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 8" , 500 m 6 " , 5 0 0 m 8", 6 00m 8", 700 m 6", 600 m
SOLUCION:
50 lt/seg 35 lt/s 1 0 lt /s 25lt/s 25lt/s 15lt/s 50 lt/seg 1 2 4 3 1ra ITERACION CIRCUITO ITubo D(pulg) L(km) CH Qo hfo (m) hfo/Qo ▲Q Q1 = Qo + ▲Q
1-2 2-3 1-3 8” 6” 6” 0.5 0.5 0.6 100 100 100 +35 +10 -15 +5.109 +2.037 -5.175 0.146 0.204 0.345 -1.533 -1.533-1.6546 -1.533 33.467 10.113 -16.533 ∑ = +1.970 ∑ = 0.695 CIRCUITO II
Tubo D(pulg) L(km) CH Qo hfo (m) hfo/Qo ▲Q Q1 = Qo + ▲Q
2-4 2-3 3-4 8” 6” 8” 0.7 0.5 0.6 100 100 100 +25 -10 -25 +3.838 -2.037 -3.29 0.154 0.204 0.132 +1.6546 +1.6546+1.533 +1.6546 26.646 -9.887 -23.354 ∑ = -1.489 ∑ = 0.489
2da ITERACION CIRCUITO I Tubo D(pulg) L(km) CH Q1 hf1 (m) hf1/Q1 ▲Q Q2 = Q1 + ▲Q 1-2 2-3 1-3 8” 6” 6” 0.5 0.5 0.6 100 100 100 +33.65 +7.00 -16.35 +4.702 +2.08 -6.196 0.141 0.206 0.375 +0.17 +0.17+0.35 +0.17 33.82 7.52 -16.18 ∑ = -0.586 ∑ = 0.721 CIRCUITO II Tubo D(pulg) L(km) CH Q1 hf1 (m) hf1/Q1 ▲Q Q2 = Q1 + ▲Q 2-4 2-3 3-4 8” 6” 8” 0.7 0.5 0.6 100 100 100 +26.65 -7.0 -23.35 +4.2 -1.05 -2.87 0.16 0.15 0.12 -0.35 -0.35-0.17 -0.35 26.30 -7.52 -23.70 ∑ = +0.28 ∑ = 0.43 3ra ITERACION CIRCUITO I Tubo D(pulg) L(km) CH Q2 hf2 (m) hf2/Q2 ▲Q Q3 = Q2 + ▲Q 1-2 2-3 1-3 8” 6” 6” 0.5 0.5 0.6 100 100 100 +33.2 +7.52 -16.18 +4.54 +1.20 -5.75 0.13 0.16 0.35 +0.008 +0.008-0.046 +0.008 33.21 7.48 -16.18 ∑ = -0.01 ∑ = 0.64 CIRCUITO II Tubo D(pulg) L(km) CH Q2 hf2 (m) hf2/Q2 ▲Q Q3 = Q2 + ▲Q 2-4 2-3 3-4 8” 6” 8” 0.7 0.5 0.6 100 100 100 +26.30 -7.52 -23.7 +4.1 -1.20 -2.92 0.15 0.16 0.12 +0.046 +0.046-0.008 +0.046 26.35 -7.48 -23.65 ∑ = -0.02 ∑ = 0.43 Error = ▲Q*100/Q = 0.008*100/16.17= 0.00005% < 1% ¡OKEY¡ 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 Q2-4 = 26.35lt/s Q3-4 = 23.65 lt/s
50 lt/seg
35l
t/s
10
lt/s
25l
t/s
25lt/s
15lt/s
50 lt/seg
1
2
4
3
red de tuberías mostradas.
10", 1200m
15 lt
/seg
12", 1200m
14", 2000m
8", 1200m
20 lt
/seg
20 lt
/seg
25 lt/seg
25 lt/seg
17 lt/seg
25
lt
/se
g
17
0 l
t/s
eg
10
",
1
50
0m
10
",
1
50
0m
10", 2000m
8", 2000m
10
",
1
50
0m
12
",
1
50
0m
16
",
1
50
0m
C = 100
C = 120
C = 100
C = 120
C = 100
C = 100
C
=
1
00
C
=
1
00
C
=
1
00
C
=
1
00
C
=
1
00
SOLUCION:
15 l
t/se
g
45lt/s
55lt/s
20 l
t/se
g
20 l
t/se
g
25 lt/seg
25 lt/seg
17 lt/seg
25
lt
/se
g
17
0
lt/
se
g
30
lt
/s
30
lt/
s
20lt/s
25
lt/
s
35
lt
/s
70
lt/
s
25lt/s
8lt/s
15lt/s
23
lt
/se
g
I
II
III
2
1
3
6
5
4
7
8
9
1ra ITERACION
CIRCUITO I
Tubo D(pulg) L(km) CH Qo hfo (m) hfo/Qo ▲Q Q1 = Qo + ▲Q
1-2 2-6 6-5 1-5 12” 10” 10” 16” 1.2 1.5 1.2 1.5 100 100 120 100 -45 -30 +25 +70 - 2.64 -3.45 +1.56 +1.27 0.0586 0.1150 0.0623 0.0182 + 6.95 + 6.95 +6.95-0.525 +6.95+5.64 -38.05 -23.05 +31.425 +82.59 ∑ = -3.26 ∑ = 0.2541 CIRCUITO II
Tubo D(pulg) L(km) CH Qo hfo (m) hfo/Qo ▲Q Q1 = Qo + ▲Q
1-3 3-4 4-5 1-5 14” 10” 10” 16” 2.0 1.5 2.0 1.5 100 100 120 100 +55 +30 -20 -70 +3.00 +3.45 -1.66 -1.88 0.0545 0.1150 0.0830 0.0268 -5.64 -5.64 -5.64-0.525 -5.64-6.95 +49.366 +24.36 - 26.165 - 82.59 ∑ = +2.91 ∑ = 0.2973 CIRCUITO III
Tubo D(pulg) L(km) CH Qo hfo (m) hfo/Qo ▲Q Q1 = Qo + ▲Q
6-5 6-9 9-8 8-7 7-4 4-5 10” 12” 8” 8” 10” 10” 1.2 1.5 1.2 2.0 1.5 2.0 120 100 100 100 100 120 -25 -35 -15 +8 +25 +20 -1.56 -2.1 -2.51 +1.3 +2.55 +1.7 0.0623 0.06 0.1676 0.1624 0.1020 0.0850 0.525-6.95 0.525 0.525 0.525 0.525 0.525+5.64 -31.425 -34.475 -14.475 8.525 +25.525 +26.165 ∑ = +0.62 ∑ = 0.6393 2da ITERACION CIRCUITO I Tubo D(pulg) L(km) CH Q1 hf1 (m) hf1/Q1 ▲Q Q2 = Q1 + ▲Q 1-2 2-6 6-5 1-5 12” 10” 10” 16” 1.2 1.5 1.2 1.5 100 100 120 100 -38.05 -23.05 +31.42 +82.59 -1.92 -2.25 +2.28 +2.40 0.0505 0.0978 0.0735 0.0291 -1.1 -1.1 -1.1+0.156 -1.1-0.76 -39.15 -24.15 +30.48 +80.73 ∑ = +0.51 ∑ = 0.2509 CIRCUITO II Tubo D(pulg) L(km) CH Q1 hf1 (m) hf1/Q1 ▲Q Q2 = Q1 + ▲Q 1-3 3-4 4-5 1-5 14” 10” 10” 16” 2.0 1.5 2.0 1.5 100 100 120 100 +49.36 +24.36 -26.16 -82.59 +2.4 +2.4 -2.8 -2.4 0.0545 0.1150 0.0830 0.0268 +0.76 +0.76 +0.76+0.156 +0.76+1.1 +50.12 +25.12 -25.249 -80.76 ∑ = -0.4 ∑ = 0.2835
6-5 6-9 9-8 8-7 7-4 4-5 10” 12” 8” 8” 10” 10” 1.2 1.5 1.2 2.0 1.5 2.0 120 100 100 100 100 120 -31.42 -34.47 -14.47 +8.52 +25.52 +26.16 -2.28 -2.025 -2.4 +1.4 +2.7 +2.8 0.0725 0.0589 0.1656 0.1640 0.1060 0.1073 -0.156+1.1 -0.156 -0.156 -0.156 -0.156 -0.156-0.76 -30.481 -34.631 -14.631 +8.369 +25.369 +25.249 ∑ = +0.195 ∑ = 0.6743 3ra ITERACION CIRCUITO I Tubo D(pulg) L(km) CH Q2 hf2 (m) hf2/Q2 ▲Q Q3 = Q2 + ▲Q 1-2 2-6 6-5 1-5 12” 10” 10” 16” 1.2 1.5 1.2 1.5 100 100 120 100 -39.15 -24.15 +31.48 +80.73 -2.1 -2.40 +2.10 +2.33 0.0538 0.0997 0.0690 0.0290 +0.15 +0.15 +0.15+0.025 +0.15+0.425 -39.00 -24.00 +30.656 +81.305 ∑ = -0.07 ∑ = 0.2515 CIRCUITO II Tubo D(pulg) L(km) CH Q2 hf2 (m) hf2/Q2 ▲Q Q3 = Q2 + ▲Q 1-3 3-4 4-5 1-5 14” 10” 10” 16” 2.0 1.5 2.0 1.5 100 100 120 100 +50.12 +25.12 -25.249 -80.73 +2.5 +2.55 -2.5 -2.33 0.050 0.1010 0.0990 0.0290 -0.425 -0.425 -0.425+0.025 -0.425-0.15 +49.695 +24.695 -25.649 -81.305 ∑ = -0.22 ∑ = 0.2790 CIRCUITO III Tubo D(pulg) L(km) CH Q2 hf2 (m) hf2/Q2 ▲Q Q3 = Q2 + ▲Q 6-5 6-9 9-8 8-7 7-4 4-5 10” 12” 8” 8” 10” 10” 1.2 1.5 1.2 2.0 1.5 2.0 120 100 100 100 100 120 -30.481 -34.631 -14.631 +8.369 +25.369 +25.249 -2.10 -2.10 -2.22 +1.4 +2.55 +2.5 0.0725 0.0589 0.1656 0.1640 0.1060 0.1073 -0.025-0.15 -0.025 -0.025 -0.025 -0.025 -0.025+0.42 -30.656 -34.656 -14.656 +8.344 +25.344 +25.649 ∑ = +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
