TRABAJO EN ALEJANDRO YURI TICONA MET. Hardy Cross.xlsx
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CURSO
B ).
DE
ABASTECIM IE NTO
DE
AGUA
Y
ALCANTARILLADO
-
DISEÑADO DISEÑADO POR: A LEJ ANDR O YURI TICONA TICONA PEÑASC O ESQUEMA GENERAL METODO DE HARDY CROSS LEYENDA: Ø
l/s lt/s. msnm mca lt/s
INFORMACION Y DATOS: Diametro de la Tuberia Propuesto Ca Caudal en Transito en el Tramo - Red de Distribucion Caudal que se Destina para Un Nudo Cota del Terreno en (msnm) Presion en el Nudo (Resultante) Sentido del Flujo (Caudal de Transito en la Red) Caudal en Transito (DISEÑO) (DISEÑO) en el Tramo - Red de Distribucion
A LT L T E R N A TI TIV A N° N° 02 T U B E R IA P V C
Se Se tiene Caudal Media Qm=
20.00 Lt/seg.
Qmd= Qmh=
Poblacion Futura = Poblacion Inicial = Incremento de Población =
26.00 Lt/seg. 36.00 Lt/seg.
11 11520 Hab 8323 Hab 3197 Hab
Q para la ZONA "A" = Q para la ZONA "B" = Q para %⧍P =
12.40 Lt/seg. 19.60 Lt/seg. 4.00 Lt/seg. Lt/seg.
D IA ME ME T R O S DE DE TU TU B ER ER IA ) I (
C=150
O T I U C R I C
GR A FIC O N ° 00 1 Cota:
2098 msnm 1.38 lt/s.
TRAMO
Diametros
1-2 2-3 3-4
3 3 4
4-1
3
) I I (
1-2 2-3 3-4
3 3 3
4-1
O T I U C R I C
4
Cota:
2100 msnm 1.38 lt/s.
Pulg Ø 3
1 35.15 mca
Cota:
2
5.0888
TRAMO
Diametros
1-2 2-3 3-4
3 3 4
4-1
3
O T I U C R I C
TRAMO
Diametros
1-2 2-3 3-4
3 3 3
4-1
4
Cota:
1
33.06 mca P
lt/s
) V I (
2102 msnm 2.23 lt/s. Ø
2.6220 l/s
Pres En Ent
) I I I (
TR T RAMO Diametros
O T I U C R I C
P
3
2
5.7725 l/s l/s
32.0 mca
2.4830
21 2 105 msnm 2.23 lt/s.
Pulg
P
30.3 mca
lt/s
400 m Ø 3 Pulg
6.4668
Q= 1. 2 4 4 0 l/s
lt/s
4.0000 l/s
i
3.7108
Q= 8.0000 l/s
lt/s
Ø
3
Pulg
4.7105 lt/s Ø 3 Pulg
-0.2555
iii
Reservorio
Ø
H=3.5m Cota: 2155 msnm L: 2km
Pres Pr esio ion n Cota: 2100 21 00 msnm msnm
16.0124
3.10 l/s
12.40 lt/s.
Qe
36.00 lt/s.
Ø 3 Pulg
lt/s
19.9 19.903 035 5 l/s l/s
4 Qe
P 55.76 mca 2098 msnm 3.10 l/s
50.9 50 .9 mc mca a
4
Ø 4
6.4243
Q= 1. 5 5 5 0 l/s
lt/s
ii
P
40.1 mca
2.9793
Qe
19.60 lt/s.
Qe
23.60 lt/s.
Ø 3 Pulg
lt/s
Ø
3
lt/s
P
2.69 2.6975 75 l/s l/s
44.5 mca
4
Ø
4
Pulg
4.7134
1.72 lt/s.
2097 msnm
4.7018
lt/s
iv
Pulg
3
3
2103 msnm 2.67 lt/s.
24
3.2775 l/s Ø 3
Pulg
2.6540 l/s
P 37.24 mca 2096 20 96 ms msnm nm 1.72 lt/s.
lt/s
4.00 lt/s.
8.0000 l/s
0.6326
Cota:
P
33.5 mca
2.0404
3
P
lt/s
600 m
lt/s
28.2 mca
2
5.3270 l/s Ø 3
Pulg
Cot ota a:
Pulg
800 m
INGRESO A RED
Q=
36.00 lt/s.
CURSO
DE
Q=
19.60 lt/s.
AGUA
Y
4.00 lt/s.
ALCANTARILLADO
-
DISEÑADO POR: AL EJA NDRO YURI TICONA PEÑA SCO
ESQUEMA GENERAL METODO DE HARDY CROSS
ℎ =∗∗1/0.54
=0.0004262 ∗ ∗2.63 ∗0.54
FORMULAS UTILIZADAS
= ∗ (1/(0.0004262∗∗2.63) 1/0.54
a ).
DE
SALIDA DE RED
Q=
23.60 lt/s.
ABASTECIMIENTO
210 21 07 msnm
2.67 lt/s.
ZONA "B"
Q=
12.40 lt/s.
B ).
900 m
L=1000m Ø=6 pulg
ZONA "A"
Q=
2106 msnm
4.90 lt/s.
500 m
45.93 mca
Cota:
3 1
-1.2985 -1.2985 l/s
Ø
Presion
Pulg
1100 m 9.2737
4
Pulg
5.0000 l/s
3
2101 msnm 4.90 lt/s.
3 1
0.3015 l/s
500 m
lt/s
3.5450 l/s
⧍ = ((− ⅀ℎ )/(1.852∗⅀(ℎ /))
ℎ = ∗ (/(0.0004262∗∗2.63) 1/0.54)
C ÁL C U L O D E C A U D A L E S D E T RA N S IT O E N L A R E D D E D IS TR IB U C IÓN PO R E L M ET OD O D E H A R D Y C R OS S O T I U C R I C
TRAMO Nudo Inicial
ii
iii
iv
Tuberia
GASTO (Asumido)
Ø
PVC "C"
MAX. HOR.
m
Pulg.
150
m³/s
Nudo Final
-
i
DIAMETRO
Km
l/s
Hf/Q
2 3 4 1
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0026 0.0012 0.0199 0.0040
1 1 -1 1
2.6220 1.2440 19.9035 4.0000
3.6833 0.4630 -38.7185 4.0261
1.4048 0.3722 1.9453 1.0065
-30.5461
4.7288
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
0.0016 0.0033 0.0050 0.0199
-1 -1 -1 1
1.5550 3.2775 5.0000 19.9035
- 0.8748 - 5.5680 - 7.6078 38.7185
0.5626 1.6989 1.5216 1.9453
24.6678
5.7283
17.8680 4.0242 - 1.0758 18.1660
3.0954 1.1352 0.3988 2.2708
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0058 0.0035 0.0027 0.0080
1 1 -1 1
5.7725 3.5450 2.6975 8.0000
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
0.0027 0.0053 0.0080 0.0027
-1 -1 -1 1
2.6540 5.3270 8.0000 2.6975
Nudo Inicial
Tramo
Nudo Final
1 2 3 4 1 2
1-2 2-3 3-4 4-1 1-2 2-3
2 3 4 1 2 3
Diametro
Tuberia
GASTO itera. Anterior
Ø
PVC "C"
MAX. HOR.
LONGITUDES Km
m
Pulg.
150
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.50 0.80
500.00 800.00
3.00 3.00
150.00 150.00
m³/s
0.0051 0.0038 -0.0159 0.0065 -0.0030 -0.0047
1 1 -1 1 -1 -1
38.9824
6.9001
- 2.8252 -15.3986 -21.7992 1.0758
1.0645 2.8907 2.7249 0.3988
-38.9473
7.0789
ITERACION N° 002
5.1326 3.7546 -15.9316 6.5106 -3.0163 -4.7388
3.4879 3.4879 3.4879 3.4879
-2.325
-2.3252 -2.3252 -2.3252 -2.3252
3.488
-3.0505 -3.0505 -3.0505 -3.0505
2.971
2.9708 2.9708 2.9708 2.9708
-3.051
Q
Hf
l/s
m
Hf/Q
1 1 -1 1
6.1099 4.7319 -14.0904 7.4879
17.6446 5.4958 -20.4234 12.8573
2.8879 1.1614 1.4495 1.7171
15.5743
7.2158
-1 -1 -1 1
-3.8802 -5.6027 -7.3252 14.0904
-4.7571 -15.0284 -15.4308 20.4234
1.2260 2.6823 2.1065 1.4495
-14.7930
7.4643
4.4411 0.1048 -9.4456 7.4661
1.6316 0.2120 1.0834 1.5085
1 1 -1 1
2.7220 0.4945 -8.7188 4.9495
2.5664
4.4354
1 -1 -1 1
0.3168 0.0551 -3.3996 -2.3562 -9.2284 -5.0292 8.7188 9.4456
0.1741 1.4428 1.8350 1.0834
-3.1273
4.5352
ITERACION N° 004 Hf
l/s
Q
m
1-2 2-3 3-4 4-1
-
i
Hf
1 2 3 4
TRAMO CIRCUITO
ITERACION N° 001
ITERACION N° 003
LONGITUDES Tramo
Hf/Q
2.4894 0.9537 1.6093 1.5242
0.6421
6.5766
-2.9839 -11.0212
0.9893 2.3257
-0.0527 -0.0527 -0.0527 -0.0527 0.0473 0.0473
0.0473
-1.1654 -1.1654 -1.1654 -1.1654 1.0701 1.0701 1.0701 1.0701 -0.3124 -0.3124 -0.3124 -0.3124 0.3723 0.3723 0.3723 0.3723
1.0701
-1.1654
0.3723
-0.3124
Q
Hf
l/s
m
Hf/Q
1 1 -1 1 -1 -1
Q
Hf
l/s
m 5.0799 3.7019 -16.0316 6.4579 -2.9690 -4.6915
Hf/Q
12.5350 3.4881 -25.9378 9.7752
2.4676 0.9423 1.6179 1.5137
1 1 -1 1
4.9445 3.5665 -16.3259 6.3225
11.9235 3.2556 -26.8263 9.3991 -2.2481
6.4541
-1 -1 -1 1
-2.8101 -4.5326 -6.2551 16.3259
-2.6172 -10.1496 -11.5181 26.8263
0.9314 2.2392 1.8414 1.6432
2.5414
6.6552
2.4115 0.9128 1.6432 1.4866
1.4706 0.0905 1.1554 1.4270
1 1 -1 1
2.4096 0.1821 -9.4035 4.6371
3.5435 0.0165 -10.8652 6.6169 -0.6883
4.1435
1 -1 -1 1
0.6891 -1.9839 -4.6569 9.4035
0.2326 -2.4723 -8.0033 10.8652
0.3375 1.2462 1.7186 1.1554
0.6222
4.4577
-0.1396
6.5414
-2.8978 -10.8183
0.9760 2.3059
-0.0124 -0.0124
-0.0124
0.1881 0.1881 0.1881 0.1881
-0.2062
-0.2062 -0.2062 -0.2062 -0.2062 0.0897 0.0897 0.0897 0.0897
0.1881
-0.0754
-0.0754 -0.0754 -0.0754 -0.0754
0.0897
1 1 -1 1
5.1326 3.7546 -15.9316 6.5106
-1 -1 -1 1
-3.0163 -4.7388 -6.4613 15.9316
1 1 -1 1
2.4993 0.2718 -9.2385 4.7268
1 -1 -1 1
0.6137 -2.0593 -4.7323 9.2385
ITERACION N° 006
Q
0.0115 0.0115 0.0115 0.0115
Q
Q
l/s
ITERACION N° 005
Q
m
12.7770 3.5807 -25.6390 9.9235
Q
1 1 -1 1 -1 -1
Q
Hf
l/s
m 5.0914 3.7134 -16.0077 6.4694 -2.9814 -4.7039
Hf/Q
Q
Q
l/s
12.5877 3.5082 -25.8662 9.8075
2.4723 0.9448 1.6159 1.5160
0.0372
6.5490
-2.9203 -10.8714
0.9795 2.3111
-0.0031 -0.0031 -0.0031 -0.0031 0.0028 0.0028
0.0028
1 1 -1 1
5.0883 3.7103 -16.0135 6.4663
-1 -1
-2.9787 -4.7012
CURSO
B ).
DE
ABASTECIMIENTO
AGUA
Y
ALCANTARILLADO
-
ℎ =∗∗1/0.54
=0.0004262 ∗ ∗2.63 ∗0.54
FORMULAS UTILIZADAS
= ∗ (1/(0.0004262∗∗2.63) 1/0.54
a ).
DE
DISEÑADO POR: AL EJA NDRO YURI TICONA PEÑA SCO
ESQUEMA GENERAL METODO DE HARDY CROSS
⧍ = ((− ⅀ℎ )/(1.852∗⅀(ℎ /))
ℎ = ∗ (/(0.0004262∗∗2.63) 1/0.54)
C ÁL C U L O D E C A U D A L E S D E T RA N S IT O E N L A R E D D E D IS TR IB U C IÓN PO R E L M ET OD O D E H A R D Y C R OS S O T I U C R I C
TRAMO Nudo Inicial
ii
iii
iv
Tuberia
GASTO (Asumido)
Ø
PVC "C"
MAX. HOR.
m
Pulg.
150
m³/s
Nudo Final
-
i
DIAMETRO
Km
ii
iii
iv
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0026 0.0012 0.0199 0.0040
1 1 -1 1
2.6220 1.2440 19.9035 4.0000
3.6833 0.4630 -38.7185 4.0261
1.4048 0.3722 1.9453 1.0065
-30.5461
4.7288
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
0.0016 0.0033 0.0050 0.0199
-1 -1 -1 1
1.5550 3.2775 5.0000 19.9035
- 0.8748 - 5.5680 - 7.6078 38.7185
0.5626 1.6989 1.5216 1.9453
24.6678
5.7283
17.8680 4.0242 - 1.0758 18.1660
3.0954 1.1352 0.3988 2.2708
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0058 0.0035 0.0027 0.0080
1 1 -1 1
5.7725 3.5450 2.6975 8.0000
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
0.0027 0.0053 0.0080 0.0027
-1 -1 -1 1
2.6540 5.3270 8.0000 2.6975
Tramo
Nudo Final
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
Pulg.
150
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
Nudo Inicial
Tramo
Nudo Final
ii
iii
0.0051 0.0038 -0.0159 0.0065 -0.0030 -0.0047 -0.0065 0.0159
1.0645 2.8907 2.7249 0.3988
-38.9473
7.0789
5.1326 3.7546 -15.9316 6.5106
3.488
-3.0505 -3.0505 -3.0505 -3.0505
2.971
2.9708 2.9708 2.9708 2.9708
-3.051
l/s
m
Hf/Q
1 1 -1 1
6.1099 4.7319 -14.0904 7.4879
17.6446 5.4958 -20.4234 12.8573 15.5743
7.2158
-1 -1 -1 1
-3.8802 -5.6027 -7.3252 14.0904
-4.7571 -15.0284 -15.4308 20.4234
1.2260 2.6823 2.1065 1.4495
-14.7930
7.4643
4.4411 0.1048 -9.4456 7.4661
1.6316 0.2120 1.0834 1.5085
12.7770 3.5807 -25.6390 9.9235
2.4894 0.9537 1.6093 1.5242
2.7220 0.4945 -8.7188 4.9495
2.5664
4.4354
1 -1 -1 1
0.3168 0.0551 -3.3996 -2.3562 -9.2284 -5.0292 8.7188 9.4456
0.1741 1.4428 1.8350 1.0834
-3.1273
4.5352
ITERACION N° 003
0.6421
6.5766
-2.9839 -11.0212 -12.2310 25.6390
0.9893 2.3257 1.8930 1.6093
-1 -1 -1 1
-3.0163 -4.7388 -6.4613 15.9316
-0.5972
6.8173
0.0025 0.0003 -0.0092 0.0047
1 1 -1 1
2.4993 0.2718 -9.2385 4.7268
3.7917 0.0346 -10.5146 6.8559
1.5171 0.1273 -1.1381 1.4504
0.1675
1.9567
0.0006 -0.0021 -0.0047 0.0092
1 -1 -1 1
0.6137 -2.0593 -4.7323 9.2385
0.1877 -2.6490 -8.2448 10.5146
0.3058 - 1.2864 - 1.7422 1.1381
-0.1915
-1.5847
ABASTECIMIENTO
DE
0.0473
0.0473 0.0473 0.0473 0.0473
-0.0527
-0.0462 -0.0462 -0.0462 -0.0462
-0.0652
-0.0652 -0.0652 -0.0652 -0.0652
-0.0462
AGUA
-1.1654 -1.1654 -1.1654 -1.1654 1.0701 1.0701 1.0701 1.0701 -0.3124 -0.3124 -0.3124 -0.3124 0.3723 0.3723 0.3723 0.3723
1.0701
-1.1654
0.3723
-0.3124
Q
Hf
l/s
m
Hf/Q
Y
Q
Hf
l/s
m
1 1 -1 1
Hf/Q
12.5350 3.4881 -25.9378 9.7752
2.4676 0.9423 1.6179 1.5137
-0.1396
6.5414
-2.9690 -4.6915 -6.4140 16.0316
-2.8978 -10.8183 -12.0657 25.9378
0.9760 2.3059 1.8812 1.6179
0.1559
6.7811
1 1 -1 1
2.4530 0.2255 -9.2195 4.6805
3.6629 0.0245 -10.4746 6.7322
1.4932 0.1086 1.1361 1.4383
-0.0550
4.1763
1 -1 -1 1
0.5485 -2.1245 -4.7975 9.2195
0.1524 -2.8066 -8.4565 10.4746
0.2779 1.3210 1.7627 1.1361
-0.6361
4.4978
5.0799 3.7019 -16.0316 6.4579
1 1 -1 1
4.9445 3.5665 -16.3259 6.3225
11.9235 3.2556 -26.8263 9.3991 -2.2481
6.4541
-1 -1 -1 1
-2.8101 -4.5326 -6.2551 16.3259
-2.6172 -10.1496 -11.5181 26.8263
0.9314 2.2392 1.8414 1.6432
2.5414
6.6552
2.4115 0.9128 1.6432 1.4866
1.4706 0.0905 1.1554 1.4270
1 1 -1 1
2.4096 0.1821 -9.4035 4.6371
3.5435 0.0165 -10.8652 6.6169 -0.6883
4.1435
1 -1 -1 1
0.6891 -1.9839 -4.6569 9.4035
0.2326 -2.4723 -8.0033 10.8652
0.3375 1.2462 1.7186 1.1554
0.6222
4.4577
-1 -1 -1 1
-0.0124 -0.0124 -0.0124 -0.0124 0.0071 0.0071 0.0071 0.0071 0.0764 0.0764 0.0764 0.0764
-0.0124
0.0115
0.0764
0.0071
0.1881 0.1881 0.1881 0.1881
-0.2062
-0.2062 -0.2062 -0.2062 -0.2062 0.0897 0.0897 0.0897 0.0897
0.1881
-0.0754
-0.0754 -0.0754 -0.0754 -0.0754
0.0897
1 1 -1 1
5.1326 3.7546 -15.9316 6.5106
-1 -1 -1 1
-3.0163 -4.7388 -6.4613 15.9316
1 1 -1 1
2.4993 0.2718 -9.2385 4.7268
1 -1 -1 1
0.6137 -2.0593 -4.7323 9.2385
ITERACION N° 006
Q
0.0115 0.0115 0.0115 0.0115
Q
Q
l/s
ITERACION N° 005
Q
-0.0527 -0.0527 -0.0527 -0.0527
Q
2.8879 1.1614 1.4495 1.7171
1 1 -1 1
m
Diametro
Tuberia
GASTO itera. Anterior
Ø
PVC "C"
MAX. HOR.
LONGITUDES
Q
Hf
l/s
m
1 1 -1 1
5.0914 3.7134 -16.0077 6.4694
-1 -1 -1 1 1 1 -1 1 1 -1 -1 1
-2.9814 -4.7039 -6.4264 16.0077
Hf/Q
Q
Q
l/s
12.5877 3.5082 -25.8662 9.8075
2.4723 0.9448 1.6159 1.5160
0.0372
6.5490
-2.9203 -10.8714 -12.1090 25.8662
0.9795 2.3111 1.8843 1.6159
-0.0346
6.7908
2.4602 0.2326 -9.2887 4.6877
3.6825 0.0259 -10.6207 6.7512
1.4969 0.1115 1.1434 1.4402
-0.1611
4.1920
0.6249 -2.0481 -4.7211 9.2887
0.1940 -2.6226 -8.2089 10.6207
0.3105 1.2805 1.7388 1.1434
-0.0168
4.4732
-0.0031 -0.0031 -0.0031 -0.0031
0.0028
0.0028 0.0028 0.0028 0.0028
-0.0031
0.0207 0.0207 0.0207 0.0207
0.0020
0.0020 0.0020 0.0020 0.0020
0.0207
1 1 -1 1
5.0883 3.7103 -16.0135 6.4663
-1 -1 -1 1
-2.9787 -4.7012 -6.4237 16.0135
1 1 -1 1
2.4809 0.2534 -9.2700 4.7084
1 -1 -1 1
0.6269 -2.0461 -4.7191 9.2700
ALCANTARILLADO
Km
m
Pulg.
150
m³/s
ITERACION N° 007 Hf
l/s
Hf/Q
-
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0051 0.0037 -0.0160 0.0065
1 1 -1 1
5.0883 3.7103 -16.0135 6.4663
12.5736 3.5029 -25.8836 9.7989 -0.0082
6.5469
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
-0.0030 -0.0047 -0.0064 0.0160
-1 -1 -1 1
-2.9787 -4.7012 -6.4237 16.0135
-2.9153 -10.8596 -12.0994 25.8836
0.9787 2.3100 1.8836 1.6164
0.0092
6.7887
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0025 0.0003 -0.0093 0.0047
1 1 -1 1
2.4809 0.2534 -9.2700 4.7084
3.7402 0.0304 -10.5811 6.8066
1.5076 0.1199 -1.1414 1.4456
-0.0039
1.9318
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
0.0006 -0.0020 -0.0047 0.0093
1 -1 -1 1
0.6269 -2.0461 -4.7191 9.2700
0.1952 -2.6178 -8.2024 10.5811
0.3114 - 1.2794 - 1.7381 1.1414
-0.0439
-1.5647
Hf
Hf/Q
Nudo Final
Diametro
Tuberia
GASTO itera. Anterior
Ø
PVC "C"
MAX. HOR.
LONGITUDES Km
m
Pulg.
150
m³/s
l/s
ITERACION N° 008
Q
m
2 3 4 1
Tramo
-2.3252 -2.3252 -2.3252 -2.3252
Hf/Q
1-2 2-3 3-4 4-1
Nudo Inicial
-2.325
Hf
ITERACION N° 004 Hf
l/s
1 1 -1 1
6.9001
1 2 3 4
-
i
DE
m³/s
38.9824
- 2.8252 -15.3986 -21.7992 1.0758
3.4879 3.4879 3.4879 3.4879
Q
DISEÑADO POR: A LEJA NDRO YURI TICONA PEÑASCO
TRAMO CIRCUITO
MAX. HOR.
1-2 2-3 3-4 4-1
-
iv
GASTO itera. Anterior
PVC "C"
m
TRAMO
iii
Tuberia
Ø Km
CURSO
ii
Diametro LONGITUDES
1 2 3 4
B ).
i
1 2 3 4
Nudo Inicial
ITERACION N° 002
Q
m
2 3 4 1
ESQUEMA GENERAL METODO DE HARDY CROSS CIRCUITO
l/s
Hf/Q
1-2 2-3 3-4 4-1
-
i
Hf
1 2 3 4
TRAMO CIRCUITO
ITERACION N° 001
LONGITUDES Tramo
2.4711 0.9441 1.6164 1.5154
0.0007 0.0007 0.0007 0.0007
-0.0007
-0.0007 -0.0007 -0.0007 -0.0007
0.0007
0.0011 0.0011 0.0011 0.0011
-0.0151
-0.0151 -0.0151 -0.0151 -0.0151
0.0011
Q
Hf
l/s
m
Hf/Q
1 1 -1 1
5.0890 3.7110 -16.0121 6.4670
12.5767 3.5041 -25.8794 9.8008
2.4714 0.9442 1.6162 1.5155
0.0022
6.5473
-1 -1 -1 1
-2.9794 -4.7019 -6.4244 16.0121
-2.9167 -10.8628 -12.1020 25.8794
0.9789 2.3103 1.8838 1.6162
-0.0020
6.7892
1 1 -1 1
2.4820 0.2545 -9.2538 4.7095
3.7433 0.0306 -10.5469 6.8095
1.5082 0.1204 1.1397 1.4459
0.0366
4.2142
1 -1 -1 1
0.6117 -2.0613 -4.7343 9.2538
0.1866 -2.6538 -8.2512 10.5469
0.3050 1.2875 1.7429 1.1397
-0.1717
4.4750
ITERACION N° 010
1-2 2-3 3-4 4-1
2 3 4 1
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0051 0.0037 -0.0160 0.0065
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
12.5761 3.5038 -25.8802 9.8004
2.4713 0.9442 1.6163 1.5155
0.0001
6.5472
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
-0.0030 -0.0047 -0.0064 0.0160
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
-2.9164 -10.8623 -12.1016 25.8802
0.9789 2.3102 1.8837 1.6163
-0.0001
6.7891
1.5087 0.1208 -1.1417 1.4462
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0025 0.0003 -0.0093 0.0047
1 1 -1 1
2.4829 0.2554 -9.2724 4.7104
3.7458 0.0308 -10.5862 6.8120 0.0025
1.9339
1
12
2
0 60
600 00
3 00
150 00
0 0006
1
0 6313
0 1977
0 3132
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0007 -0.0007 -0.0007 -0.0007 0 0041
0.0000
0.0000
-0.0041
-0.0002 -0.0002 -0.0002 -0.0002 0.0002 0.0002 0.0002 0.0002 -0.0047 -0.0047 -0.0047 -0.0047 0.0207 0.0207 0.0207 0.0207
0.0002
-0.0002
0.0207
-0.0047
Q
Hf
l/s
m
Hf/Q
Q
Hf
l/s
m
Hf/Q
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
12.5760 3.5038 -25.8802 9.8004
2.4713 0.9442 1.6163 1.5155
1 1 -1 1
5.0888 3.7108 -16.0125 6.4668
12.5759 3.5037 -25.8804 9.8003
2.4713 0.9442 1.6163 1.5155
-0.0005
6.5472
-1 -1 -1 1
-2.9792 -4.7017 -6.4242 16.0125
-2.9164 -10.8621 -12.1014 25.8804
0.9789 2.3102 1.8837 1.6163
0.0005
6.7891
1 1 -1 1
2.4773 0.2498 -9.2792 4.7048
3.7302 0.0296 -10.6005 6.7970
1.5058 0.1185 1.1424 1.4447
-0.0438
4.2113
1 -1 -1 1
0.6324 -2.0406 -4.7136 9.2792
0.1984 -2.6047 -8.1845 10.6005
0.3137 1.2764 1.7364 1.1424
0.0098
4.4690
0.0000
6.5472
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
-2.9164 -10.8622 -12.1015 25.8802
0.9789 2.3102 1.8837 1.6163
0.0000
6.7891
3.7439 0.0307 -10.5790 6.8101
1.5083 0.1205 1.1413 1.4460
0.0057
4.2161
0 1954
0 3115
1 1 -1 1
2.4822 0.2547 -9.2690 4.7097
1
0.6272
0.0000 0.0000 0.0000 0.0000 -0.0007 -0.0007 -0.0007 -0.0007 0 0054
0.0000
0.0000
0.0054
0.0000 0.0000 0.0000 0.0000
0.0000
0.0000 0.0000 0.0000 0.0000 0.0056 0.0056 0.0056 0.0056
0.0000
-0.0012
-0.0012 -0.0012 -0.0012 -0.0012
0.0056
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
1 1 -1 1
2.4829 0.2554 -9.2724 4.7104
1 -1 -1 1
0.6313 -2.0417 -4.7147 9.2724
ITERACION N° 012
Q
0.0000 0.0000 0.0000 0.0000
Q
Q
l/s
ITERACION N° 011
Q
m
1 2 3 4
ITERACION N° 009
Q
Q
Hf
l/s
m
Hf/Q
l/s
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
12.5760 3.5038 -25.8802 9.8004
2.4713 0.9442 1.6163 1.5155
0.0000
6.5472
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
-2.9164 -10.8622 -12.1015 25.8802
0.9789 2.3102 1.8837 1.6163
0.0000
6.7891
3.7418 0.0305 -10.5918 6.8082
1.5079 0.1202 1.1420 1.4458
-0.0113
4.2158
0.1985
0.3138
1 1 -1 1
2.4815 0.2540 -9.2750 4.7090
1
0.6325
Q
Q
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0015 0.0015 0.0015 0.0015 -0.0002
0.0000
0.0000
-0.0002
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
1 1 -1 1
2.4829 0.2554 -9.2734 4.7104
1
0.6323
CURSO
B ).
TRAMO CIRCUITO
Nudo Inicial
Tramo
Nudo Final
-
i
ii
iii
iv
ii
iii
iv
Pulg.
150
b).
m³/s
l/s
Hf/Q
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0051 0.0037 -0.0160 0.0065
1 1 -1 1
5.0883 3.7103 -16.0135 6.4663
12.5736 3.5029 -25.8836 9.7989 -0.0082
6.5469
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
-0.0030 -0.0047 -0.0064 0.0160
-1 -1 -1 1
-2.9787 -4.7012 -6.4237 16.0135
-2.9153 -10.8596 -12.0994 25.8836
0.9787 2.3100 1.8836 1.6164
0.0092
6.7887
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0025 0.0003 -0.0093 0.0047
1 1 -1 1
2.4809 0.2534 -9.2700 4.7084
3.7402 0.0304 -10.5811 6.8066
1.5076 0.1199 -1.1414 1.4456
-0.0039
1.9318
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
0.0006 -0.0020 -0.0047 0.0093
1 -1 -1 1
0.6269 -2.0461 -4.7191 9.2700
0.1952 -2.6178 -8.2024 10.5811
0.3114 - 1.2794 - 1.7381 1.1414
-0.0439
-1.5647
Hf
Hf/Q
Tramo
Nudo Final
Diametro
Tuberia
GASTO itera. Anterior
Ø
PVC "C"
MAX. HOR.
LONGITUDES Km
m
Pulg.
150
m³/s
l/s
2.4711 0.9441 1.6164 1.5154
2 3 4 1
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0051 0.0037 -0.0160 0.0065
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
12.5761 3.5038 -25.8802 9.8004 0.0001
6.5472
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
-0.0030 -0.0047 -0.0064 0.0160
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
-2.9164 -10.8623 -12.1016 25.8802
0.9789 2.3102 1.8837 1.6163
-0.0001
6.7891
2.4713 0.9442 1.6163 1.5155
1.5087 0.1208 -1.1417 1.4462
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0025 0.0003 -0.0093 0.0047
1 1 -1 1
2.4829 0.2554 -9.2724 4.7104
3.7458 0.0308 -10.5862 6.8120 0.0025
1.9339
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
0.0006 -0.0020 -0.0047 0.0093
1 -1 -1 1
0.6313 -2.0417 -4.7147 9.2724
0.1977 -2.6074 -8.1883 10.5862
0.3132 - 1.2771 - 1.7368 1.1417
-0.0119
-1.5589
DE
0.0007 0.0007 0.0007 0.0007
-0.0007
-0.0007 -0.0007 -0.0007 -0.0007
0.0007
0.0011 0.0011 0.0011 0.0011
-0.0151
-0.0151 -0.0151 -0.0151 -0.0151
0.0011
Q
Hf
l/s
m 5.0890 3.7110 -16.0121 6.4670
12.5767 3.5041 -25.8794 9.8008
2.4714 0.9442 1.6162 1.5155
0.0022
6.5473
-1 -1 -1 1
-2.9794 -4.7019 -6.4244 16.0121
-2.9167 -10.8628 -12.1020 25.8794
0.9789 2.3103 1.8838 1.6162
-0.0020
6.7892
1 1 -1 1
2.4820 0.2545 -9.2538 4.7095
3.7433 0.0306 -10.5469 6.8095
1.5082 0.1204 1.1397 1.4459
0.0366
4.2142
1 -1 -1 1
0.6117 -2.0613 -4.7343 9.2538
0.1866 -2.6538 -8.2512 10.5469
0.3050 1.2875 1.7429 1.1397
-0.1717
4.4750
ABASTECIMIENTO
DE
0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
-0.0007 -0.0007 -0.0007 -0.0007
-0.0041
-0.0041 -0.0041 -0.0041 -0.0041
-0.0007
AGUA
Hf
l/s
m
-0.0002 -0.0002 -0.0002 -0.0002
0.0002
0.0002 0.0002 0.0002 0.0002
-0.0002
-0.0047 -0.0047 -0.0047 -0.0047
0.0207
0.0207 0.0207 0.0207 0.0207
-0.0047
Nudo Final
Diametro
Tuberia
GASTO itera. Anterior
Ø
PVC "C"
MAX. HOR.
LONGITUDES
Y
Q
Hf
l/s
m
Hf/Q
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
12.5760 3.5038 -25.8802 9.8004
2.4713 0.9442 1.6163 1.5155
0.0000
6.5472
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
-2.9164 -10.8622 -12.1015 25.8802
0.9789 2.3102 1.8837 1.6163
0.0000
6.7891
1 1 -1 1
2.4822 0.2547 -9.2690 4.7097
3.7439 0.0307 -10.5790 6.8101
1.5083 0.1205 1.1413 1.4460
0.0057
4.2161
1 -1 -1 1
0.6272 -2.0458 -4.7188 9.2690
0.1954 -2.6172 -8.2015 10.5790
0.3115 1.2793 1.7380 1.1413
-0.0444
4.4701
0.0000 0.0000 0.0000 0.0000
0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
-0.0007 -0.0007 -0.0007 -0.0007
0.0054
0.0054 0.0054 0.0054 0.0054
-0.0007
Q
Q
l/s
1 1 -1 1
5.0888 3.7108 -16.0125 6.4668
12.5759 3.5037 -25.8804 9.8003
2.4713 0.9442 1.6163 1.5155
-0.0005
6.5472
-1 -1 -1 1
-2.9792 -4.7017 -6.4242 16.0125
-2.9164 -10.8621 -12.1014 25.8804
0.9789 2.3102 1.8837 1.6163
0.0005
6.7891
1 1 -1 1
2.4773 0.2498 -9.2792 4.7048
3.7302 0.0296 -10.6005 6.7970
1.5058 0.1185 1.1424 1.4447
-0.0438
4.2113
1 -1 -1 1
0.6324 -2.0406 -4.7136 9.2792
0.1984 -2.6047 -8.1845 10.6005
0.3137 1.2764 1.7364 1.1424
0.0098
4.4690
0.0000 0.0000 0.0000 0.0000
0.0000
0.0000 0.0000 0.0000 0.0000 0.0056 0.0056 0.0056 0.0056
0.0000
-0.0012
-0.0012 -0.0012 -0.0012 -0.0012
0.0056
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
1 1 -1 1
2.4829 0.2554 -9.2724 4.7104
1 -1 -1 1
0.6313 -2.0417 -4.7147 9.2724
ITERACION N° 012 Q
Hf
l/s
m
Q
Hf/Q
l/s
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
12.5760 3.5038 -25.8802 9.8004
2.4713 0.9442 1.6163 1.5155
0.0000
6.5472
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
-2.9164 -10.8622 -12.1015 25.8802
0.9789 2.3102 1.8837 1.6163
0.0000
6.7891
3.7418 0.0305 -10.5918 6.8082
1.5079 0.1202 1.1420 1.4458
-0.0113
4.2158
0.1985 -2.6045 -8.1843 10.5918
0.3138 1.2764 1.7364 1.1420
0.0015
4.4685
1 1 -1 1
2.4815 0.2540 -9.2750 4.7090
1 -1 -1 1
0.6325 -2.0405 -4.7135 9.2750
Q
Q
0.0000 0.0000 0.0000 0.0000
0.0000
0.0000 0.0000 0.0000 0.0000 0.0015 0.0015 0.0015 0.0015
0.0000
-0.0002
-0.0002 -0.0002 -0.0002 -0.0002
0.0015
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
1 1 -1 1
2.4829 0.2554 -9.2734 4.7104
1 -1 -1 1
0.6323 -2.0407 -4.7137 9.2734
ALCANTARILLADO
Km
m
Pulg.
150
m³/s
ITERACION N° 013 Hf
l/s
Hf/Q
-
ITERACION N° 014
Q
m
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0051 0.0037 -0.0160 0.0065
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
12.5760 3.5038 -25.8802 9.8004 0.0000
6.5472
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
-0.0030 -0.0047 -0.0064 0.0160
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
-2.9164 -10.8622 -12.1015 25.8802
0.9789 2.3102 1.8837 1.6163
0.0000
6.7891
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0025 0.0003 -0.0093 0.0047
1 1 -1 1
2.4829 0.2554 -9.2734 4.7104
3.7459 0.0308 -10.5884 6.8120
1.5087 0.1208 - 1.1418 1.4462
0.0004
1.9338
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
0.0006 -0.0020 -0.0047 0.0093
1 -1 -1 1
0.6323 -2.0407 -4.7137 9.2734
0.1984 -2.6049 -8.1849 10.5884
0.3137 -1.2765 -1.7364 1.1418
-0.0031
-1.5574
TRAMO
2.4713 0.9442 1.6163 1.5155
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0001 -0.0001 -0.0001 -0.0001 -0.0011 -0.0011 -0.0011 -0.0011
0.0000
0.0000
-0.0011
-0.0001
Q
Hf
l/s
m
Diametro
Tuberia
GASTO de DISEÑO
Ø
PVC "C"
MAX. HOR.
Hf/Q
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
12.5760 3.5038 -25.8802 9.8004
2.4713 0.9442 1.6163 1.5155
0.0000
6.5472
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
-2.9164 -10.8622 -12.1015 25.8802
0.9789 2.3102 1.8837 1.6163
0.0000
6.7891
1 1 -1 1
2.4828 0.2553 -9.2725 4.7103
3.7456 0.0308 -10.5864 6.8117
1.5086 0.1207 1.1417 1.4461
0.0018
4.2172
1 -1 -1 1
0.6313 -2.0417 -4.7147 9.2725
0.1977 -2.6074 -8.1883 10.5864
0.3132 1.2771 1.7368 1.1417
-0.0116
4.4688
Perdida de carga
Perdida Menrs
Perdida Totales
Hf
Hfm
Hf + hfm
Cota Inicial
Cota Final
m
msnm
msnm
Cotas de Terreno
ITERACION N° 015 Q
Hf
l/s
m
Q
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0002 -0.0002 -0.0002 -0.0002 0.0014 0.0014 0.0014 0.0014
0.0000
0.0000
0.0014
-0.0002
Perdidas de Carga
12.5760 3.5038 -25.8802 9.8004
2.4713 0.9442 1.6163 1.5155
0.0000
6.5472
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
-2.9164 -10.8622 -12.1015 25.8802
0.9789 2.3102 1.8837 1.6163
0.0000
6.7891
1 1 -1 1
2.4826 0.2551 -9.2741 4.7101
3.7449 0.0308 -10.5898 6.8111
1.5085 0.1206 1.1419 1.4461
-0.0030
4.2171
1 -1 -1 1
0.6327 -2.0403 -4.7133 9.2741
0.1986 -2.6041 -8.1838 10.5898
0.3138 1.2763 1.7363 1.1419
0.0005
4.4683
Cotas Piezometricas
Tramo Nudo Final
-
Km
m
Pulg.
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
150
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
m³/s
0.0051 0.0037 -0.0160 0.0065
l/s
m
5.0888 12.5760 3.7108 3.5038 -16.0124 -25.8802 6.4668 9.8004 0.0000
3.5229
3.5229
-1 -1 -1 1
-2.9793 - 2.9164 -4.7018 -10.8622 -6.4243 -12.1015 16.0124 25.8802
0.7339 1.1743 0.7339 1.1743
-2.1825 -9.6879 -11.3676 27.0545
0.00000 -0.0030 -0.0047 -0.0064 0.0160
m
1 1 -1 1
1.1743 0.5872 1.1743 0.5872
13.7504 4.0909 -24.7059 10.3875
C = f-i m
Pi
Pf
m
m
Cota Piez. Inicial msnm
Cota Piez. Final msnm
2098.00 2100.00 2100.00 2098.00 2098.00 2100.00 2100.00 2098.00
2.000 -2.0000 2.0000 -2.0000
50.8996 35.1492 33.0583 55.7642
35.1492 33.0583 55.7642 47.3766
2148.90 2135.15 2104.09 2046.33
2135.15 2104.09 2046.33 2000.95
2098.00 2096.00 2097.00 2100.00
-2.000 1.0000 3.0000 -2.0000
33.0583 37.2407 45.9287 54.2963
37.2407 45.9287 54.2963 29.2417
2104.09 2068.85 2021.92 1964.63
2068.85 2021.92 1964.63 1937.38
2096.00 2097.00 2100.00 2098.00
Q
Q
l/s
5.0888 3.7108 -16.0124 6.4668
P =−(+⧍)
Diferencia de cotas
Hf/Q
1 1 -1 1
LONGITUDES Nudo Inicial
Hf/Q
ITERACION N° 011
Q
0.0000 0.0000 0.0000 0.0000
ITERACION N° 009 Q
Q
DISEÑADO POR: A LEJA NDRO YURI TICONA PEÑASCO
CIRCUITO
ii
Hf/Q
1 1 -1 1
C ÁL C U L O Y DIS T RIB U C IÓN D E PR E SIO N ES E N L A R E D DE D IS T RIB U C IÓN P OR E L M E TO D O D E H A R DY C R OS S
i
-
ITERACION N° 008
Q
m
1-2 2-3 3-4 4-1
Tramo
ALCANTARILLADO
ITERACION N° 010
1 2 3 4
Nudo Inicial
Y
m
800.00 400.00 800.00 400.00
Nudo Inicial
AGUA
ITERACION N° 007 Hf
0.80 0.40 0.80 0.40
-
iv
MAX. HOR.
m
TRAMO
iii
GASTO itera. Anterior
PVC "C"
Km
CURSO
ii
Tuberia
Ø
2 3 4 1
B ).
i
Diametro
1-2 2-3 3-4 4-1
ESQUEMA GENERAL METODO DE HARDY CROSS CIRCUITO
DE
1 2 3 4
-
i
ABASTECIMIENTO
LONGITUDES
TRAMO CIRCUITO
DE
DISEÑADO POR: A LEJA NDRO YURI TICONA PEÑASCO
ESQUEMA GENERAL METODO DE HARDY CROSS
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0004 0.0004 0.0004 -0.0001 -0.0001 -0.0001 -0.0001
0.0000
0.0000
-0.0001
0.0004
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
1 1 -1 1
2.4830 0.2555 -9.2737 4.7105
1 -1 -1 1
0.6326 -2.0404 -4.7134 9.2737
CURSO
B ).
DE
TRAMO CIRCUITO
Nudo Inicial
Tramo
ii
iii
iv
b).
Diametro
Tuberia
GASTO itera. Anterior
Ø
PVC "C"
MAX. HOR.
DE
AGUA
Y
ALCANTARILLADO
ITERACION N° 013
LONGITUDES
Nudo Final
-
i
ABASTECIMIENTO
-
DISEÑADO POR: A LEJA NDRO YURI TICONA PEÑASCO
ESQUEMA GENERAL METODO DE HARDY CROSS
Km
m
Pulg.
150
m³/s
Hf l/s
Hf/Q
ITERACION N° 014
Q
m
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0051 0.0037 -0.0160 0.0065
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
12.5760 3.5038 -25.8802 9.8004
2.4713 0.9442 1.6163 1.5155
0.0000
6.5472
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
-0.0030 -0.0047 -0.0064 0.0160
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
-2.9164 -10.8622 -12.1015 25.8802
0.9789 2.3102 1.8837 1.6163
0.0000
6.7891
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
0.0025 0.0003 -0.0093 0.0047
1 1 -1 1
2.4829 0.2554 -9.2734 4.7104
3.7459 0.0308 -10.5884 6.8120
1.5087 0.1208 - 1.1418 1.4462
0.0004
1.9338
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
0.0006 -0.0020 -0.0047 0.0093
1 -1 -1 1
0.6323 -2.0407 -4.7137 9.2734
0.1984 -2.6049 -8.1849 10.5884
0.3137 -1.2765 -1.7364 1.1418
-0.0031
-1.5574
0.0000 0.0000 0.0000 0.0000
0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
-0.0001 -0.0001 -0.0001 -0.0001
-0.0011
-0.0011 -0.0011 -0.0011 -0.0011
-0.0001
Q
Hf
l/s
m
Hf/Q
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
12.5760 3.5038 -25.8802 9.8004
2.4713 0.9442 1.6163 1.5155
0.0000
6.5472
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
-2.9164 -10.8622 -12.1015 25.8802
0.9789 2.3102 1.8837 1.6163
0.0000
6.7891
1 1 -1 1
2.4828 0.2553 -9.2725 4.7103
3.7456 0.0308 -10.5864 6.8117
1.5086 0.1207 1.1417 1.4461
0.0018
4.2172
1 -1 -1 1
0.6313 -2.0417 -4.7147 9.2725
0.1977 -2.6074 -8.1883 10.5864
0.3132 1.2771 1.7368 1.1417
-0.0116
4.4688
Diametro
Tuberia
GASTO de DISEÑO
Ø
PVC "C"
MAX. HOR.
Perdida de carga
Perdida Menrs
Perdida Totales
Diferencia de cotas
Hf
Hfm
Hf + hfm
Cota Inicial
Cota Final
m
msnm
msnm
Cotas de Terreno
Hf
l/s
m
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0002 -0.0002 -0.0002 -0.0002 0.0014 0.0014 0.0014 0.0014
0.0000
0.0000
0.0014
-0.0002
Hf/Q
Q
Q
l/s
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
12.5760 3.5038 -25.8802 9.8004
2.4713 0.9442 1.6163 1.5155
0.0000
6.5472
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
-2.9164 -10.8622 -12.1015 25.8802
0.9789 2.3102 1.8837 1.6163
0.0000
6.7891
1 1 -1 1
2.4826 0.2551 -9.2741 4.7101
3.7449 0.0308 -10.5898 6.8111
1.5085 0.1206 1.1419 1.4461
-0.0030
4.2171
1 -1 -1 1
0.6327 -2.0403 -4.7133 9.2741
0.1986 -2.6041 -8.1838 10.5898
0.3138 1.2763 1.7363 1.1419
0.0005
4.4683
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0004 0.0004 0.0004 0.0004 -0.0001 -0.0001 -0.0001 -0.0001
0.0000
0.0000
-0.0001
0.0004
1 1 -1 1
5.0888 3.7108 -16.0124 6.4668
-1 -1 -1 1
-2.9793 -4.7018 -6.4243 16.0124
1 1 -1 1
2.4830 0.2555 -9.2737 4.7105
1 -1 -1 1
0.6326 -2.0404 -4.7134 9.2737
P =−(+⧍)
C ÁL C U L O Y DIS T RIB U C IÓN D E PR E SIO N ES E N L A R E D DE D IS T RIB U C IÓN P OR E L M E TO D O D E H A R DY C R OS S
TRAMO
ITERACION N° 015 Q
Q
Perdidas de Carga
Cotas Piezometricas
LONGITUDES
CIRCUITO Nudo Inicial
Tramo Nudo Final
-
i
Km
m
Pulg.
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
150
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
3.00 3.00 4.00 3.00
150.00 150.00 150.00 150.00
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
3.00 3.00 3.00 4.00
150.00 150.00 150.00 150.00
m³/s
0.0051 0.0037 -0.0160 0.0065
l/s
m
5.0888 12.5760 3.7108 3.5038 -16.0124 -25.8802 6.4668 9.8004 0.0000
3.5229
3.5229
-1 -1 -1 1
-2.9793 - 2.9164 -4.7018 -10.8622 -6.4243 -12.1015 16.0124 25.8802
0.7339 1.1743 0.7339 1.1743
-2.1825 -9.6879 -11.3676 27.0545
0.0000
3.8165
3.8165
1 1 -1 1
2.4830 0.2555 -9.2737 4.7105
3.7460 0.0309 -10.5889 6.8122
1.3211 0.7339 1.3211 0.7339
5.0671 0.7648 -9.2678 7.5461
1 -1 -1 1
0.6326 -2.0404 -4.7134 9.2737
0.00000
ii
-0.0030 -0.0047 -0.0064 0.0160 0.00000
iii
0.0025 0.0003 -0.0093 0.0047 0.00000
iv
0.0006 -0.0020 -0.0047 0.0093 0.00000
CURSO
A ).
DE
m
1 1 -1 1
1.1743 0.5872 1.1743 0.5872
13.7504 4.0909 -24.7059 10.3875
0.0001
4.1101
4.1102
0.1985 - 2.6042 - 8.1840 10.5889
0.8807 1.3211 0.8807 1.3211
1.0793 -1.2831 -7.3032 11.9100
-0.0008
4.4037
4.4029
ABAS TECIMIENTO
DE
AGUA
Pi
C = f-i m
Pf
m
m
Cota Piez. Inicial
Cota Piez. Final
msnm
msnm
2098.00 2100.00 2100.00 2098.00 2098.00 2100.00 2100.00 2098.00
2.000 -2.0000 2.0000 -2.0000
50.8996 35.1492 33.0583 55.7642
35.1492 33.0583 55.7642 47.3766
2148.90 2135.15 2104.09 2046.33
2135.15 2104.09 2046.33 2000.95
2098.00 2096.00 2097.00 2100.00
2096.00 2097.00 2100.00 2098.00
-2.000 1.0000 3.0000 -2.0000
33.0583 37.2407 45.9287 54.2963
37.2407 45.9287 54.2963 29.2417
2104.09 2068.85 2021.92 1964.63
2068.85 2021.92 1964.63 1937.38
2102.00 2105.00 2105.00 2106.00 2106.00 2101.00 2101.00 2102.00
3.000 1.0000 -5.0000 1.0000
40.0828 32.0157 30.2509 44.5186
32.0157 30.2509 44.5186 35.9726
2142.08 2137.02 2105.76 2066.25
2137.02 2105.76 2066.25 2029.27
2106.00 2107.00 2103.00 2101.00
1.000 -4.0000 -2.0000 5.0000
30.2509 28.1716 33.4548 34.5740
28.1716 33.4548 34.5740 17.6640
2105.76 2076.59 2047.14 2014.56
2076.59 2047.14 2014.56 1991.90
Y
2107.00 2103.00 2101.00 2106.00
ALCANTARILLADO
-
DISEÑADO POR: A LEJ ANDR O YURI TICONA PEÑAS CO ESQUEMA GENERAL METODO DE HARDY CROSS LEYENDA: Ø
l/s lt/s. msnm mca lt/s
INFORMACION Y DATOS: Diametro de la Tuberia Propuesto Caudal en Transito en el Tramo - Red de Distribucion Caudal que se Destina para Un Nudo Cota del Terreno en (msnm) Presion en el Nudo (Resultante) Sentido del Flujo (Caudal de Transito en la Red) Caudal en Transito (DISEÑO) en el Tramo - Red de Distribucion
A LTERNA TIVA N° 01 TUB ERIA PVC
Se tiene Caudal Media Qm=
20.00 Lt/seg.
Qmd= Qmh=
Poblacion Futura = Poblacion Inicial = Incremento de Población =
26.00 Lt/seg. 36.00 Lt/seg.
11520 Hab 8323 Hab 3197 Hab
Q para la ZONA "A" = Q para la ZONA "B" = Q para %⧍P =
12.40 Lt/seg. 19.60 Lt/seg. 4.00 Lt/seg.
DIA METROS DE TUB ERIA C=150
) I ( O T I U C R I C
GR A FIC O N ° 00 1 Cota:
2098 msnm 1.38 lt/s.
1 Pres Ent
TRAMO
Diametros
1-2 2-3 3-4
3 3 6
4-1
3
) I I ( O T I U C R I C
1-2 2-3 3-4 4-1
O T I U C R I C
6
Pulg Ø 3
2.2301
2100 msnm 1.38 lt/s.
Cota:
TRAMO
Diametros
1-2 2-3 3-4
4 4 6
4-1
4
2 lt/s
) V I ( O T I U C R I C
TRAMO
Diametros
1-2 2-3 3-4
4 4 4
4-1
6
2102 msnm 2.23 lt/s.
Cota: Ø 4
2.6220 l/s 45.00 mca
(
3 3 3
Cota:
) I I I
TRAMO Diametros
1
46.18 mca P
P
35.2 mca
2
5.7725 l/s l/s 1.8677
2105 msnm 2.23 lt/s.
Pulg
P
33.5 mca
lt/s
400 m Ø 3 Pulg
3.6081
Q= 1.2440 l/s
lt/s
4.0000 l/s
i
0.8521 lt/s Ø 3 Pulg
Q= 8.0000 l/s
4.0952 lt/s Ø 4 Pulg
0.3598
iii
Reservorio
Ø 4
H=3.5m Cota: 2155 msnm L: 2km
Presion Cota: 2100 msnm
50.9 mca 21.6607
3.10 l/s
4 Qe
12.40 lt/s.
Qe
36.00 lt/s.
Ø 3 Pulg
Ø 6
5.0000 l/s
19.9035 l/s
0.3015 l/s
4
3.6347
lt/s
lt/s
P 49.29 mca 2098 msnm 3.10 l/s
500 m
lt/s
3.5450 l/s
Pulg
1100 m
2101 msnm 4.90 lt/s.
3 1
P
40.1 mca
4
Pulg
Q= 1.5550
10.4244
0.1897 Ø
lt/s
3
Qe
19.60 lt/s.
Qe
23.60 lt/s.
Ø 4 Pulg
lt/s
P
2.6975 l/s
39.0 mca
4
Ø 6
Pulg
4.90 lt/s.
4.1778
8.0000 l/s
lt/s
Cota:
3 1
-1.2985 l/s
2106 msnm 4.00 lt/s.
CURSO
A ).
DE
ABAS TECIMIENTO
DE
AGUA
Y
ALCANTARILLADO
-
DISEÑADO POR: A LEJ ANDR O YURI TICONA PEÑAS CO ESQUEMA GENERAL METODO DE HARDY CROSS LEYENDA: Ø
l/s lt/s. msnm mca lt/s
INFORMACION Y DATOS: Diametro de la Tuberia Propuesto Caudal en Transito en el Tramo - Red de Distribucion Caudal que se Destina para Un Nudo Cota del Terreno en (msnm) Presion en el Nudo (Resultante) Sentido del Flujo (Caudal de Transito en la Red) Caudal en Transito (DISEÑO) en el Tramo - Red de Distribucion
A LTERNA TIVA N° 01 TUB ERIA PVC
Se tiene Caudal Media Qm=
20.00 Lt/seg.
Qmd= Qmh=
Poblacion Futura = Poblacion Inicial = Incremento de Población =
26.00 Lt/seg. 36.00 Lt/seg.
11520 Hab 8323 Hab 3197 Hab
Q para la ZONA "A" = Q para la ZONA "B" = Q para %⧍P =
12.40 Lt/seg. 19.60 Lt/seg. 4.00 Lt/seg.
DIA METROS DE TUB ERIA C=150
) I ( O T I U C R I C
GR A FIC O N ° 00 1 Cota:
2098 msnm 1.38 lt/s.
TRAMO
Diametros
1-2 2-3 3-4
3 3 6
4-1
3
) I I (
1-2 2-3 3-4
(
3 3 3
4-1
O T I U C R I C
6
Cota:
2100 msnm 1.38 lt/s.
Pulg Ø 3
1 45.00 mca
Cota:
2
2.2301
TRAMO
Diametros
1-2 2-3 3-4
4 4 6
4-1
4
O T I U C R I C
TRAMO
Diametros
1-2 2-3 3-4
4 4 4
4-1
6
Cota:
1
46.18 mca P
lt/s
) V I (
2102 msnm 2.23 lt/s. Ø 4
2.6220 l/s
Pres Ent
) I I I
TRAMO Diametros
O T I U C R I C
P
2
5.7725 l/s l/s
35.2 mca
1.8677
2105 msnm 2.23 lt/s.
Pulg
P
33.5 mca
lt/s
400 m Ø 3 Pulg
3.6081
Q= 1.2440 l/s
lt/s
4.0000 l/s
i
0.8521 lt/s Ø 3 Pulg
Q= 8.0000 l/s
4.0952 lt/s Ø 4 Pulg
0.3598
iii
Reservorio
Ø 4
H=3.5m Cota: 2155 msnm L: 2km
Presion Cota: 2100 msnm
21.6607
3.10 l/s
12.40 lt/s.
Qe
36.00 lt/s.
Ø 3 Pulg
lt/s
19.9035 l/s
4 Qe
P 49.29 mca 2098 msnm 3.10 l/s
50.9 mca
4
Ø 6
3.6347
Q= 1.5550 l/s
lt/s
ii
P
40.1 mca
0.1897 Ø
Qe
19.60 lt/s.
Qe
23.60 lt/s.
Ø 4 Pulg
lt/s
3
lt/s
P
2.6975 l/s
39.0 mca
4
Ø 6
Pulg
4.1778
1.72 lt/s.
2097 msnm
1.9122
lt/s
iv
Pulg
3
2103 msnm 2.67 lt/s.
24
3.2775 l/s Ø 3
Pulg
2.6540 l/s
P 47.46 mca 2096 msnm 1.72 lt/s.
lt/s
4.00 lt/s.
8.0000 l/s
1.1682
Cota:
P
34.5 mca
1.5048
3
P
lt/s
600 m
lt/s
31.5 mca
2
5.3270 l/s Ø 4
Pulg
Cota:
Pulg
800 m
INGRESO A RED
Q=
36.00 lt/s.
CURSO
DE
Q=
19.60 lt/s.
AGUA
Y
4.00 lt/s.
ALCANTARILLADO
-
DISEÑA DO POR: AL EJA NDRO YURI TICONA PEÑA SCO
ESQUEMA GENERAL METODO DE HARDY CROSS
ℎ =∗∗1/0.54
=0.0004262 ∗ ∗2.63 ∗0.54
FORMULAS UTILIZADAS
= ∗ (1/(0.0004262∗∗2.63) 1/0.54
a ).
DE
SALIDA DE RED
Q=
23.60 lt/s.
ABASTECIMIENTO
2107 msnm
2.67 lt/s.
ZONA "B"
Q=
12.40 lt/s.
A ).
900 m
L=1000m Ø=6 pulg
ZONA "A"
Q=
2106 msnm
4.90 lt/s.
500 m
47.34 mca
Cota:
3 1
-1.2985 l/s
Ø 4
Presion
Pulg
1100 m 10.4244
4
Pulg
5.0000 l/s
2101 msnm 4.90 lt/s.
3 1
0.3015 l/s
500 m
lt/s
3.5450 l/s
⧍ = ((− ⅀ℎ )/(1.852∗⅀(ℎ /))
ℎ = ∗ (/(0.0004262∗∗2.63) 1/0.54)
C ÁL C U L O D E C A U DA L E S DE TR A N S IT O E N L A R E D D E D IS TR IB U C IÓN PO R E L M ET OD O D E H A R D Y C R OS S O T I U C R I C
TRAMO Nudo Inicial
ii
iii
iv
Tuberia
GASTO (Asumido)
Ø
PVC "C"
MAX. HOR.
m
Pulg.
150
m³/s
Nudo Final
-
i
DIAMETRO
Km
l/s
Hf/Q
2 3 4 1
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 6.00 3.00
150.00 150.00 150.00 150.00
0.0026 0.0012 0.0199 0.0040
1 1 -1 1
2.6220 1.2440 19.9035 4.0000
3.6833 0.4630 -5.3739 4.0261
1.4048 0.3722 0.2700 1.0065
2.7985
3.0535
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 6.00
150.00 150.00 150.00 150.00
0.0016 0.0033 0.0050 0.0199
-1 -1 -1 1
1.5550 3.2775 5.0000 19.9035
-0.8748 -5.5680 -7.6078 5.3739
0.5626 1.6989 1.5216 0.2700
-8.6768
4.0530
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
4.00 4.00 6.00 4.00
150.00 150.00 150.00 150.00
0.0058 0.0035 0.0027 0.0080
1 1 -1 1
5.7725 3.5450 2.6975 8.0000
4.4013 0.9912 -0.1493 4.4747
0.7625 0.2796 0.0554 0.5593
9.7179
1.6568
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
4.00 4.00 4.00 6.00
150.00 150.00 150.00 150.00
0.0027 0.0053 0.0080 0.0027
-1 -1 -1 1
2.6540 5.3270 8.0000 2.6975
-0.6959 -3.7930 -5.3696 0.1493
0.2622 0.7120 0.6712 0.0554
-9.7092
1.7008
Nudo Inicial
Tramo
Nudo Final
1 2 3 4 1 2
1-2 2-3 3-4 4-1 1-2 2-3
2 3 4 1 2 3
Diametro
Tuberia
GASTO itera. Anterior
Ø
PVC "C"
MAX. HOR.
LONGITUDES Km
m
Pulg.
150
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 6.00 3.00
150.00 150.00 150.00 150.00
0.50 0.80
500.00 800.00
3.00 3.00
150.00 150.00
m³/s
ITERACION N° 002
0.0022 0.0009 -0.0217 0.0036 -0.0002 -0.0019
1 1 -1 1 -1 -1
2.2281 0.8501 -21.6602 3.6061 -0.1921 -1.9146
-0.4949 -0.4949 -0.4949 -0.4949
1.156
1.1559 1.1559 1.1559 1.1559
-0.495
-3.1672 -3.1672 -3.1672 -3.1672
3.082
3.0824 3.0824 3.0824 3.0824
-3.167
Q
Hf
l/s
m
Hf/Q
1 1 -1 1
2.1271 0.7491 -21.5543 3.5051
2.5004 0.1810 -6.2283 3.1526
1.1755 0.2416 0.2890 0.8994
-0.3943
2.6055
-1 -1 -1 1
-0.3990 -2.1215 -3.8441 21.5543
-0.0705 -2.4883 -4.6753 6.2283
0.1766 1.1729 1.2163 0.2890
1 1 -1 1
2.6053 0.3778 -8.9471 4.8328
1.4087
0.9465
1 -1 -1 1
0.0238 0.4284 -0.7654 -2.2446 -2.1806 -4.9176 8.9471 1.3753
0.0555 0.3410 0.4434 0.1537
-1.5470
0.9936
-1.0058
2.8547
1.0087 0.0157 -1.3753 1.7596
0.3872 0.0415 0.1537 0.3641
ITERACION N° 004 Hf
l/s
Q
m
1-2 2-3 3-4 4-1
-
i
Hf
1 2 3 4
TRAMO CIRCUITO
ITERACION N° 001
ITERACION N° 003
LONGITUDES Tramo
Hf/Q
1.2229 0.2691 0.2902 0.9215
-0.0086
2.7036
-0.0182 -2.0576
0.0947 1.0747
0.0017 0.0017 0.0017 0.0017 0.0022 0.0022
0.0022
0.0817 0.0817 0.0817 0.0817 0.1902 0.1902 0.1902 0.1902 -0.8036 -0.8036 -0.8036 -0.8036 0.8407 0.8407 0.8407 0.8407
0.1902
0.0817
0.8407
-0.8036
Q
Hf
l/s
m
Hf/Q
1 1 -1 1 -1 -1
Q
Hf
l/s
m 2.2299 0.8519 -21.6607 3.6079 -0.1899 -1.9124
Hf/Q
2.7287 0.2296 -6.2854 3.3259
1.2237 0.2696 0.2902 0.9218
1 1 -1 1
2.2088 0.8308 -21.6629 3.5868
2.6812 0.2192 -6.2865 3.2901 -0.0960
2.6852
-1 -1 -1 1
-0.2088 -1.9313 -3.6538 21.6629
-0.0212 -2.0910 -4.2559 6.2865
0.1017 1.0827 1.1648 0.2902
-0.0816
2.6394
1 -1 -1 1
1.8017 -0.4258 -10.5914 4.0292
0.5095 -0.0196 -1.8797 1.2565
0.2828 0.0460 0.1775 0.3118
-0.1333
0.8181
1 -1 -1 1
1.2691 -1.4039 -4.0769 10.5914
0.1775 -0.3210 -1.5410 1.8797
0.1399 0.2286 0.3780 0.1775
0.1952
0.9240
1.2139 0.2639 0.2902 0.9173
-0.0012
2.7053
-0.0178 -2.0532
0.0938 1.0736
0.0002 0.0002
0.0002
0.0193 0.0193 0.0193 0.0193
0.0167
0.0167 0.0167 0.0167 0.0167
0.0193
0.0880 0.0880 0.0880 0.0880
-0.1141
-0.1141 -0.1141 -0.1141 -0.1141
0.0880
1 1 -1 1
2.2281 0.8501 -21.6602 3.6061
-1 -1 -1 1
-0.1921 -1.9146 -3.6371 21.6602
1 -1 -1 1
1.8897 -0.3378 -10.3893 4.1172
1 -1 -1 1
1.1550 -1.5180 -4.1910 10.3893
ITERACION N° 006
Q
0.0002 0.0002 0.0002 0.0002
Q
Q
l/s
ITERACION N° 005
Q
m
2.7248 0.2288 - 6.2851 3.3229
Q
1 1 -1 1 -1 -1
Q
Hf
l/s
m 2.2301 0.8521 -21.6607 3.6081 -0.1897 -1.9122
Hf/Q
Q
Q
l/s
2.7292 0.2297 -6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
-0.0001
2.7055
-0.0178 -2.0529
0.0937 1.0735
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
-1 -1
-0.1897 -1.9122
CURSO
A ).
DE
ABASTECIMIENTO
AGUA
Y
ALCANTARILLADO
-
ℎ =∗∗1/0.54
=0.0004262 ∗ ∗2.63 ∗0.54
FORMULAS UTILIZADAS
= ∗ (1/(0.0004262∗∗2.63) 1/0.54
a ).
DE
DISEÑA DO POR: AL EJA NDRO YURI TICONA PEÑA SCO
ESQUEMA GENERAL METODO DE HARDY CROSS
⧍ = ((− ⅀ℎ )/(1.852∗⅀(ℎ /))
ℎ = ∗ (/(0.0004262∗∗2.63) 1/0.54)
C ÁL C U L O D E C A U DA L E S DE TR A N S IT O E N L A R E D D E D IS TR IB U C IÓN PO R E L M ET OD O D E H A R D Y C R OS S O T I U C R I C
TRAMO Nudo Inicial
ii
iii
iv
Tuberia
GASTO (Asumido)
Ø
PVC "C"
MAX. HOR.
m
Pulg.
150
m³/s
Nudo Final
-
i
DIAMETRO
Km
ii
iii
iv
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 6.00 3.00
150.00 150.00 150.00 150.00
0.0026 0.0012 0.0199 0.0040
1 1 -1 1
2.6220 1.2440 19.9035 4.0000
3.6833 0.4630 -5.3739 4.0261
1.4048 0.3722 0.2700 1.0065
2.7985
3.0535
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 6.00
150.00 150.00 150.00 150.00
0.0016 0.0033 0.0050 0.0199
-1 -1 -1 1
1.5550 3.2775 5.0000 19.9035
-0.8748 -5.5680 -7.6078 5.3739
0.5626 1.6989 1.5216 0.2700
-8.6768
4.0530
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
4.00 4.00 6.00 4.00
150.00 150.00 150.00 150.00
0.0058 0.0035 0.0027 0.0080
1 1 -1 1
5.7725 3.5450 2.6975 8.0000
4.4013 0.9912 -0.1493 4.4747
0.7625 0.2796 0.0554 0.5593
9.7179
1.6568
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
4.00 4.00 4.00 6.00
150.00 150.00 150.00 150.00
0.0027 0.0053 0.0080 0.0027
-1 -1 -1 1
2.6540 5.3270 8.0000 2.6975
-0.6959 -3.7930 -5.3696 0.1493
0.2622 0.7120 0.6712 0.0554
-9.7092
1.7008
Nudo Inicial
1 2 3 4 1 2 3 4
Tramo
Nudo Final
1-2 2-3 3-4 4-1
2 3 4 1
1-2 2-3 3-4 4-1
2 3 4 1
Pulg.
150
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 6.00 3.00
150.00 150.00 150.00 150.00
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
ii
iii
-0.0002 -0.0019 -0.0036 0.0217
1 1 -1 1 -1 -1 -1 1
2.2281 0.8501 -21.6602 3.6061 -0.1921 -1.9146 -3.6371 21.6602
2.7248 0.2288 - 6.2851 3.3229
1.2229 0.2691 0.2902 0.9215
-0.0086
2.7036
-0.0182 -2.0576 -4.2200 6.2851
0.0947 1.0747 1.1603 0.2902
-0.0107
2.6199
0.2945 -0.0377 -0.1746 0.3176
4.00 4.00 6.00 4.00
150.00 150.00 150.00 150.00
0.0019 -0.0003 -0.0104 0.0041
1 -1 -1 1
1.8897 -0.3378 -10.3893 4.1172
0.5565 -0.0128 -1.8138 1.3077 0.0377
0.3998
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
4.00 4.00 4.00 6.00
150.00 150.00 150.00 150.00
0.0012 -0.0015 -0.0042 0.0104
1 -1 -1 1
1.1550 -1.5180 -4.1910 10.3893
0.1491 -0.3710 -1.6218 1.8138
0.1291 -0.2444 -0.3870 0.1746
-0.0298
-0.3277
Tramo
DE
ABASTE CIMIENTO
DE
Nudo Final
Diametro
Tuberia
GASTO itera. Anterior
Ø
PVC "C"
MAX. HOR.
LONGITUDES
3.0824 3.0824 3.0824 3.0824
-3.167
m
1 1 -1 1
2.1271 0.7491 -21.5543 3.5051
2.5004 0.1810 -6.2283 3.1526
1.1755 0.2416 0.2890 0.8994
-0.3943
2.6055
-1 -1 -1 1
-0.3990 -2.1215 -3.8441 21.5543
-0.0705 -2.4883 -4.6753 6.2283
0.1766 1.1729 1.2163 0.2890
1 1 -1 1
2.6053 0.3778 -8.9471 4.8328
1.4087
0.9465
1 -1 -1 1
0.0238 0.4284 -0.7654 -2.2446 -2.1806 -4.9176 8.9471 1.3753
0.0555 0.3410 0.4434 0.1537
-1.5470
0.9936
-1.0058
2.8547
1.0087 0.0157 -1.3753 1.7596
0.3872 0.0415 0.1537 0.3641
0.0017 0.0017 0.0017 0.0017
0.0022
0.0022 0.0022 0.0022 0.0022
0.0017
-0.0509 -0.0509 -0.0509 -0.0509
-0.0492
-0.0492 -0.0492 -0.0492 -0.0492
-0.0509
AGUA
Q
ITERACION N° 003
0.0817 0.0817 0.0817 0.0817 0.1902 0.1902 0.1902 0.1902 -0.8036 -0.8036 -0.8036 -0.8036 0.8407 0.8407 0.8407 0.8407
0.1902
0.0817
0.8407
-0.8036
Q
Hf
l/s
m
Hf/Q
Q
Hf
l/s
m
1 1 -1 1
2.2299 0.8519 -21.6607 3.6079
-1 -1 -1 1
-0.1899 -1.9124 -3.6349 21.6607
Hf/Q
2.7287 0.2296 -6.2854 3.3259
1.2237 0.2696 0.2902 0.9218
1 1 -1 1
2.2088 0.8308 -21.6629 3.5868
2.6812 0.2192 -6.2865 3.2901 -0.0960
2.6852
-1 -1 -1 1
-0.2088 -1.9313 -3.6538 21.6629
-0.0212 -2.0910 -4.2559 6.2865
0.1017 1.0827 1.1648 0.2902
-0.0816
2.6394
1 -1 -1 1
1.8017 -0.4258 -10.5914 4.0292
0.5095 -0.0196 -1.8797 1.2565
0.2828 0.0460 0.1775 0.3118
-0.1333
0.8181
1 -1 -1 1
1.2691 -1.4039 -4.0769 10.5914
0.1775 -0.3210 -1.5410 1.8797
0.1399 0.2286 0.3780 0.1775
0.1952
0.9240
1.2139 0.2639 0.2902 0.9173
-0.0012
2.7053
-0.0178 -2.0532 -4.2153 6.2854
0.0938 1.0736 1.1597 0.2902
-0.0009
2.6173
0.2877 0.0425 0.1746 0.3143
1 -1 -1 1
1.8388 -0.3887 -10.3911 4.0663
0.5291 -0.0165 -1.8144 1.2779 -0.0239
0.8192
1 -1 -1 1
1.1059 -1.5671 -4.2401 10.3911
0.1376 -0.3935 -1.6572 1.8144
0.1244 0.2511 0.3908 0.1746
-0.0988
0.9409
Y
0.0002 0.0002 0.0002 0.0002 0.0157 0.0157 0.0157 0.0157 0.0567 0.0567 0.0567 0.0567
0.0002
0.0002
0.0567
0.0157
0.0193 0.0193 0.0193 0.0193
0.0167
0.0167 0.0167 0.0167 0.0167
0.0193
0.0880 0.0880 0.0880 0.0880
-0.1141
-0.1141 -0.1141 -0.1141 -0.1141
0.0880
1 1 -1 1
2.2281 0.8501 -21.6602 3.6061
-1 -1 -1 1
-0.1921 -1.9146 -3.6371 21.6602
1 -1 -1 1
1.8897 -0.3378 -10.3893 4.1172
1 -1 -1 1
1.1550 -1.5180 -4.1910 10.3893
ITERACION N° 006
Q
0.0002 0.0002 0.0002 0.0002
Q
Q
l/s
ITERACION N° 005
Q
Q
Hf
l/s
m
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
Hf/Q
Q
Q
l/s
2.7292 0.2297 -6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
-0.0001
2.7055
-0.0178 -2.0529 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
-0.0001
2.6171
0.2898 0.0411 0.1752 0.3153
1 -1 -1 1
1.8545 -0.3730 -10.4320 4.0820
0.5375 -0.0153 -1.8276 1.2871 -0.0183
0.8214
1 -1 -1 1
1.1625 -1.5105 -4.1835 10.4320
0.1509 -0.3676 -1.6164 1.8276
0.1298 0.2433 0.3864 0.1752
-0.0054
0.9347
0.0000 0.0000 0.0000 0.0000
0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0120 0.0120 0.0120 0.0120
0.0031
0.0031 0.0031 0.0031 0.0031
0.0120
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
1 -1 -1 1
1.8666 -0.3609 -10.4231 4.0941
1 -1 -1 1
1.1657 -1.5073 -4.1803 10.4231
ALCANTARILLADO
Km
m
Pulg.
150
m³/s
ITERACION N° 007 Hf
l/s
Hf/Q
-
2 3 4 1
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 6.00 3.00
150.00 150.00 150.00 150.00
0.0022 0.0009 -0.0217 0.0036
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 - 6.2854 3.3263 0.0000
2.7055
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 6.00
150.00 150.00 150.00 150.00
-0.0002 -0.0019 -0.0036 0.0217
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
4.00 4.00 6.00 4.00
150.00 150.00 150.00 150.00
0.0019 -0.0004 -0.0104 0.0041
1 -1 -1 1
1.8666 -0.3609 -10.4231 4.0941
0.5440 -0.0144 -1.8247 1.2942
0.2914 -0.0399 -0.1751 0.3161
-0.0010
0.3925
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
4.00 4.00 4.00 6.00
150.00 150.00 150.00 150.00
0.0012 -0.0015 -0.0042 0.0104
1 -1 -1 1
1.1657 -1.5073 -4.1803 10.4231
0.1517 -0.3661 -1.6141 1.8247
0.1301 -0.2429 -0.3861 0.1751
-0.0039
-0.3239
Nudo Final
Diametro
Tuberia
GASTO itera. Anterior
Ø
PVC "C"
MAX. HOR.
LONGITUDES Km
m
Pulg.
150
m³/s
1.2238 0.2696 0.2902 0.9219
0.0000 0.0000 0.0000 0.0000
0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0014 0.0014 0.0014 0.0014
-0.0065
-0.0065 -0.0065 -0.0065 -0.0065
0.0014
Q
Hf
l/s
m
Hf/Q
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 -6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
0.0000
2.7055
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
1 -1 -1 1
1.8679 -0.3596 -10.4152 4.0954
0.5447 -0.0143 -1.8222 1.2950
0.2916 0.0398 0.1750 0.3162
0.0032
0.8226
1 -1 -1 1
1.1592 -1.5138 -4.1868 10.4152
0.1501 -0.3691 -1.6188 1.8222
0.1295 0.2438 0.3866 0.1750
-0.0156
0.9349
ITERACION N° 010 Hf
l/s
ITERACION N° 008
Q
m
1-2 2-3 3-4 4-1
Tramo
3.082
l/s
Hf/Q
DISEÑADO POR: A LEJA NDRO YURI TICONA PEÑASCO
1 2 3 4
Nudo Inicial
-0.495
-3.1672 -3.1672 -3.1672 -3.1672
Hf
m
900.00 500.00 900.00 500.00
-
i
150.00 150.00 150.00 150.00
0.0022 0.0009 -0.0217 0.0036
l/s
1.156
1.1559 1.1559 1.1559 1.1559
Hf/Q
0.90 0.50 0.90 0.50
TRAMO CIRCUITO
3.00 3.00 3.00 6.00
m³/s
-0.4949 -0.4949 -0.4949 -0.4949
Q
ITERACION N° 004 Hf
2 3 4 1
-
iv
MAX. HOR.
m
TRAMO
iii
GASTO itera. Anterior
PVC "C"
Km
CURSO
ii
Tuberia
Ø
1-2 2-3 3-4 4-1
A ).
i
Diametro LONGITUDES
1 2 3 4
Nudo Inicial
ITERACION N° 002
Q
m
2 3 4 1
ESQUEMA GENERAL METODO DE HARDY CROSS CIRCUITO
l/s
Hf/Q
1-2 2-3 3-4 4-1
-
i
Hf
1 2 3 4
TRAMO CIRCUITO
ITERACION N° 001
LONGITUDES Tramo
Hf/Q
1-2 2-3 3-4 4-1
2 3 4 1
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 6.00 3.00
150.00 150.00 150.00 150.00
0.0022 0.0009 -0.0217 0.0036
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 - 6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
0.0000
2.7055
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 6.00
150.00 150.00 150.00 150.00
-0.0002 -0.0019 -0.0036 0.0217
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
0.2916 -0.0398 -0.1751 0.3162
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
4.00 4.00 6.00 4.00
150.00 150.00 150.00 150.00
0.0019 -0.0004 -0.0104 0.0041
1 -1 -1 1
1.8677 -0.3598 -10.4241 4.0952
0.5446 -0.0143 -1.8250 1.2949 0.0001
0.3929
1
12
2
0 60
600 00
4 00
150 00
0 0012
1
1 1678
0 1522
0 1303
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0002 -0.0002 -0.0002 -0.0002 0 0010
0.0000
0.0000
-0.0010
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0021 -0.0021 -0.0021 -0.0021
0.0000
0.0000
0.0090
0.0090 0.0090 0.0090 0.0090
-0.0021
Q
Hf
l/s
m
Hf/Q
Q
Hf
l/s
m
Hf/Q
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 -6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 -6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
0.0000
2.7055
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
1 -1 -1 1
1.8658 -0.3617 -10.4264 4.0933
0.5436 -0.0145 -1.8258 1.2937
0.2913 0.0400 0.1751 0.3161
-0.0029
0.8225
1 -1 -1 1
1.1682 -1.5048 -4.1778 10.4264
0.1523 -0.3650 -1.6123 1.8258
0.1303 0.2426 0.3859 0.1751
0.0007
0.9339
0.0000
2.7055
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
0.5445 -0.0143 -1.8247 1.2948
0.2916 0.0398 0.1751 0.3162
0.0002
0.8226
0 1519
0 1302
1 -1 -1 1
1.8676 -0.3599 -10.4232 4.0951
1
1.1668
0.0000 0.0000 0.0000 0.0000 -0.0001 -0.0001 -0.0001 -0.0001 0 0014
0.0000
0.0000
0.0014
0.0000 0.0000 0.0000 0.0000
0.0000
0.0000 0.0000 0.0000 0.0000 0.0019 0.0019 0.0019 0.0019
0.0000
-0.0004
-0.0004 -0.0004 -0.0004 -0.0004
0.0019
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
1 -1 -1 1
1.8677 -0.3598 -10.4241 4.0952
1 -1 -1 1
1.1678 -1.5052 -4.1782 10.4241
ITERACION N° 012
Q
0.0000 0.0000 0.0000 0.0000
Q
Q
l/s
ITERACION N° 011
Q
m
1 2 3 4
ITERACION N° 009
Q
Q
Hf
l/s
m
Hf/Q
l/s
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 -6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
0.0000
2.7055
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
0.5444 -0.0143 -1.8252 1.2947
0.2915 0.0399 0.1751 0.3162
-0.0004
0.8227
0.1522
0.1303
1 -1 -1 1
1.8674 -0.3601 -10.4247 4.0949
1
1.1681
Q
Q
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0003 0.0003 0.0003 0.0003 0.0000
0.0000
0.0000
0.0000
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
1 -1 -1 1
1.8677 -0.3598 -10.4244 4.0952
1
1.1681
CURSO
A ).
TRAMO CIRCUITO
Nudo Inicial
Tramo
Nudo Final
-
i
ii
iii
iv
ii
iii
iv
Pulg.
150
b).
m³/s
l/s
Hf/Q
3.00 3.00 6.00 3.00
150.00 150.00 150.00 150.00
0.0022 0.0009 -0.0217 0.0036
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 - 6.2854 3.3263 0.0000
2.7055
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 6.00
150.00 150.00 150.00 150.00
-0.0002 -0.0019 -0.0036 0.0217
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
4.00 4.00 6.00 4.00
150.00 150.00 150.00 150.00
0.0019 -0.0004 -0.0104 0.0041
1 -1 -1 1
1.8666 -0.3609 -10.4231 4.0941
0.5440 -0.0144 -1.8247 1.2942
0.2914 -0.0399 -0.1751 0.3161
-0.0010
0.3925
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
4.00 4.00 4.00 6.00
150.00 150.00 150.00 150.00
0.0012 -0.0015 -0.0042 0.0104
1 -1 -1 1
1.1657 -1.5073 -4.1803 10.4231
0.1517 -0.3661 -1.6141 1.8247
0.1301 -0.2429 -0.3861 0.1751
-0.0039
-0.3239
Tramo
Nudo Final
Diametro
Tuberia
GASTO itera. Anterior
Ø
PVC "C"
MAX. HOR.
LONGITUDES Km
m
Pulg.
150
m³/s
0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0014 0.0014 0.0014 0.0014
-0.0065
-0.0065 -0.0065 -0.0065 -0.0065
0.0014
Hf
l/s
m
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 6.00 3.00
150.00 150.00 150.00 150.00
0.0022 0.0009 -0.0217 0.0036
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 - 6.2854 3.3263 0.0000
2.7055
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 6.00
150.00 150.00 150.00 150.00
-0.0002 -0.0019 -0.0036 0.0217
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
1.2238 0.2696 0.2902 0.9219
0.2916 -0.0398 -0.1751 0.3162
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
4.00 4.00 6.00 4.00
150.00 150.00 150.00 150.00
0.0019 -0.0004 -0.0104 0.0041
1 -1 -1 1
1.8677 -0.3598 -10.4241 4.0952
0.5446 -0.0143 -1.8250 1.2949 0.0001
0.3929
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
4.00 4.00 4.00 6.00
150.00 150.00 150.00 150.00
0.0012 -0.0015 -0.0042 0.0104
1 -1 -1 1
1.1678 -1.5052 -4.1782 10.4241
0.1522 -0.3652 -1.6126 1.8250
0.1303 -0.2426 -0.3860 0.1751
-0.0006
-0.3232
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 -6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
0.0000
2.7055
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
1 -1 -1 1
1.8679 -0.3596 -10.4152 4.0954
0.5447 -0.0143 -1.8222 1.2950
0.2916 0.0398 0.1750 0.3162
0.0032
0.8226
1 -1 -1 1
1.1592 -1.5138 -4.1868 10.4152
0.1501 -0.3691 -1.6188 1.8222
0.1295 0.2438 0.3866 0.1750
-0.0156
0.9349
ABASTECIMIENTO
DE
0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
-0.0002 -0.0002 -0.0002 -0.0002
-0.0010
-0.0010 -0.0010 -0.0010 -0.0010
-0.0002
AGUA
Hf
l/s
m
0.0000 0.0000 0.0000 0.0000
0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
-0.0021 -0.0021 -0.0021 -0.0021
0.0090
0.0090 0.0090 0.0090 0.0090
-0.0021
Nudo Final
Diametro
Tuberia
GASTO itera. Anterior
Ø
PVC "C"
MAX. HOR.
LONGITUDES
Q
Hf
l/s
m
Hf/Q
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 -6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
0.0000
2.7055
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
1 -1 -1 1
1.8676 -0.3599 -10.4232 4.0951
0.5445 -0.0143 -1.8247 1.2948
0.2916 0.0398 0.1751 0.3162
0.0002
0.8226
1 -1 -1 1
1.1668 -1.5062 -4.1792 10.4232
0.1519 -0.3657 -1.6134 1.8247
0.1302 0.2428 0.3860 0.1751
-0.0024
0.9341
Y
0.0000 0.0000 0.0000 0.0000
0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
-0.0001 -0.0001 -0.0001 -0.0001
0.0014
0.0014 0.0014 0.0014 0.0014
-0.0001
Q
Q
l/s
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 -6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
0.0000
2.7055
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
1 -1 -1 1
1.8658 -0.3617 -10.4264 4.0933
0.5436 -0.0145 -1.8258 1.2937
0.2913 0.0400 0.1751 0.3161
-0.0029
0.8225
1 -1 -1 1
1.1682 -1.5048 -4.1778 10.4264
0.1523 -0.3650 -1.6123 1.8258
0.1303 0.2426 0.3859 0.1751
0.0007
0.9339
0.0000 0.0000 0.0000 0.0000
0.0000
0.0000 0.0000 0.0000 0.0000 0.0019 0.0019 0.0019 0.0019
0.0000
-0.0004
-0.0004 -0.0004 -0.0004 -0.0004
0.0019
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
1 -1 -1 1
1.8677 -0.3598 -10.4241 4.0952
1 -1 -1 1
1.1678 -1.5052 -4.1782 10.4241
ITERACION N° 012 Q
Hf
l/s
m
Q
Hf/Q
l/s
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 -6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
0.0000
2.7055
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
0.5444 -0.0143 -1.8252 1.2947
0.2915 0.0399 0.1751 0.3162
-0.0004
0.8227
0.1522 -0.3650 -1.6124 1.8252
0.1303 0.2426 0.3859 0.1751
0.0000
0.9339
1 -1 -1 1
1.8674 -0.3601 -10.4247 4.0949
1 -1 -1 1
1.1681 -1.5049 -4.1779 10.4247
Q
Q
0.0000 0.0000 0.0000 0.0000
0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0003 0.0003 0.0003 0.0003
0.0000
0.0000 0.0000 0.0000 0.0000
0.0003
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
1 -1 -1 1
1.8677 -0.3598 -10.4244 4.0952
1 -1 -1 1
1.1681 -1.5049 -4.1779 10.4244
ALCANTARILLADO
Km
m
Pulg.
150
m³/s
ITERACION N° 013 Hf
l/s
Hf/Q
-
ITERACION N° 014
Q
m
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 6.00 3.00
150.00 150.00 150.00 150.00
0.0022 0.0009 -0.0217 0.0036
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 -6.2854 3.3263 0.0000
2.7055
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 6.00
150.00 150.00 150.00 150.00
-0.0002 -0.0019 -0.0036 0.0217
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
4.00 4.00 6.00 4.00
150.00 150.00 150.00 150.00
0.0019 -0.0004 -0.0104 0.0041
1 -1 -1 1
1.8677 -0.3598 -10.4244 4.0952
0.5446 -0.0143 -1.8251 1.2949
0.2916 -0.0398 -0.1751 0.3162
0.0000
0.3929
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
4.00 4.00 4.00 6.00
150.00 150.00 150.00 150.00
0.0012 -0.0015 -0.0042 0.0104
1 -1 -1 1
1.1681 -1.5049 -4.1779 10.4244
0.1522 -0.3651 -1.6124 1.8251
0.1303 -0.2426 -0.3859 0.1751
-0.0001
-0.3231
TRAMO
1.2238 0.2696 0.2902 0.9219
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0002 -0.0002 -0.0002 -0.0002
0.0000
0.0000
-0.0002
0.0000
Q
Hf
l/s
m
Diametro
Tuberia
GASTO de DISEÑO
Ø
PVC "C"
MAX. HOR.
Hf/Q
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 -6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
0.0000
2.7055
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
1 -1 -1 1
1.8677 -0.3598 -10.4242 4.0952
0.5446 -0.0143 -1.8251 1.2949
0.2916 0.0398 0.1751 0.3162
0.0000
0.8227
1 -1 -1 1
1.1680 -1.5050 -4.1780 10.4242
0.1522 -0.3651 -1.6125 1.8251
0.1303 0.2426 0.3860 0.1751
-0.0004
0.9339
Perdida de carga
Perdida Menrs
Perdida Totales
Hf
Hfm
Hf + hfm
Cota Inicial
Cota Final
m
m
msnm
msnm
Cotas de Terreno
ITERACION N° 015 Q
Hf
l/s
m
Q
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0002 0.0002 0.0002
0.0000
0.0000
0.0002
0.0000
Perdidas de Carga
2.7293 0.2298 -6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
0.0000
2.7055
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
1 -1 -1 1
1.8677 -0.3598 -10.4245 4.0952
0.5446 -0.0143 -1.8252 1.2948
0.2916 0.0398 0.1751 0.3162
-0.0001
0.8227
1 -1 -1 1
1.1682 -1.5048 -4.1778 10.4245
0.1523 -0.3650 -1.6124 1.8252
0.1303 0.2426 0.3859 0.1751
0.0000
0.9339
Cotas Piezometricas
Tramo Nudo Final
-
Km
m
Pulg.
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 6.00 3.00
150.00 150.00 150.00 150.00
150
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 6.00
150.00 150.00 150.00 150.00
m³/s
0.0022 0.0009 -0.0217 0.0036
l/s 2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 -6.2854 3.3263
1.1743 0.5872 1.1743 0.5872
0.0000
3.5229
3.5229
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.7339 1.1743 0.7339 1.1743
0.7162 -0.8785 -3.4808 7.4597
0.00000 -0.0002 -0.0019 -0.0036 0.0217
m
1 1 -1 1
3.9036 0.8169 -5.1110 3.9135
C = f-i m
Pi
Pf
m
m
Cota Piez. Inicial msnm
Cota Piez. Final msnm
2098.00 2100.00 2100.00 2098.00 2098.00 2100.00 2100.00 2098.00
2.000 -2.0000 2.0000 -2.0000
50.8996 44.9960 46.1791 49.2901
44.9960 46.1791 49.2901 47.3766
2148.90 2145.00 2100.82 2049.53
2145.00 2100.82 2049.53 2004.15
2098.00 2096.00 2097.00 2100.00
-2.000 1.0000 3.0000 -2.0000
46.1791 47.4629 47.3414 47.8222
47.4629 47.3414 47.8222 42.3626
2100.82 2055.35 2007.01 1956.19
2055.35 2007.01 1956.19 1915.83
2096.00 2097.00 2100.00 2098.00
Q
Q
l/s
2.2301 0.8521 -21.6607 3.6081
P =−(+⧍)
Diferencia de cotas
Hf/Q
1 1 -1 1
LONGITUDES Nudo Inicial
Hf/Q
ITERACION N° 011
Q
0.0000 0.0000 0.0000 0.0000
ITERACION N° 009 Q
Q
DISEÑADO POR: A LEJA NDRO YURI TICONA PEÑASCO
CIRCUITO
ii
Hf/Q
1 1 -1 1
m
2 3 4 1
DE
0.0000 0.0000 0.0000 0.0000
Q
C ÁL C U L O Y D IS T RIB U C IÓN D E PR E SIO N ES E N L A R E D DE D IS T RIB U C IÓN P OR E L M E TO D O D E HA R D Y C RO S S
i
-
ITERACION N° 008
Q
Hf/Q
1-2 2-3 3-4 4-1
Tramo
ALCANTARILLADO
ITERACION N° 010 Hf
l/s
1.2238 0.2696 0.2902 0.9219
1 2 3 4
Nudo Inicial
Y
m
800.00 400.00 800.00 400.00
Nudo Inicial
AGUA
ITERACION N° 007 Hf
0.80 0.40 0.80 0.40
-
iv
MAX. HOR.
m
TRAMO
iii
GASTO itera. Anterior
PVC "C"
Km
CURSO
ii
Tuberia
Ø
2 3 4 1
A ).
i
Diametro
1-2 2-3 3-4 4-1
ESQUEMA GENERAL METODO DE HARDY CROSS CIRCUITO
DE
1 2 3 4
-
i
ABASTE CIMIENTO
LONGITUDES
TRAMO CIRCUITO
DE
DISEÑADO POR: A LEJA NDRO YURI TICONA PEÑASCO
ESQUEMA GENERAL METODO DE HARDY CROSS
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000
0.0000
0.0000
0.0000
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
1 -1 -1 1
1.8677 -0.3598 -10.4244 4.0952
1 -1 -1 1
1.1682 -1.5048 -4.1778 10.4244
CURSO
A ).
TRAMO CIRCUITO
Nudo Inicial
Tramo
Nudo Final
-
i
ii
iii
iv
b).
DE
ABASTECIMIENTO
DE
AGUA
Y
ALCANTARILLADO
Diametro
Tuberia
GASTO itera. Anterior
Ø
PVC "C"
MAX. HOR.
LONGITUDES Km
m
Pulg.
150
m³/s
ITERACION N° 013 Hf
l/s
Hf/Q
ITERACION N° 014
Q
m
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 6.00 3.00
150.00 150.00 150.00 150.00
0.0022 0.0009 -0.0217 0.0036
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 -6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
0.0000
2.7055
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 6.00
150.00 150.00 150.00 150.00
-0.0002 -0.0019 -0.0036 0.0217
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
4.00 4.00 6.00 4.00
150.00 150.00 150.00 150.00
0.0019 -0.0004 -0.0104 0.0041
1 -1 -1 1
1.8677 -0.3598 -10.4244 4.0952
0.5446 -0.0143 -1.8251 1.2949
0.2916 -0.0398 -0.1751 0.3162
0.0000
0.3929
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
4.00 4.00 4.00 6.00
150.00 150.00 150.00 150.00
0.0012 -0.0015 -0.0042 0.0104
1 -1 -1 1
1.1681 -1.5049 -4.1779 10.4244
0.1522 -0.3651 -1.6124 1.8251
0.1303 -0.2426 -0.3859 0.1751
-0.0001
-0.3231
0.0000 0.0000 0.0000 0.0000
0.0000
0.0000 0.0000 0.0000 0.0000
0.0000
0.0000 0.0000 0.0000 0.0000
-0.0002
-0.0002 -0.0002 -0.0002 -0.0002
0.0000
Q
Hf
l/s
m
Hf/Q
TRAMO
Diametro
Tuberia
GASTO de DISEÑO
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 -6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
0.0000
2.7055
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
1 -1 -1 1
1.8677 -0.3598 -10.4242 4.0952
0.5446 -0.0143 -1.8251 1.2949
0.2916 0.0398 0.1751 0.3162
0.0000
0.8227
1 -1 -1 1
1.1680 -1.5050 -4.1780 10.4242
0.1522 -0.3651 -1.6125 1.8251
0.1303 0.2426 0.3860 0.1751
-0.0004
0.9339
Ø
PVC "C"
MAX. HOR.
Nudo Inicial
Tramo Nudo Final
-
Km
m
Pulg.
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.80 0.40 0.80 0.40
800.00 400.00 800.00 400.00
3.00 3.00 6.00 3.00
150.00 150.00 150.00 150.00
150
m³/s
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.50 0.80 0.50 0.80
500.00 800.00 500.00 800.00
3.00 3.00 3.00 6.00
150.00 150.00 150.00 150.00
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.90 0.50 0.90 0.50
900.00 500.00 900.00 500.00
4.00 4.00 6.00 4.00
150.00 150.00 150.00 150.00
1 2 3 4
1-2 2-3 3-4 4-1
2 3 4 1
0.60 0.90 0.60 0.90
600.00 900.00 600.00 900.00
4.00 4.00 4.00 6.00
150.00 150.00 150.00 150.00
0.0022 0.0009 -0.0217 0.0036
l/s
Hf
Hfm
Hf + hfm
Cota Inicial
Cota Final
m
m
msnm
msnm
-0.0002 -0.0019 -0.0036 0.0217 0.0019 -0.0004 -0.0104 0.0041
2.7293 0.2298 -6.2854 3.3263
1.1743 0.5872 1.1743 0.5872
0.0000
3.5229
3.5229
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.7339 1.1743 0.7339 1.1743
0.7162 -0.8785 -3.4808 7.4597
0.0000
3.8165
3.8165
1 -1 -1 1
1.8677 -0.3598 -10.4244 4.0952
0.5446 -0.0143 -1.8251 1.2949
1.3211 0.7339 1.3211 0.7339
1.8657 0.7196 -0.5040 2.0288
0.0000
4.1101
4.1101
1 -1 -1 1
1.1682 -1.5048 -4.1778 10.4244
0.1523 -0.3650 -1.6124 1.8251
0.8807 1.3211 0.8807 1.3211
1.0330 0.9561 -0.7316 3.1462
0.0000
4.4037
4.4037
0.00000 0.0012 -0.0015 -0.0042 0.0104 0.00000
m
2.2301 0.8521 -21.6607 3.6081
0.00000
iv
Perdida Totales
1 1 -1 1
0.00000
iii
Perdida Menrs
Cotas de Terreno
Hf
l/s
m
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0002 0.0002 0.0002 0.0002
0.0000
0.0000
0.0002
0.0000
Hf/Q
Q
Q
l/s
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
2.7293 0.2298 -6.2854 3.3263
1.2238 0.2696 0.2902 0.9219
0.0000
2.7055
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
-0.0178 -2.0528 -4.2148 6.2854
0.0937 1.0735 1.1596 0.2902
0.0000
2.6170
1 -1 -1 1
1.8677 -0.3598 -10.4245 4.0952
0.5446 -0.0143 -1.8252 1.2948
0.2916 0.0398 0.1751 0.3162
-0.0001
0.8227
1 -1 -1 1
1.1682 -1.5048 -4.1778 10.4245
0.1523 -0.3650 -1.6124 1.8252
0.1303 0.2426 0.3859 0.1751
0.0000
0.9339
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000
0.0000
0.0000
0.0000
P =−(+⧍)
Diferencia de cotas
Perdidas de Carga
Cotas Piezometricas
LONGITUDES
CIRCUITO
ii
Perdida de carga
ITERACION N° 015 Q
Q
1 1 -1 1
C ÁL C U L O Y D IS T RIB U C IÓN D E PR E SIO N ES E N L A R E D DE D IS T RIB U C IÓN P OR E L M E TO D O D E HA R D Y C RO S S
i
-
DISEÑADO POR: A LEJA NDRO YURI TICONA PEÑASCO
ESQUEMA GENERAL METODO DE HARDY CROSS
UNIVERSIDAD
3.9036 0.8169 -5.1110 3.9135
ALAS
C = f-i m
Pi
Pf
m
m
Cota Piez. Inicial msnm
Cota Piez. Final msnm
2098.00 2100.00 2100.00 2098.00 2098.00 2100.00 2100.00 2098.00
2.000 -2.0000 2.0000 -2.0000
50.8996 44.9960 46.1791 49.2901
44.9960 46.1791 49.2901 47.3766
2148.90 2145.00 2100.82 2049.53
2145.00 2100.82 2049.53 2004.15
2098.00 2096.00 2097.00 2100.00
2096.00 2097.00 2100.00 2098.00
-2.000 1.0000 3.0000 -2.0000
46.1791 47.4629 47.3414 47.8222
47.4629 47.3414 47.8222 42.3626
2100.82 2055.35 2007.01 1956.19
2055.35 2007.01 1956.19 1915.83
2102.00 2105.00 2105.00 2106.00 2106.00 2101.00 2101.00 2102.00
3.000 1.0000 -5.0000 1.0000
40.0828 35.2171 33.4974 39.0015
35.2171 33.4974 39.0015 35.9727
2142.08 2140.22 2105.72 2071.72
2140.22 2105.72 2071.72 2034.75
2106.00 2107.00 2103.00 2101.00
1.000 -4.0000 -2.0000 5.0000
33.4974 31.4645 34.5084 35.6277
31.4645 34.5084 35.6277 27.4814
2105.72 2073.26 2042.75 2009.12
2073.26 2042.75 2009.12 1976.64
2107.00 2103.00 2101.00 2106.00
PERUANAS
-
AREQUIPA
CURSO DE ABASTECIMIENTO DE AGUA Y ALCANTARILLADO
TRABAJO ENCARGADO: SISTEMA DE RED (METODO CROSS) ALUMNO Y DISEÑADO POR: AL EJANDRO YURI TICONA PEÑASCO
ENUNCIADO:
Determinar la solucion para el sistema indicado, e indicar los siguientes resultados: a). Caudales en transito de la RED DE AGUA POTABLE b). Presiones en los nudos de la RED DE AGUA POTABLE, siendo el mas desfavorable 12mca c). Presion de entrada a la Red de AGUA POTABLE y diametros en la Linea de Aduccion Nota.El fondo del Reservorio se encuentra a 2155msnm, con una altura de agua 3.5m; la linea de aduccion tiene una longitud de 2000 m. todas las tuberías son de PVC. Las perdidas menores tanto para linea de aducción como para la Red de Distribución se determina mediante la siguiente relación: 20L(V 2/2g), donde (L) esta en (Km) El Qmd es de 26 lps, y el clima es f rio, la población futura ha sido calculada del promedio de los tres metodos cuya t asas de crecimiento poblacional son de 50.00; 0.022; y 0.025 (Aritmetico Logaritmico y Geometrico) respectivamente. La población actual está distribuida en un 20% en la Zona (A), y el 60% restante ocupa la Zona (B) El incremento de la población está distribuida en un 20% en la Zona (A); un 40% en la zona (B), el resto estará establecido según se muestra en el gráfico.
1 1 -1 1
2.2301 0.8521 -21.6607 3.6081
-1 -1 -1 1
-0.1897 -1.9122 -3.6347 21.6607
1 -1 -1 1
1.8677 -0.3598 -10.4244 4.0952
1 -1 -1 1
1.1682 -1.5048 -4.1778 10.4244
UNIVERSIDAD
ALAS
PERUANAS
-
AREQUIPA
CURSO DE ABASTECIMIENTO DE AGUA Y ALCANTARILLADO
TRABAJO ENCARGADO: SISTEMA DE RED (METODO CROSS) ALUMNO Y DISEÑADO POR: AL EJANDRO YURI TICONA PEÑASCO
ENUNCIADO:
Determinar la solucion para el sistema indicado, e indicar los siguientes resultados: a). Caudales en transito de la RED DE AGUA POTABLE b). Presiones en los nudos de la RED DE AGUA POTABLE, siendo el mas desfavorable 12mca c). Presion de entrada a la Red de AGUA POTABLE y diametros en la Linea de Aduccion Nota.El fondo del Reservorio se encuentra a 2155msnm, con una altura de agua 3.5m; la linea de aduccion tiene una longitud de 2000 m. todas las tuberías son de PVC. Las perdidas menores tanto para linea de aducción como para la Red de Distribución se determina mediante la siguiente relación: 20L(V 2/2g), donde (L) esta en (Km) El Qmd es de 26 lps, y el clima es f rio, la población futura ha sido calculada del promedio de los tres metodos cuya t asas de crecimiento poblacional son de 50.00; 0.022; y 0.025 (Aritmetico Logaritmico y Geometrico) respectivamente. La población actual está distribuida en un 20% en la Zona (A), y el 60% restante ocupa la Zona (B) El incremento de la población está distribuida en un 20% en la Zona (A); un 40% en la zona (B), el resto estará establecido según se muestra en el gráfico. SOLUCION: Primero.-
Como dato tenemos
Qmd =
26.00 l/s.
El Caudal máximo diario se calcula Multiplicando por un coeficiente K1=1.3 al Qm Caudal Medio (Qm)
Consumo Clima Frio 150 l/ha/día
=( ∗ )/86400*1.3 Pf
:
11520.00 Hab.
Calculo de la Población Pf (M. Arit.) Pf (M. Geo.) Pf (M. Log.) Pf = 3 M. Aritmet. P f (M. Arit.) = Pi+r(Tf-Ti)
Pi (M. Arit.) =
Tasa de Crecimiento Poblacional (r) r Aritmetico = 50 10520 Hab.
r Geometrico = r Logaritmico = (Tf-Ti) =
M. Geomet. Pf (M. Geo.) Pi*(1+r)(Tf-Ti)
Pi (M. Arit.) =
###### Hab.
M. Logarit. lnPf (M. Lg.) ln(Pi)+r(Tf-Ti)
Pi (M. Arit.) =
7419.3 Hab.
Pi
:
8323.21 Hab.
Increment.P
:
3196.79 Hab.
Distribucion de la Población actual :
ZONA "A" ZONA "B"
40.00% Pi 60.00% Pi
3329.3 Hab 4993.9 Hab
ZONA "A" ZONA "B"
20.00% Pi 40.00% Pi
639.36 Hab 1278.7 Hab
ZONA "%Incremt"
40.00% Pi
1278.7 Hab 11520 Hab
Increment.P
:
0.025 0.022 20 años
Pf (Zona "A") =
3968.6 Hab
Pf (Zona "B") =
6272.6 Hab
Segundo.-
CALCULO DE LOS CAUDALES POR ZONAS
ℎ =∗2
=( ∗ )/86400/K1 Qm = 20 K1 = 1.3
de la teoria se tiene para poblacion futura mayor a 10000 hab. El K2 = 1.8 1.8
Lt/seg
Qmd (Para Zona "A") :
8.96 Lt/seg
Qmh (Para Zona "A") :
12.40 Lt/seg
Qmd (Para Zona "B") :
14.16 Lt/seg
Qmh (Para Zona "B") :
19.60 Lt/seg
Qmd (Para"%Incremt"):
2.89 Lt/seg
Qmh (Para"%Incremt"):
4.00 Lt/seg
Qmd :
26.00 Lt/seg
Qmh :
36.00 Lt/seg
Qmh (Zona B + %Inc):
23.60 Lt/seg
Tercero.DIMENCIONAMIENTO DEL RESERVORIO CIRCULAR
Para el calculo del volumen del reservorio se tiene que t rabajar con Qmd Qmd =
26.00 l/s.
Y ademas el Volumen total del Reservorio es
. =.+.+. V.r = Volumen de Reservorio = 0.25(Qmd *(86.4)) = 561.6 m3 V.i = Volumen de Incendios = ? Nota.- para poblaciones de 10000 a 20000 se tiene 02 hidrante V.i = Volumen de Incendios = 36 * N° de Hidrantes = 72 m3 V.e = Volumen de Emerg = (V.r + V.i)*(25%) = 158.4 m3 V. total del Reservorio =
792 m3
Predimencionamiento de la altura del Reservorio =(. )/300 ∗()
Nota.- para Reservorios que tienen volumen entre 400 a 600 m3, el valor de K = 1.8 H= Reservorio Circular
V = A. * H.
4.752 m donde: V : A :
Volumen del Reserv Area del Reserv
=(3.1416 ∗^2)/4 ∗()
D=
14.5673 m
Nota.- la altura de del reservorio es muy alta, por razon de estabilidad; asumimos una altura mayor (H=3.5m) y finalmente el Diametro del reservorio resulta de D = 16.97 m, equivalente a D= 17 m D= 17 m
H = 3.5m
Cuarto.DISE O DE LA LINEA DE ADUCCION Y CALCULO DE LA PRESION DE ENTRADA A LA RED DE DISTRIBUCION Altura del Reservorio = 3.5 m Cota del Nivel de Agua en Reservorio = 2159 m Cota inicio 2155 Cota final 2100 Del Grafico N° 001 Donde: S : Perdida ? se tiene hf: 58.5 m =ℎ /L L: 2.00 km del enunciado se tiene : hfm = 20L(V2/2g) S : 29.25 m/Km la tuberias es PVC C=150 Qmh =
con la formula
36.00 l/s.
=0.0004262 ∗ ∗2.63 ∗0.54
ITERACION N° 001 D : D1 :
entonces tomaremos
5.5568 Pulg.
6 Pulg.
V1=
De la Teoria se tiene que la Velocidad de flujo en las tuberias de conduccion Oscila entre 0.6 m/seg al 1.5 m/seg. Entonces Asumimos V = 0.9 m/seg. Qmh= 36.00 m/seg.
Calculado la velocidad del flujo en el tubo PVC =(6.2 ∗)/(3.1416∗2)
D=
La Velocidad del Flujo en el conducto es muy fuerte y por tanto no es aceptable
1.9735 m/seg.
8.8849 Pulg.
Ok
usar
S
=
L. Total
Qmh = L total = Calculo de hf
=
10 Pulg.
Ok
hfm = 20L(V2/2g)
del enunciado se tiene :
ITERACION N° 002
D=
m/Km
36.00 l/s.
2.00 Km
ℎ = ∗(/(0.0004262 ∗ ∗ 2.63))^(1/0.54) 1.8519 36.00 2.00 -----------------------------------------------------0.0004262 150 313
hf =
hf =
5.9491 m
Calculo de Perdida Totales = hf linea aduccion + hf menores
hfm = hfm =
Perdidas Totales =
20L(V2/2g) 1.6514 m
gravedad g =
9.81 m/seg2
7.600 m
CALCULO DE LA PRESION EN LA ANTRADA A LA RED DE DISTRIBUCI N …. (QUE CORRESPONDE A LA ZONA "A") Presion de entrada a RED Dist. = Carga Total - Perdidas de Linea Aducc.
Diferencia de alturas Presion de entrada a RED Dist. =
=
58.5
50.900 mca
m
CALCULO DE LAS PERDIDAS MENORES (hfm) EN LA RED DE DISTRIBUCION
20L(V /2g) Del enunciado se tiene : hfm = Por la teoria tambien, se sabe que las v elocidades de flujo permisibles en tuberia, estan entre los valores de 0. 9 a 1.5 m/seg. V = 1.2 m/seg. gravedad g = 9.81 m/seg Por tanto las perdidas menores (hfm) son como sigue: ZONA "A" ) I ( O T I U C R I C ) I I ( O T I U C R I C
TRAMO 1-2 2-3 3-4 4-1
Long (L :km) 0.80 0.40 0.80 0.40
hfm (m) 1.17 0.59 1.17 0.59
TRAMO 1-2 2-3 3-4 4-1
Long (L :km) 0.50 0.80 0.50 0.80
hfm (m) 0.73 1.17 0.73 1.17
TRAMO 1-2 2-3 3-4 4-1
Long (L :km) 0.90 0.50 0.90 0.50
hfm (m) 1.32 0.73 1.32 0.73
TRAMO 1-2 2-3 3-4 4-1
Long (L :km) 0.60 0.90 0.60 0.90
hfm (m) 0.88 1.32 0.88 1.32
ZONA "B" I I I ( O T I U C R I C V I ( O T I U C R I C
CALCULO DE LA PRESION EN LA ANTRADA A LA RED DE DISTRIBUCI N …. (A LA ZONA "B") Una vez hecho la corrida de calculos y presiones en los circuitos I y II de la Zona "A" se tiene una presion en el Punto de entrega hacia la Zona "B" que es en el Nudo 3 del circuito "I" Presión 40.0828 mca DISE O DE LA LINEA DE ADUCCION Y CALCULO DE LA PRESION DE ENTRADA A LA RED DE DISTRIBUCION Donde:
S : Perdida ? hf: 40.0828 m L: 1.00 km
=ℎ /L S
Q (Zona B) Q (%Inc) con la formula
19.60 4.00
:
40.08 m/Km
Qmh =
se tiene la tuberias es PVC C=150
23.60 l/s.
=0.0004262 ∗ ∗2.63 ∗0.54
Comprobando el Diametro de la Tuberia D : D1 : V1=
entonces tomaremos
4.4359 Pulg.
6 Pulg. 1.2936 m/seg.
Calculado la velocidad del flujo en el tubo PVC =(6.2 ∗)/(3.1416∗2) V=
1.2936 Pulg.
OK!!!!!!
De la Teoria se tiene que la Velocidad de flujo en las tuberias de conduccion Entonces Se tiene D = 6 Pulg Qmh= 23.60 l/s. Ok
Calculo de las Perdidas en este tramo S
=
L. Total
Qmh = L total = Calculo de hf
=
m/Km
23.60 l/s.
1.00 Km
ℎ = ∗(/(0.0004262 ∗ ∗ 2.63))^(1/0.54) 1.8519 23.60 1.00 -----------------------------------------------------0.0004262 150 111
hf =
hf =
9.2073 m
Perdidas Totales =
9.207 m
CALCULO DE LA PRESION EN LA ANTRADA A LA RED DE DISTRIBUCI N …. (QUE CORRESPONDE A LA ZONA "B") Presion de entrada a RED Dist. = Carga Total - Perdidas de Linea Aducc.
Presion a la Salida de la Zona "A" Presion de entrada a RED Dist. =
A ).
=
49.290
m
40.083 mca
A L TERNA TIVA N° 01 a). CÁLCULO DE CAUDALES DE TRANSITO EN LA RED DE DISTRIBUCIÓN POR EL METODO DE HARDY CROSS b). CÁLCULO Y DISTRIBUCIÓN DE PRESIONES EN LA RED DE DISTRIBUCIÓN POR EL METODO DE HARDY CROSS
B ).
A L TERNA TIVA N° 02 a). CÁLCULO DE CAUDALES DE TRANSITO EN LA RED DE DISTRIBUCIÓN POR EL METODO DE HARDY CROSS b). CÁLCULO Y DISTRIBUCIÓN DE PRESIONES EN LA RED DE DISTRIBUCIÓN POR EL METODO DE HARDY CROSS
CONCLUSION: DESPUES DE LOS CALCULOS (METODO HARDY CROS) SE ELIGE LA ALTERNATIVA N° 02 "B" Por Resultar mas economico en precios de los tubos y mantiene m ejores presiones en los nudos Como Resultado Final se tiene: 1.- Construir un Reservorio Circular de Concreto Armado de dismenciones Diametro Reserv = 17 m 2.- La Linea de Aducción será los siguienteL=2 km Diametro de Tuberia PVC 10 Pulg. 3.- RED DE DISTRIBUCION, ZONA "A" ) I (
O T I U C R I C ) I I ( O T I U C R I C
TRAMO 1-2 2-3 3-4 4-1
Long (L :km) 0.8 0.4 0.8 0.4
hfm (m) 1.174311927 0.587155963 1.174311927 0.587155963
D. Tub PVC (Pulg) Presion (mca) Clase 50.90 7.5 3 35.15 5 3 4 33.06 5 55.76 7.5 3
TRAMO 1-2 2-3 3-4 4-1
Long (L :km) 0.5 0.8 0.5 0.8
hfm (m) 0.733944954 1.174311927 0.733944954 1.174311927
D. Tub PVC (Pulg) Presion (mca) Clase 3 33.06 5 37.24 5 3 45.93 5 3 54.30 7.5 4
4.- La Linea de Aducción será los siguienteL=1 km 5.- RED DE DISTRIBUCION, ZONA "B" I I I (
O T I U C R I C V I ( O T I U C R I C
H = 3.5m clase 5
Diametro de Tuberia PVC
4 Pulg.
clase
TRAMO 1-2 2-3 3-4 4-1
Long (L :km) 0.9 0.5 0.9 0.5
hfm (m) 1.321100917 0.733944954 1.321100917 0.733944954
D. Tub PVC (Pulg) Presion (mca) Clase 40.08 3 32.02 3 30.25 4 44.52 3
5 5 5 5
TRAMO 1-2 2-3 3-4 4-1
Long (L :km) 0.6 0.9 0.6 0.9
hfm (m) 0.880733945 1.321100917 0.880733945 1.321100917
D. Tub PVC (Pulg) Presion (mca) Clase 3 30.25 28.17 3 33.45 3 34.57 4
5 5 5 5
5
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