 -2.095
-6.6173 0.26469 -7.833 -32.833 -10.9567 0.33371 -2.146
-2.9409 0.02941 -6.460 -106.460 -3.3020 0.03102 0.631
6.6173 0.26469 -0.470 24.530 6.3888 0.26045 1.586
15.2741 1.04112 3.9374 1.01580
dq -7.930193 dq -2.09522
10.4477 0.32649 -0.097 31.903 10.3894 0.32565 0.050
12.2615 1.02179 -0.097 11.903 12.0793 1.01479 0.050
9.8538 1.97076 -0.097 4.903 9.5040 1.93830 0.050
-27.5898 9.19661 -0.438 -3.438 -35.4964 10.32545 0.493
-9.2663 0.20592 1.373 -43.627 -8.7499 0.20056 2.777
6.6173 0.26469 7.833 32.833 10.9567 0.33371 2.146
2.3243 12.98627 -1.3170 14.13846
dq -0.096745 dq 0.050352
27.5898 9.19661 0.438 3.438 35.4964 10.32545 -0.493
-6.5211 1.63028 0.341 -3.659 -5.5300 1.51136 -0.443
-6.6173 0.26469 0.341 -24.659 -6.4513 0.26162 -0.443
-4.4459 0.10339 0.341 -42.659 -4.3809 0.10270 -0.443
 -8.2342 0.13724 0.341 -59.659 -8.1478 0.13657 -0.443
-13.0311 6.51554 1.811 -0.189 -0.1654 0.87629 2.284
-11.2598 17.84775 10.8209 13.21399
dq 0.3410166 dq -0.44265
7.9821 0.13529 -7.460 51.540 6.2160 0.12061 -3.681
5.2411 0.11151 -7.460 39.540 3.8068 0.09628 -3.681
-6.6173 0.26469 0.470 -24.530 -6.3888 0.26045 -1.586
-6.2265 0.04151 -5.990 -155.990 -6.6943 0.04292 -0.955
4.8394 0.05975 -7.460 73.540 4.0473 0.05503 -3.681
3.9924 0.05469 -7.460 65.540 3.2706 0.04990 -3.681
9.2112 0.66744 4.2576 0.62519
dq -7.459821 dq -3.68112
-3.7924 0.05341 -1.470 -72.470 -3.9390 0.05435 -2.726
-4.7294 0.05912 -1.470 -81.470 -4.8915 0.06004 -2.726
6.2265 0.04151 5.990 155.990 6.6943 0.04292 0.955
2.9409 0.02941 6.460 106.460 3.3020 0.03102 -0.631
4.8360 0.10747 -1.373 43.627 4.5665 0.10467 -2.777
13.0311 6.51554 -1.811 0.189 0.1654 0.87629 -2.284
18.5126 6.80645 5.8977 1.16929
dq -1.470198 dq -2.72641
 Q3 HF(m) HF/Q dq Q4 HF(m) HF/Q dq

46.975 1.7662 0.03760 -1.020 45.955 1.6959 0.03690 -0.430

36.975 3.3625 0.09094 -1.020 35.955 3.1929 0.08880 -0.430
21.975 5.2125 0.23721 -1.020 20.955 4.7737 0.22781 -0.430
-34.979 -12.3179 0.35215 -0.593 -35.572 -12.7069 0.35722 -0.096
-105.829 -3.2658 0.03086 -1.749 -107.578 -3.3664 0.03129 -0.114
26.116 7.1739 0.27470 0.089 26.205 7.2193 0.27550 -0.020
1.9314 1.02346 0.8086 1.01753
dq -1.02004 dq -0.42954
31.954 10.4197 0.32609 -0.427 31.526 10.1634 0.32238 -0.334
11.954 12.1740 1.01843 -0.427 11.526 11.3812 0.98741 -0.334
4.954 9.6853 1.95521 -0.427 4.526 8.1968 1.81090 -0.334
-2.945 -26.6574 9.05247 0.012 -2.933 -26.4551 9.02084 -0.277
-40.850 -7.7476 0.18966 -1.156 -42.006 -8.1582 0.19421 -0.018
34.979 12.3179 0.35215 0.593 35.572 12.7069 0.35722 0.096
10.1920 ### 7.8350 ###
dq -0.42727 dq -0.33366
2.945 26.6574 9.05247 -0.012 2.933 26.4551 9.02084 0.277
-4.102 -6.8309 1.66542 -0.439 -4.541 -8.2460 1.81589 -0.057
-25.102 -6.6672 0.26561 -0.439 -25.541 -6.8847 0.26955 -0.057
-43.102 -4.4654 0.10360 -0.439 -43.541 -4.5499 0.10450 -0.057
-60.102 -8.2600 0.13743 -0.439 -60.541 -8.3721 0.13829 -0.057
2.095 14.1989 6.77761 -1.169 0.926 3.1380 3.38729 0.259
14.6328 ### 1.5404 ###
dq -0.43937 dq -0.0565
47.859 5.4197 0.11324 -1.109 46.750 5.1896 0.11101 -0.409
35.859 3.1772 0.08860 -1.109 34.750 2.9978 0.08627 -0.409
-26.116 -7.1739 0.27470 -0.089 -26.205 -7.2193 0.27550 0.020
-156.944 -6.7703 0.04314 -1.839 -158.783 -6.9177 0.04357 -0.094
69.859 3.6805 0.05268 -1.109 68.750 3.5731 0.05197 -0.409
61.859 2.9389 0.04751 -1.109 60.750 2.8422 0.04678 -0.409
1.2721 0.61988 0.4656 0.61510
dq -1.10929 dq -0.40912
-75.197 -4.2175 0.05609 0.729 -74.467 -4.1422 0.05562 -0.315
-84.197 -5.1986 0.06174 0.729 -83.467 -5.1156 0.06129 -0.315
156.944 6.7703 0.04314 1.839 158.783 6.9177 0.04357 0.094
105.829 3.2658 0.03086 1.749 107.578 3.3664 0.03129 0.114
40.850 4.0434 0.09898 1.156 42.006 4.2577 0.10136 0.018
-2.095 -14.1989 6.77761 1.169 -0.926 -3.1380 3.38729 -0.259
-9.5355 7.06842 2.1461 3.68042
dq 0.72921 dq -0.31519
 Q5 HF(m) HF/Q dq Q6 VEL.FINAL
m/s
45.525 1.6667 0.03661 14.062 59.587 1.176
35.525 1.0534 0.02965 14.062 49.587 1.529
20.525 0.3818 0.01860 14.062 34.587 1.897
-35.668 -1.0612 0.02975 14.111 -21.557 1.182
-107.692 -8.1966 0.07611 14.097 -93.596 1.283
26.184 0.5991 0.02288 14.278 40.463 2.219
-5.5569 0.21360
dq 14.06212
31.193 9.9653 0.31948 -0.049 31.144 1.708
11.193 10.7792 0.96306 -0.049 11.144 1.375
4.193 7.1141 1.69679 -0.049 4.144 0.909
-3.210 -31.2654 9.74054 0.214 -2.996 1.478
-42.025 -8.1648 0.19429 -0.014 -42.039 1.694
35.668 12.7703 0.35804 -14.111 21.557 1.182
1.1987 13.27219
dq -0.048821
3.210 31.2654 9.74054 -0.214 2.996 1.478
-4.598 -8.4368 1.83508 -0.263 -4.861 1.066
-25.598 -6.9129 0.27006 -0.263 -25.861 1.418
-43.598 -4.5609 0.10461 -0.263 -43.861 1.353
 -60.598 -8.3866 0.13840 -0.263 -60.861 1.877
1.185 4.9490 4.17603 -0.229 0.956 0.472
7.9173 16.26472
dq -0.263122
46.341 5.1059 0.11018 -0.216 46.124 1.423
34.341 2.9328 0.08540 -0.216 34.124 1.053
-26.184 -7.2089 0.27532 -14.278 -40.463 2.219
-158.877 -6.9253 0.04359 -0.182 -159.059 2.180
68.341 3.5338 0.05171 -0.216 68.124 1.345
60.341 2.8068 0.04652 -0.216 60.124 1.187
0.2452 0.61272
dq -0.216282
-74.783 -4.1747 0.05582 -0.034 -74.817 1.477
-83.783 -5.1514 0.06149 -0.034 -83.817 1.655
158.877 6.9253 0.04359 0.182 159.059 2.180
107.692 3.3730 0.03132 -14.097 93.596 1.283
42.025 4.2611 0.10140 0.014 42.039 1.297
-1.185 -4.9490 4.17603 0.229 -0.956 0.472
0.2845 4.46964
dq -0.034402

NOTA: ver que Vmax = 6 m/s y Vmin = 0.5 m/s

HARDY CROSS PARA TUBERIA
100 C = HIERRO GALVANIZADO

CIR.No. TRAMO V(m/s) DIAM" LONG(m)

TEORICO COMERCIAL
AaB 1.5 1.43740043 1.5 300
BaE 1.5 1.43740043 1 300
1 EaD 1.5 1.43740043 1.5 300
DaA 1.5 2.79118613 3 300

BaC 1.5 2.89077844 4 300

CaF 1.5 2.89077844 4 300
2 FaE 1.5 1.43740043 1.5 300
EaB 1.5 1.43740043 1 300

DaE 1.5 1.43740043 1.5 300

EaH 1.5 3.24468797 4 300
3
HaG 1.5 1.43740043 1.5 300
GaD 1.5 3.24468797 3 300

EaF 1.5 1.43740043 1.5 300

FaI 1.5 4.44297198 4 300
4 IaH 1.5 1.43740043 1.5 300
HaE 1.5 3.24468797 3 300

RESOLVER EL SIGUIENTE CIRCUITO POR HARDY CROSS

A B
C


UNO DOS

UNO DOS

D E
F

TRES CUATRO

G H
I
Q1(l/s) HF(m) HF/Q dq Q2 HF(m)

-1.57 -33.3787903 21.260376 -0.69301913 -2.26301913 -65.6492022

1.57 240.455671 153.156479 -1.33048353 0.23951647 7.41978179
1.57 33.3787903 21.260376 -0.48804318 1.08195682 16.7627243
5.92 13.2995 2.24653717 -0.69301913 5.22698087 10.563415
253.75517 197.92377 -30.903281
dq -0.6930191 dq
-6.35 -3.73009508 0.58741655 0.6374644 -5.7125356 -3.06705816
6.35 3.73009508 0.58741655 0.6374644 6.9874644 4.45225248
1.57 33.3787903 21.260376 1.11853127 2.68853127 90.2940546
-1.57 -240.455671 153.156479 1.33048353 -0.23951647 -7.41978179
-207.07688 175.59169 84.259467
dq 0.6374644 dq
-1.57 -33.3787903 21.260376 0.48804318 -1.08195682 -16.7627243
-8 -5.71880102 0.71485013 0.27609092 -7.72390908 -5.35904301
1.57 33.3787903 21.260376 -0.20497595 1.36502405 25.7671152
8 23.2143556 2.90179445 -0.20497595 7.79502405 22.125977
17.495555 46.137397 25.771325
dq -0.2049759 dq
-1.57 -33.3787903 21.260376 -1.11853127 -2.68853127 -90.2940546
15 18.29605 1.21973667 -0.48106687 14.5189331 17.2253365
1.57 33.3787903 21.260376 -0.48106687 1.08893313 16.9632271
8 23.2143556 2.90179445 -0.27609092 7.72390908 21.7539883
41.510406 46.642283 -34.351503
dq -0.4810669 dq
 NOTA: ver que Vmax = 6 m/s y Vmin = 0.5 m/s

HF/Q dq Q3 HF(m) HF/Q dq

29.0095657 0.21553706 -2.04748208 -54.5523466 26.643626 -0.413201189

30.9781691 0.90838213 1.1478986 134.723139 117.365017 -0.791282749
15.4929698 0.58307614 1.66503296 37.2124684 22.3493885 -0.532240968
2.02094005 0.21553706 5.44251792 11.3833454 2.09155864 -0.413201189
77.501645 128.76661 168.44959
0.2155371 dq -0.4132012
0.53689961 -0.69284507 -6.40538068 -3.79050138 0.59176832 0.37808156
0.63717713 -0.69284507 6.29461932 3.67013492 0.58305908 0.37808156
33.5849003 -1.04210064 1.64643062 36.4469836 22.136969 0.794971953
30.9781691 -0.90838213 -1.1478986 -134.723139 117.365017 0.791282749
65.737146 -98.396522 140.67681
-0.6928451 dq 0.3780816
15.4929698 -0.58307614 -1.66503296 -37.2124684 22.3493885 0.532240968
0.69382523 -0.71679465 -8.44070373 -6.31522786 0.74818736 0.535930172
18.8766748 -0.36753908 0.99748497 14.4222494 14.4586133 0.119039779
2.83847451 -0.36753908 7.42748497 20.2347318 2.72430465 0.119039779
37.901944 -8.870715 40.280494
-0.3675391 dq 0.1190398
33.5849003 1.04210064 -1.64643062 -36.4469836 22.136969 -0.794971953
1.18640511 0.34925557 14.8681887 17.9997274 1.21062006 -0.416890393
15.577841 0.34925557 1.4381887 28.3802096 19.7333004 -0.416890393
2.816448 0.71679465 8.44070373 25.6354339 3.03712044 -0.535930172
53.165594 35.568387 46.11801
0.3492556 dq -0.4168904
Vmin = 0.5 m/s

Q4 VEL.FINAL
m/s
-2.46068326 2.16
0.35661585 0.70
1.13279199 0.99
5.02931674 1.10

-6.02729912 0.74
6.67270088 0.82
2.44140258 2.14
-0.35661585 0.70

-1.13279199 0.99
-7.90477356 0.98
1.11652475 0.98
7.54652475 1.66

-2.44140258 2.14
14.4512983 1.78
1.0212983 0.90
7.90477356 1.73
HARDY CROSS PARA TUBERIA
110 C = HIERRO GALVANIZADO

CIR.No. TRAMO V(m/s) DIAM" LONG(m)

TEORICO COMERCIAL
AaC 1.5 7.6954532 8 60
CaD 1.5 3.62767143 6 60
1 DaB 1.5 4.44297198 3 60
BaA 1.5 5.13030214 4 60

CaE 1.5 5.73585216 6 60

EaF 1.5 3.62767143 4 60
2 FaD 1.5 3.62767143 2 60
DaC 1.5 3.62767143 4 60

5 10
70
A 45 C

1
-20
10 -10

B -15 D

5 15
Q1(l/s) HF(m) HF/Q dq Q2 HF(m)

45 0.80069867 0.0177933 7.98145567 52.9814557 1.08306656

10 0.20113035 0.02011303 3.10016519 13.1001652 0.33146649
-15 -12.452671 0.83017807 7.98145567 -7.01854433 -3.05527793
-20 -5.22333079 0.26116654 7.98145567 -12.0185443 -2.03595417
-16.674173 1.1292509 -3.676699
dq 7.9814557 dq
25 1.09563683 0.04382547 4.88129048 29.8812905 1.52393486
10 1.4489121 0.14489121 4.88129048 14.8812905 3.02292336
-10 -42.3699661 4.23699661 4.88129048 -5.11870952 -12.274534
-10 -1.4489121 0.14489121 -3.10016519 -13.1001652 -2.38783364
-41.274329 4.5706045 -10.115509
dq 4.8812905 dq

15

25 E
1743.811 L Q 1.85
HF
C 1.85 D 4.87
2
H F C 1.85 D 4.87
L
10 1743.811 Q 1.85

-10 F
1743 .811
DTeorico
20 C 5
1.8
 NOTA: ver que Vmax = 6 m/s y Vmin = 0.5 m/s

HF/Q dq Q3 HF(m) HF/Q dq

0.02044237 3.05537928 56.0368349 1.20144008 0.02144018 0.79215484

0.02530247 1.12626831 14.2264335 0.38610487 0.02713996 0.16822488
0.43531504 3.05537928 -3.96316505 -1.06138191 0.26781168 -7.20784516
0.16940106 3.05537928 -8.96316505 -1.18330205 0.13201833 0.79215484
0.6504609 -0.657139 0.4484102
3.0553793 dq 0.7921548
0.05099963 1.92911096 31.8104014 1.71092327 0.05378503 0.62392996
0.20313583 1.92911096 16.8104014 3.78757721 0.22531153 0.62392996
2.39797432 1.92911096 -3.18959855 -5.11646214 1.6041085 0.62392996
0.18227508 -1.12626831 -14.2264335 -2.78144008 0.19551211 -0.16822488
2.8343849 -2.3994017 2.0787172
1.929111 dq 0.62393

3.811 L Q 1.85 Hf 17.22863 m

Q 70 l/s
C 1.85 D 4.87 D 8 pl
L 570.092 m

1.85
D 4.87
L
11 Q 1.85

1
1743 .811 LQ 1.85
4.87

C 5 HF
1.8

y Vmin = 0.5 m/s

Q4 VEL.FINAL
m/s
56.8289898 1.75
14.3946584 0.79
-11.1710102 2.45
-8.17101021 1.01

32.4343314 1.78
17.4343314 2.15
-2.5656686 1.27
-14.3946584 1.78