Hardy Cross

ESTUDIO DE REDES DE TUBERIA (METODO DE HARDY CROSS) SOLUCION PROBLEMA N° 01 Determinar por el método de Hardy Cross, los caudales que circulan por cada tubería, coeficiente de Hazen y Williams es 100 para todos los tubos.

50 lt/seg

0m

8" ,7 00 m

6", 500m

0 ,5 " 8

6" ,6 00 m

0 ,6 " 8

0m

SOLUCION:

2 lt 35

50 lt/seg

/s

25 lt/s

10 lt/s

1 15 lt/s

3

4 lt 25

50 lt/seg

/s

1ra ITERACION Tubo 1-2 2-3 1-3

D(pulg) 8” 6” 6”

L(km) CH 0.5 100 0.5 100 0.6 100

Tubo 2-4 2-3 3-4

D(pulg) 8” 6” 8”

L(km) CH 0.7 100 0.5 100 0.6 100

CIRCUITO I Qo hfo (m) +35 +5.109 +10 +2.037 -15 -5.175 ∑ = +1.970 CIRCUITO II Qo hfo (m) +25 +3.838 -10 -2.037 -25 -3.29 ∑ = -1.489

hfo/Qo 0.146 0.204 0.345 ∑ = 0.695

▲Q -1.533 -1.533-1.6546 -1.533

Q1 = Qo + ▲Q 33.467 10.113 -16.533

hfo/Qo 0.154 0.204 0.132 ∑ = 0.489

▲Q +1.6546 +1.6546+1.533 +1.6546

Q1 = Qo + ▲Q 26.646 -9.887 -23.354

2da ITERACION Tubo 1-2 2-3 1-3

Tubo 2-4 2-3 3-4

D(pulg) 8” 6” 6”

D(pulg) 8” 6” 8”

L(km) CH 0.5 100 0.5 100 0.6 100

CIRCUITO I Q1 hf1 (m) hf1/Q1 +33.65 +4.702 0.141 +7.00 +2.08 0.206 -16.35 -6.196 0.375 ∑ = -0.586 ∑ = 0.721

L(km) CH 0.7 100 0.5 100 0.6 100

CIRCUITO II Q1 hf1 (m) +26.65 +4.2 -7.0 -1.05 -23.35 -2.87 ∑ = +0.28

hf1/Q1 0.16 0.15 0.12 ∑ = 0.43

L(km) CH 0.5 100 0.5 100 0.6 100

CIRCUITO I Q2 hf2 (m) +33.2 +4.54 +7.52 +1.20 -16.18 -5.75 ∑ = -0.01

hf2/Q2 0.13 0.16 0.35 ∑ = 0.64

▲Q +0.17 +0.17+0.35 +0.17

▲Q -0.35 -0.35-0.17 -0.35

Q2 = Q1 + ▲Q 33.82 7.52 -16.18

Q2 = Q1 + ▲Q 26.30 -7.52 -23.70

3ra ITERACION Tubo 1-2 2-3 1-3

D(pulg) 8” 6” 6”

▲Q +0.008 +0.008-0.046 +0.008

Q3 = Q2 + ▲Q 33.21 7.48 -16.18

▲Q +0.046 +0.046-0.008 +0.046

Q3 = Q2 + ▲Q 26.35 -7.48 -23.65

Q2-4 = 26.35lt/s

Q3-4 = 23.65 lt/s

CIRCUITO II Q2 hf2 (m) hf2/Q2 +26.30 +4.1 0.15 -7.52 -1.20 0.16 -23.7 -2.92 0.12 ∑ = -0.02 ∑ = 0.43 Error = ▲Q*100/Q = 0.008*100/16.17= 0.00005% < 1%  ¡OKEY¡

Tubo 2-4 2-3 3-4

D(pulg) 8” 6” 8”

L(km) CH 0.7 100 0.5 100 0.6 100

Error = ▲Q*100/Q = 0.046*100/23.65 = 0.002% < 1%  ¡OKEY¡  Q1-2 = 33.21 lt/s

Q2-3 = 7.48 lt/s

Q1-3 = 16.17 lt/s

2 25l t /s

lt/s 35

50 lt/seg

10lt/s

1 15l t/s

3

4 lt/s 5 2

50 lt/seg

t/ 20 l

g

8", 2000m C = 100

8", 1200m C = 100

10", 1500m C = 100

10", 2000m C = 120

25 lt/seg

25 lt/seg

10", 1500m C = 100

seg

10", 1200m C = 120

14", 2000m C = 100

25 lt/s e

C = 100 12", 1500m

t/seg 20 l

C = 100 16", 1500m

12", 1200m C = 100

seg 5 lt/

C = 100 10", 1500m

1

17 0l

t/se

g

PROBLEMA N° 02 Determinar por el método de Hardy Cross los caudales que circulan por cada uno de los ramales de la red de tuberías mostradas.

17 lt/seg

II

3

eg

15lt/s

lt/seg

25lt/s

lt/s

20lt/s

III

eg

9

8 lt/s

/seg t l 0

25

35lt/s

/seg t l 0

25lt/s

25 lt/seg

4 25

5

23

2

55lt/s

30lt/s

I

6 2

1

17

45lt/s

70lt/s

30lt/s

15

2

eg lt/s

0l t/s eg

SOLUCION:

8lt/s

7 17 lt/seg

1ra ITERACION Tubo 1-2 2-6 6-5 1-5

Tubo 1-3 3-4 4-5 1-5

Tubo 6-5 6-9 9-8 8-7 7-4 4-5

D(pulg) 12” 10” 10” 16”

D(pulg) 14” 10” 10” 16”

D(pulg) 10” 12” 8” 8” 10” 10”

L(km) 1.2 1.5 1.2 1.5

L(km) 2.0 1.5 2.0 1.5

L(km) 1.2 1.5 1.2 2.0 1.5 2.0

CIRCUITO I hfo (m) - 2.64 -3.45 +1.56 +1.27 ∑ = -3.26

CH 100 100 120 100

Qo -45 -30 +25 +70

hfo/Qo 0.0586 0.1150 0.0623 0.0182 ∑ = 0.2541

▲Q + 6.95 + 6.95 +6.95-0.525 +6.95+5.64

Q1 = Qo + ▲Q -38.05 -23.05 +31.425 +82.59

CH 100 100 120 100

CIRCUITO II Qo hfo (m) +55 +3.00 +30 +3.45 -20 -1.66 -70 -1.88 ∑ = +2.91

hfo/Qo 0.0545 0.1150 0.0830 0.0268 ∑ = 0.2973

▲Q -5.64 -5.64 -5.64-0.525 -5.64-6.95

Q1 = Qo + ▲Q +49.366 +24.36 - 26.165 - 82.59

CH 120 100 100 100 100 120

CIRCUITO III Qo hfo (m) hfo/Qo -25 -1.56 0.0623 -35 -2.1 0.06 -15 -2.51 0.1676 +8 +1.3 0.1624 +25 +2.55 0.1020 +20 +1.7 0.0850 ∑ = +0.62 ∑ = 0.6393

▲Q 0.525-6.95 0.525 0.525 0.525 0.525 0.525+5.64

Q1 = Qo + ▲Q -31.425 -34.475 -14.475 8.525 +25.525 +26.165

CH 100 100 120 100

CIRCUITO I Q1 hf1 (m) -38.05 -1.92 -23.05 -2.25 +31.42 +2.28 +82.59 +2.40 ∑ = +0.51

▲Q -1.1 -1.1 -1.1+0.156 -1.1-0.76

Q2 = Q1 + ▲Q -39.15 -24.15 +30.48 +80.73

CH 100 100 120 100

CIRCUITO II Q1 hf1 (m) hf1/Q1 +49.36 +2.4 0.0545 +24.36 +2.4 0.1150 -26.16 -2.8 0.0830 -82.59 -2.4 0.0268 ∑ = -0.4 ∑ = 0.2835

▲Q +0.76 +0.76 +0.76+0.156 +0.76+1.1

Q2 = Q1 + ▲Q +50.12 +25.12 -25.249 -80.76

2da ITERACION Tubo 1-2 2-6 6-5 1-5

D(pulg) 12” 10” 10” 16”

L(km) 1.2 1.5 1.2 1.5

Tubo 1-3 3-4 4-5 1-5

D(pulg) 14” 10” 10” 16”

L(km) 2.0 1.5 2.0 1.5

hf1/Q1 0.0505 0.0978 0.0735 0.0291 ∑ = 0.2509

Tubo 6-5 6-9 9-8 8-7 7-4 4-5

D(pulg) 10” 12” 8” 8” 10” 10”

L(km) 1.2 1.5 1.2 2.0 1.5 2.0

CH 120 100 100 100 100 120

CIRCUITO III Q1 hf1 (m) Hf1/Q1 -31.42 -2.28 0.0725 -34.47 -2.025 0.0589 -14.47 -2.4 0.1656 +8.52 +1.4 0.1640 +25.52 +2.7 0.1060 +26.16 +2.8 0.1073 ∑ = +0.195 ∑ = 0.6743

CH 100 100 120 100

CIRCUITO I Q2 hf2 (m) -39.15 -2.1 -24.15 -2.40 +31.48 +2.10 +80.73 +2.33 ∑ = -0.07

▲Q -0.156+1.1 -0.156 -0.156 -0.156 -0.156 -0.156-0.76

Q2 = Q1 + ▲Q -30.481 -34.631 -14.631 +8.369 +25.369 +25.249

▲Q +0.15 +0.15 +0.15+0.025 +0.15+0.425

Q3 = Q2 + ▲Q -39.00 -24.00 +30.656 +81.305

▲Q -0.425 -0.425 -0.425+0.025 -0.425-0.15

Q3 = Q2 + ▲Q +49.695 +24.695 -25.649 -81.305

▲Q -0.025-0.15 -0.025 -0.025 -0.025 -0.025 -0.025+0.42

Q3 = Q2 + ▲Q -30.656 -34.656 -14.656 +8.344 +25.344 +25.649

3ra ITERACION Tubo 1-2 2-6 6-5 1-5

Tubo 1-3 3-4 4-5 1-5

Tubo 6-5 6-9 9-8 8-7 7-4 4-5

D(pulg) 12” 10” 10” 16”

D(pulg) 14” 10” 10” 16”

D(pulg) 10” 12” 8” 8” 10” 10”

L(km) 1.2 1.5 1.2 1.5

L(km) 2.0 1.5 2.0 1.5

L(km) 1.2 1.5 1.2 2.0 1.5 2.0

CH 100 100 120 100

CH 120 100 100 100 100 120

hf2/Q2 0.0538 0.0997 0.0690 0.0290 ∑ = 0.2515

CIRCUITO II Q2 hf2 (m) hf2/Q2 +50.12 +2.5 0.050 +25.12 +2.55 0.1010 -25.249 -2.5 0.0990 -80.73 -2.33 0.0290 ∑ = -0.22 ∑ = 0.2790 CIRCUITO III Q2 hf2 (m) hf2/Q2 -30.481 -2.10 0.0725 -34.631 -2.10 0.0589 -14.631 -2.22 0.1656 +8.369 +1.4 0.1640 +25.369 +2.55 0.1060 +25.249 +2.5 0.1073 ∑ = +0.03 ∑ = 0.6482

Como: ▲Q < 1% Q3  los caudales Q3 en cada tramo son: Q1-2 = 39l/s

Q2-6 = 24l/s

Q6-5 = 30.656l/s

Q1-5 = 81.305l/s

Q1-3 = 49.695l/s

Q3-4 = 24.695l/s

Q4-5 = 25.649l/s

Q6-9 = 34.656l/s

Q9-8 = 14.655l/s

Q8-7 = 8.344l/s

Q7-4 = 25.344l/s