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CIRCUITO TRAMO D (m) L (m) I 1-2 0.200 1000.00 2-4 0.150 800.00 4-3 0.125 500.00 3-1 0.200 800.00 II 4-6 0.125 500.00 6-5 0.125 500.00 5-3 0.150 500.00 3-4 0.125 500.00 CIRCUITO TRAMO D (m) L (m) I 1-2 0.200 1000.00 2-4 0.150 800.00 4-3 0.125 500.00 3-1 0.200 800.00 II 4-6 0.125 500.00 6-5 0.125 500.00 5-3 0.150 500.00 3-4 0.125 500.00 CIRCUITO TRAMO D (m) L (m) I 1-2 0.200 1000.00 2-4 0.150 800.00 4-3 0.125 500.00 3-1 0.200 800.00 II 4-6 0.125 500.00 6-5 0.125 500.00 5-3 0.150 500.00 3-4 0.125 500.00 CIRCUITO TRAMO D (m) L (m) I 1-2 0.200 1000.00 2-4 0.150 800.00 4-3 0.125 500.00
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PD4. Problema 4. Hardy Cross

Feb 19, 2016

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Jordano Roque

HARDY CROSS!!1
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Page 1: PD4. Problema 4. Hardy Cross

CIRCUITO TRAMO D (m) L (m) Q (l/s)

I

1-2 0.200 1000.00 25.002-4 0.150 800.00 16.004-3 0.125 500.00 10.003-1 0.200 800.00 25.00

II

4-6 0.125 500.00 11.006-5 0.125 500.00 9.005-3 0.150 500.00 15.003-4 0.125 500.00 11.54

CIRCUITO TRAMO D (m) L (m) Q (l/s)

I

1-2 0.200 1000.00 23.462-4 0.150 800.00 14.464-3 0.125 500.00 10.373-1 0.200 800.00 26.54

II

4-6 0.125 500.00 9.836-5 0.125 500.00 10.175-3 0.150 500.00 16.173-4 0.125 500.00 10.82

CIRCUITO TRAMO D (m) L (m) Q (l/s)

I

1-2 0.200 1000.00 23.012-4 0.150 800.00 14.014-3 0.125 500.00 10.693-1 0.200 800.00 26.99

II

4-6 0.125 500.00 9.696-5 0.125 500.00 10.315-3 0.150 500.00 16.313-4 0.125 500.00 10.74

CIRCUITO TRAMO D (m) L (m) Q (l/s)

I

1-2 0.200 1000.00 22.952-4 0.150 800.00 13.954-3 0.125 500.00 10.72

Page 2: PD4. Problema 4. Hardy Cross

I

3-1 0.200 800.00 27.05

II

4-6 0.125 500.00 9.686-5 0.125 500.00 10.325-3 0.150 500.00 16.323-4 0.125 500.00 10.73

Page 3: PD4. Problema 4. Hardy Cross

S H H/Q Q1 CIRCUITO0.00358 3.58 143.28 -1.54 23.46

I0.00637 5.09 318.40 -1.54 14.46-0.00649 -3.24 324.31 -1.54 -8.83-0.00358 -2.87 114.62 -1.54 -26.54

2.57 900.610.00774 3.87 351.68 -1.17 9.83 CIRCUITO-0.00534 -2.67 296.53 -1.17 -10.17

I-0.00565 -2.83 188.38 -1.17 -16.170.00846 4.23 366.33 -1.17 10.82

2.60 1202.91S H H/Q Q2

0.00318 3.18 135.73 -0.45 23.01 CIRCUITO0.00528 4.22 292.14 -0.45 14.01

I-0.00694 -3.47 334.53 -0.45 -10.69-0.00400 -3.20 120.60 -0.45 -26.99

0.74 883.000.00628 3.14 319.64 -0.14 9.69-0.00669 -3.35 328.97 -0.14 -10.31-0.00649 -3.25 200.79 -0.14 -16.310.00751 3.75 346.87 -0.14 10.69

0.30 1196.27S H H/Q Q3

0.00307 3.07 133.51 -0.05 22.950.00498 3.98 284.36 -0.05 13.95-0.00733 -3.67 343.12 -0.05 -10.72-0.00413 -3.30 122.34 -0.05 -27.05

0.09 883.330.00612 3.06 315.83 -0.02 9.68-0.00686 -3.43 332.75 -0.02 -10.32-0.00660 -3.30 202.24 -0.02 -16.320.00740 3.70 344.56 -0.02 10.72

0.03 1195.38S H H/Q Q3

0.00306 3.06 133.25 -0.01 22.950.00494 3.96 283.45 -0.01 13.95-0.00738 -3.69 344.14 -0.01 -10.73

ΔQ

ΔQ1

ΔQ2

ΔQ2

Page 4: PD4. Problema 4. Hardy Cross

-0.00414 -3.31 122.54 -0.01 -27.050.00973 883.39

0.00610 3.05 315.41 0.00 9.68-0.00688 -3.44 333.17 0.00 -10.32-0.00661 -3.30 202.40 0.00 -16.320.00739 3.69 344.30 0.00 10.73

0.003793 1195.28

Page 5: PD4. Problema 4. Hardy Cross

TRAMO D (m) L (m) Q (l/s) S H H/Q1-2 0.300 1500.00 150.00 0.01579 23.68 0.162-1 0.400 900.00 306.00 -0.01456 -13.11 0.04

10.58 0.20TRAMO D (m) L (m) Q (l/s) S H H/Q

1-2 0.300 1500.00 121.52 0.01069 16.03 0.132-1 0.400 900.00 334.48 -0.01717 -15.45 0.05

0.58 0.18TRAMO D (m) L (m) Q (l/s) S H H/Q

1-2 0.300 1500.00 119.76 0.01040 15.61 0.132-1 0.400 900.00 336.24 0.01734 -15.61 0.05

0.00 0.18

Page 6: PD4. Problema 4. Hardy Cross

Q1-28.48 121.52-28.48 334.48

Q1-1.76 119.76-1.76 336.24

Q1-0.01 119.75-0.01 336.25

456.00

ΔQ

ΔQ

ΔQ

Page 7: PD4. Problema 4. Hardy Cross

MÉTODO DE HARDY CROSS

CIRCUITO TRAMO D (m) L (m) Qo (l/s)

I

1-2 0.200 1000.00 0.0252-4 0.150 800.00 0.0164-3 0.125 500.00 0.0103-1 0.200 800.00 0.025

II

4-6 0.125 500.00 0.011006-5 0.125 500.00 0.009005-3 0.150 500.00 0.015003-4 0.125 500.00 0.01154

CIRCUITO TRAMO D (m) L (m) Q1 (l/s)

I

1-2 0.200 1000.00 0.023462-4 0.150 800.00 0.014464-3 0.125 500.00 0.010373-1 0.200 800.00 0.02654

II

4-6 0.125 500.00 0.009836-5 0.125 500.00 0.010175-3 0.150 500.00 0.016173-4 0.125 500.00 0.01075

CIRCUITO TRAMO D (m) L (m) Q2 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

Page 8: PD4. Problema 4. Hardy Cross

II

4-6 0.125 500.00 0.009726-5 0.125 500.00 0.010285-3 0.150 500.00 0.016283-4 0.125 500.00 0.01071

CIRCUITO TRAMO D (m) L (m) Q3 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

II

4-6 0.125 500.00 0.009696-5 0.125 500.00 0.010315-3 0.150 500.00 0.016313-4 0.125 500.00 0.01080

CIRCUITO TRAMO D (m) L (m) Q4 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

II

4-6 0.125 500.00 0.009666-5 0.125 500.00 0.010345-3 0.150 500.00 0.016343-4 0.125 500.00 0.01079

CIRCUITO TRAMO D (m) L (m) Q4 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

II

4-6 0.125 500.00 0.009666-5 0.125 500.00 0.010345-3 0.150 500.00 0.016343-4 0.125 500.00 0.01082

CIRCUITO TRAMO D (m) L (m) Q4 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

II

4-6 0.125 500.00 0.00965

Page 9: PD4. Problema 4. Hardy Cross

II6-5 0.125 500.00 0.010355-3 0.150 500.00 0.016353-4 0.125 500.00 0.01081

CIRCUITO TRAMO D (m) L (m) Q4 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

II

4-6 0.125 500.00 0.009646-5 0.125 500.00 0.010365-3 0.150 500.00 0.016363-4 0.125 500.00 0.01082

CIRCUITO TRAMO D (m) L (m) Q4 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

II

4-6 0.125 500.00 0.009646-5 0.125 500.00 0.010365-3 0.150 500.00 0.016363-4 0.125 500.00 0.01082

CIRCUITO TRAMO D (m) L (m) Q4 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

II

4-6 0.125 500.00 0.009646-5 0.125 500.00 0.010365-3 0.150 500.00 0.016363-4 0.125 500.00 0.01082

CIRCUITO TRAMO D (m) L (m) Q4 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

II

4-6 0.125 500.00 0.009646-5 0.125 500.00 0.010365-3 0.150 500.00 0.01636

Page 10: PD4. Problema 4. Hardy Cross

II

3-4 0.125 500.00 0.01082

CIRCUITO TRAMO D (m) L (m) Q4 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

II

4-6 0.125 500.00 0.009646-5 0.125 500.00 0.010365-3 0.150 500.00 0.016363-4 0.125 500.00 0.01082

CIRCUITO TRAMO D (m) L (m) Q4 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

II

4-6 0.125 500.00 0.009646-5 0.125 500.00 0.010365-3 0.150 500.00 0.016363-4 0.125 500.00 0.01082

CIRCUITO TRAMO D (m) L (m) Q4 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

II

4-6 0.125 500.00 0.009646-5 0.125 500.00 0.010365-3 0.150 500.00 0.016363-4 0.125 500.00 0.01082

CIRCUITO TRAMO D (m) L (m) Q4 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

II

4-6 0.125 500.00 0.009646-5 0.125 500.00 0.010365-3 0.150 500.00 0.016363-4 0.125 500.00 0.01082

Page 11: PD4. Problema 4. Hardy Cross

CIRCUITO TRAMO D (m) L (m) Q4 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

II

4-6 0.125 500.00 0.009646-5 0.125 500.00 0.010365-3 0.150 500.00 0.016363-4 0.125 500.00 0.01082

CIRCUITO TRAMO D (m) L (m) Q4 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

II

4-6 0.125 500.00 0.009646-5 0.125 500.00 0.010365-3 0.150 500.00 0.016363-4 0.125 500.00 0.01082

CIRCUITO TRAMO D (m) L (m) Q4 (l/s)

I

1-2 0.200 1000.00 0.023012-4 0.150 800.00 0.014014-3 0.125 500.00 0.010823-1 0.200 800.00 0.02699

II

4-6 0.125 500.00 0.009646-5 0.125 500.00 0.010365-3 0.150 500.00 0.016363-4 0.125 500.00 0.01082

Solución:

CIRCUITO TRAMO D (m) L (m) Q19 (l/s)

I

1-2 0.200 1000.00 0.0230082-4 0.150 800.00 0.0140084-3 0.125 500.00 0.0108223-1 0.200 800.00 0.026992

II

4-6 0.125 500.00 0.0096396-5 0.125 500.00 0.0103615-3 0.150 500.00 0.0163613-4 0.125 500.00 0.010822

Page 12: PD4. Problema 4. Hardy Cross
Page 13: PD4. Problema 4. Hardy Cross

So Ho Ho/Qo Q1 CIRCUITO0.00355 3.55 142.11 -0.00154 0.02346

I0.00631 5.05 315.58 -0.00154 0.01446-0.00642 -3.21 321.18 -0.00154 ###-0.00355 -2.84 113.69 -0.00154 0.02654

2.55 892.560.00766 3.83 348.35 -0.00117 0.00983 CIRCUITO-0.00529 -2.64 293.61 -0.00117 0.01017

I-0.00560 -2.80 186.69 -0.00117 0.016170.00838 4.19 362.95 -0.00117 0.01037

2.58 1191.59S1 H1 H1/Q1 Q2

0.00316 3.16 134.60 -0.00045 0.02301 CIRCUITO0.00523 4.18 289.46 -0.00045 0.01401

I-0.00687 -3.44 331.37 -0.00045 0.01082-0.00397 -3.18 119.64 -0.00045 0.02699

0.73 875.080.00622 3.11 316.53 -0.00011 0.00972-0.00663 -3.31 325.82 -0.00011 0.01028-0.00644 -3.22 199.02 -0.00011 0.01628 CIRCUITO0.00734 3.67 341.50 -0.00011 0.01063

I0.25 1182.88

S2 H2 H2/Q2 Q30.00305 3.05 132.40 0.00000 0.023010.00493 3.95 281.76 0.00000 0.01401-0.00744 -3.72 343.59 0.00000 0.01082-0.00410 -3.28 121.37 0.00000 0.02699

ΔQo

ΔQ1

ΔQ2

Page 14: PD4. Problema 4. Hardy Cross

-0.00242 879.120.00609 3.04 313.40 -0.00002 0.00969-0.00677 -3.38 328.94 -0.00002 0.01031-0.00652 -3.26 200.22 -0.00002 0.016310.00729 3.65 340.49 -0.00002 0.01069

0.04832 1183.04S3 H3 H3/Q3 Q4

0.00305 3.05 132.41 0.00000 0.023010.00493 3.95 281.79 0.00000 0.01401-0.00744 -3.72 343.55 0.00000 0.01082-0.00409 -3.28 121.36 0.00000 0.02699

0.00000 879.100.00606 3.03 312.79 -0.00003 0.00966-0.00679 -3.40 329.54 -0.00003 0.01034-0.00654 -3.27 200.45 -0.00003 0.016340.00741 3.70 342.91 -0.00003 0.01077

0.07035 1185.68S4 H4 H4/Q4 Q5

0.00305 3.05 132.41 0.00000 0.023010.00493 3.95 281.79 0.00000 0.01401-0.00744 -3.72 343.55 0.00000 0.01082-0.00409 -3.28 121.36 0.00000 0.02699

0.00000 879.100.00603 3.01 311.91 -0.000007 0.00966-0.00683 -3.42 330.41 -0.000007 0.01034-0.00656 -3.28 200.78 -0.000007 0.016340.00740 3.70 342.68 -0.000007 0.01078

0.01489 1185.78S4 H4 H4/Q4 Q5 6

0.00305 3.05 132.41 0.000000 0.023010.00493 3.95 281.79 0.000000 0.01401-0.00744 -3.72 343.55 0.000000 0.01082-0.00409 -3.28 121.36 0.000000 0.02699

0.00000 879.100.00602 3.01 311.72 -0.000009 0.00965-0.00684 -3.42 330.60 -0.000009 0.01035-0.00657 -3.28 200.85 -0.000009 0.016350.00743 3.71 343.36 -0.000009 0.01081

0.02035 1186.53 7S4 H4 H4/Q4 Q5

0.00305 3.05 132.41 0.000000 0.023010.00493 3.95 281.79 0.000000 0.01401-0.00744 -3.72 343.55 0.000000 0.01082-0.00409 -3.28 121.36 0.000000 0.02699

0.00000 879.100.00601 3.00 311.47 -0.000002 0.00964

ΔQ3

ΔQ4

ΔQ4

ΔQ4

Page 15: PD4. Problema 4. Hardy Cross

-0.00685 -3.43 330.85 -0.000002 0.01036-0.00657 -3.29 200.95 -0.000002 0.016360.00742 3.71 343.30 -0.000002 0.01081

0.00429 1186.56S4 H4 H4/Q4 Q5 8

0.00305 3.05 132.41 0.000000 0.023010.00493 3.95 281.79 0.000000 0.01401-0.00744 -3.72 343.55 0.000000 0.01082-0.00409 -3.28 121.36 0.000000 0.02699

0.00000 879.100.00601 3.00 311.41 -0.000003 0.00964-0.00685 -3.43 330.90 -0.000003 0.01036-0.00657 -3.29 200.97 -0.000003 0.016360.00743 3.72 343.49 -0.000003 0.01082

0.00589 1186.78S4 H4 H4/Q4 Q5 9

0.00305 3.05 132.41 0.000000 0.023010.00493 3.95 281.79 0.000000 0.01401-0.00744 -3.72 343.55 0.000000 0.01082-0.00409 -3.28 121.36 0.000000 0.02699

0.00000 879.100.00600 3.00 311.34 -0.000001 0.00964-0.00686 -3.43 330.98 -0.000001 0.01036-0.00658 -3.29 201.00 -0.000001 0.016360.00743 3.72 343.47 -0.000001 0.01082

0.00124 1186.79S4 H4 H4/Q4 Q5 10

0.00305 3.05 132.41 0.000000 0.023010.00493 3.95 281.79 0.000000 0.01401-0.00744 -3.72 343.55 0.000000 0.01082-0.00409 -3.28 121.36 0.000000 0.02699

0.00000 879.100.00600 3.00 311.32 -0.000001 0.00964-0.00686 -3.43 330.99 -0.000001 0.01036-0.00658 -3.29 201.01 -0.000001 0.016360.00744 3.72 343.53 -0.000001 0.01082

0.00171 1186.85S4 H4 H4/Q4 Q5 11

0.00305 3.05 132.41 0.000000 0.023010.00493 3.95 281.79 0.000000 0.01401-0.00744 -3.72 343.55 0.000000 0.01082-0.00409 -3.28 121.36 0.000000 0.02699

0.00000 879.100.00600 3.00 311.30 0.000000 0.00964-0.00686 -3.43 331.01 0.000000 0.01036-0.00658 -3.29 201.01 0.000000 0.01636

ΔQ4

ΔQ4

ΔQ4

ΔQ4

Page 16: PD4. Problema 4. Hardy Cross

0.00743 3.72 343.53 0.000000 0.010820.00036 1186.85

S4 H4 H4/Q4 Q5 120.00305 3.05 132.41 0.000000 0.023010.00493 3.95 281.79 0.000000 0.01401-0.00744 -3.72 343.55 0.000000 0.01082-0.00409 -3.28 121.36 0.000000 0.02699

0.00000 879.100.00600 3.00 311.30 0.000000 0.00964-0.00686 -3.43 331.02 0.000000 0.01036-0.00658 -3.29 201.02 0.000000 0.016360.00744 3.72 343.54 0.000000 0.01082

0.00049 1186.87S4 H4 H4/Q4 Q5 13

0.00305 3.05 132.41 0.000000 0.023010.00493 3.95 281.79 0.000000 0.01401-0.00744 -3.72 343.55 0.000000 0.01082-0.00409 -3.28 121.36 0.000000 0.02699

0.00000 879.100.00600 3.00 311.29 0.000000 0.00964-0.00686 -3.43 331.02 0.000000 0.01036-0.00658 -3.29 201.02 0.000000 0.016360.00744 3.72 343.54 0.000000 0.01082

0.00010 1186.87S4 H4 H4/Q4 Q5 14

0.00305 3.05 132.41 0.000000 0.023010.00493 3.95 281.79 0.000000 0.01401-0.00744 -3.72 343.55 0.000000 0.01082-0.00409 -3.28 121.36 0.000000 0.02699

0.00000 879.100.00600 3.00 311.29 0.000000 0.00964-0.00686 -3.43 331.02 0.000000 0.01036-0.00658 -3.29 201.02 0.000000 0.016360.00744 3.72 343.55 0.000000 0.01082

0.00014 1186.88S4 H4 H4/Q4 Q5 15

0.00305 3.05 132.41 0.000000 0.023010.00493 3.95 281.79 0.000000 0.01401-0.00744 -3.72 343.55 0.000000 0.01082-0.00409 -3.28 121.36 0.000000 0.02699

0.00000 879.100.00600 3.00 311.29 0.000000 0.00964-0.00686 -3.43 331.03 0.000000 0.01036-0.00658 -3.29 201.02 0.000000 0.016360.00744 3.72 343.54 0.000000 0.01082

0.00003 1186.88

ΔQ4

ΔQ4

ΔQ4

ΔQ4

Page 17: PD4. Problema 4. Hardy Cross

S4 H4 H4/Q4 Q5 160.00305 3.05 132.41 0.000000 0.023010.00493 3.95 281.79 0.000000 0.01401-0.00744 -3.72 343.55 0.000000 0.01082-0.00409 -3.28 121.36 0.000000 0.02699

0.00000 879.100.00600 3.00 311.29 0.000000 0.00964-0.00686 -3.43 331.03 0.000000 0.01036-0.00658 -3.29 201.02 0.000000 0.016360.00744 3.72 343.55 0.000000 0.01082

0.00004 1186.88S4 H4 H4/Q4 Q5 17

0.00305 3.05 132.41 0.000000 0.023010.00493 3.95 281.79 0.000000 0.01401-0.00744 -3.72 343.55 0.000000 0.01082-0.00409 -3.28 121.36 0.000000 0.02699

0.00000 879.100.00600 3.00 311.29 0.000000 0.00964-0.00686 -3.43 331.03 0.000000 0.01036-0.00658 -3.29 201.02 0.000000 0.016360.00744 3.72 343.55 0.000000 0.01082

0.00001 1186.88S4 H4 H4/Q4 Q5 18

0.00305 3.05 132.41 0.000000 0.023010.00493 3.95 281.79 0.000000 0.01401-0.00744 -3.72 343.55 0.000000 0.01082-0.00409 -3.28 121.36 0.000000 0.02699

0.00000 879.100.00600 3.00 311.29 0.000000 0.00964-0.00686 -3.43 331.03 0.000000 0.01036-0.00658 -3.29 201.02 0.000000 0.016360.00744 3.72 343.55 0.000000 0.01082

0.00001 1186.88

S19 H19 H19/Q19 Q20 190.00305 3.04642 132.41 0.00000 0.0230080.00493 3.94730 281.79 0.00000 0.014008-0.00744 -3.71795 343.55 0.00000 0.010822-0.00409 -3.27577 121.36 0.00000 0.026992

0.00000 879.100.00600 3.00057 311.29 0.00000 0.009639-0.00686 -3.42968 331.03 0.00000 0.010361-0.00658 -3.28883 201.02 0.00000 0.0163610.00744 3.71794 343.55 0.00000 0.010822

ΔQ4

ΔQ4

ΔQ4

ΔQ19

Page 18: PD4. Problema 4. Hardy Cross

0.00000 1186.88

Page 19: PD4. Problema 4. Hardy Cross

TRAMO D (m) L (m) Qo (l/s) So Ho Ho/Qo1-2 0.300 1500.00 150.00 0.01579 23.68 0.162-1 0.400 900.00 306.00 -0.01456 -13.11 0.04

10.58 0.20TRAMO D (m) L (m) Q (l/s) S H H/Q

1-2 0.300 1500.00 121.52 0.01069 16.03 0.132-1 0.400 900.00 334.48 -0.01717 -15.45 0.05

0.58 0.18TRAMO D (m) L (m) Q1 (l/s) S1 H1 H1/Q1

1-2 0.300 1500.00 119.76 0.01040 15.61 0.132-1 0.400 900.00 336.24 0.01734 -15.61 0.05

0.00174 0.18

TRAMO D (m) L (m) Q2 (l/s) S2 H2 H2/Q21-2 0.300 1500.00 119.75 0.01040 15.61 0.132-1 0.400 900.00 336.25 0.01734 -15.61 0.05

0.00000 0.18

Page 20: PD4. Problema 4. Hardy Cross

Q1-28.48 121.52-28.48 334.48

Q1-1.76 119.76-1.76 336.24

Q2-0.01 119.75-0.01 336.25

456.00

Q30.00 119.75 Solución0.00 336.25

456.00

ΔQo

ΔQ

ΔQ1

ΔQ2

Page 21: PD4. Problema 4. Hardy Cross

CIRCUITO TRAMO D (m) L (m) Qo (l/s)

I

A-B 0.500 900 0.160B-E 0.400 1200 0.040E-F 0.400 900 0.080F-A 0.600 1200 0.240

II

B-C 0.500 900 0.120C-D 0.400 1200 0.080D-E 0.300 900 0.060E-B 0.400 1200 0.040

III

F-E 0.400 900 0.080E-H 0.300 1200 0.040H-G 0.400 900 0.080G-F 0.400 1200 0.160

IV

E-D 0.300 900.00 0.060D-I 0.300 1200.00 0.040I-H 0.300 900.00 0.040H-E 0.300 1200.00 0.040

CIRCUITO TRAMO D (m) L (m) Qo (l/s)

I

A-B 0.500 900 0.173B-E 0.400 1200 0.053E-F 0.400 900 0.067F-A 0.600 1200 0.227

II

B-C 0.500 900 0.125C-D 0.400 1200 0.085D-E 0.300 900 0.055E-B 0.400 1200 0.035

III

F-E 0.400 900 0.099E-H 0.300 1200 0.059H-G 0.400 900 0.061G-F 0.400 1200 0.141

IV

E-D 0.300 900.00 0.055D-I 0.300 1200.00 0.035I-H 0.300 900.00 0.045H-E 0.300 1200.00 0.045

CIRCUITO TRAMO D (m) L (m) Qo (l/s)

I

A-B 0.500 900 0.160

Page 22: PD4. Problema 4. Hardy Cross

IB-E 0.400 1200 0.040E-F 0.400 900 0.080F-A 0.600 1200 0.240

II

B-C 0.500 900 0.120C-D 0.400 1200 0.080D-E 0.300 900 0.060E-B 0.400 1200 0.040

III

F-E 0.400 900 0.080E-H 0.300 1200 0.040H-G 0.400 900 0.080G-F 0.400 1200 0.160

IV

E-D 0.300 900.00 0.060D-I 0.300 1200.00 0.040I-H 0.300 900.00 0.040H-E 0.300 1200.00 0.040

CIRCUITO TRAMO D (m) L (m) Qo (l/s)

I

A-B 0.500 900 0.173B-E 0.400 1200 0.053E-F 0.400 900 0.067F-A 0.600 1200 0.227

II

B-C 0.500 900 0.125C-D 0.400 1200 0.085D-E 0.300 900 0.055E-B 0.400 1200 0.035

III

F-E 0.400 900 0.099E-H 0.300 1200 0.059H-G 0.400 900 0.061G-F 0.400 1200 0.141

IV

E-D 0.300 900.00 0.055D-I 0.300 1200.00 0.035I-H 0.300 900.00 0.045H-E 0.300 1200.00 0.045

CIRCUITO TRAMO D (m) L (m) Qo (l/s)

I

A-B 0.500 900 0.172B-E 0.400 1200 0.053E-F 0.400 900 0.067F-A 0.600 1200 0.227

II

B-C 0.500 900 0.125C-D 0.400 1200 0.085

Page 23: PD4. Problema 4. Hardy Cross

IID-E 0.300 900 0.055E-B 0.400 1200 0.035

III

F-E 0.400 900 0.099E-H 0.300 1200 0.059H-G 0.400 900 0.061G-F 0.400 1200 0.141

IV

E-D 0.300 900.00 0.055D-I 0.300 1200.00 0.035I-H 0.300 900.00 0.045H-E 0.300 1200.00 0.045

Page 24: PD4. Problema 4. Hardy Cross

So Ho Ho/Qo Q10.00207 1.86 11.65 0.01271 0.172710.00047 0.57 14.14 0.01271 0.05271-0.00170 -1.53 19.15 0.01271 0.06729-0.00181 -2.17 9.03 0.01271 0.22729

-1.27 53.980.00122 1.09 9.12 0.00532 0.125320.00170 2.04 25.53 0.00532 0.085320.00406 -3.65 60.83 0.00532 0.054680.00047 -0.57 14.14 0.00532 0.03468

-1.08 109.62

0.00170 1.53 19.15 0.01935 0.099350.00191 2.30 57.42 0.01935 0.059350.00170 -1.53 19.15 0.01935 0.060650.00614 -7.37 46.07 0.01935 0.14065

-5.07 141.780.00406 3.65 60.83 -0.00476 0.055240.00191 2.30 57.42 -0.00476 0.035240.00191 -1.72 43.07 -0.00476 0.044760.00191 -2.30 57.42 -0.00476 0.04476

1.93 218.74So Ho Ho/Qo Q1

0.00239 2.15 12.44 -0.00019 0.172520.00079 0.94 17.89 -0.00019 0.05252-0.00124 -1.11 16.52 -0.00019 0.06748-0.00163 -1.96 8.62 -0.00019 0.22748

0.02 55.480.00132 1.19 9.47 0.00011 0.125430.00192 2.30 26.97 0.00011 0.085430.00341 -3.07 56.21 0.00011 0.054570.00036 -0.43 12.52 0.00011 0.03457

-0.02 105.16

0.00254 2.29 23.03 -0.00113 0.098220.00397 4.77 80.36 -0.00113 0.058220.00102 -0.92 15.12 -0.00113 0.061780.00484 -5.81 41.28 -0.00113 0.14178

0.33 159.790.00348 3.13 56.70 0.00000 0.055240.00151 1.82 51.55 0.00000 0.035240.00236 -2.12 47.39 0.00000 0.044760.00236 -2.83 63.19 0.00000 0.04476

0.00 218.83So Ho Ho/Qo Q1

0.00207 1.86 11.65 0.01271 0.17271

ΔQo

ΔQo

ΔQo

Page 25: PD4. Problema 4. Hardy Cross

0.00047 0.57 14.14 0.01271 0.05271-0.00170 -1.53 19.15 0.01271 0.06729-0.00181 -2.17 9.03 0.01271 0.22729

-1.27 53.980.00122 1.09 9.12 0.00532 0.125320.00170 2.04 25.53 0.00532 0.085320.00406 -3.65 60.83 0.00532 0.054680.00047 -0.57 14.14 0.00532 0.03468

-1.08 109.62

0.00170 1.53 19.15 0.01935 0.099350.00191 2.30 57.42 0.01935 0.059350.00170 -1.53 19.15 0.01935 0.060650.00614 -7.37 46.07 0.01935 0.14065

-5.07 141.780.00406 3.65 60.83 -0.00476 0.055240.00191 2.30 57.42 -0.00476 0.035240.00191 -1.72 43.07 -0.00476 0.044760.00191 -2.30 57.42 -0.00476 0.04476

1.93 218.74So Ho Ho/Qo Q1

0.00238 2.14 12.43 -0.00015 0.172370.00079 0.94 17.89 -0.00015 0.05256-0.00124 -1.11 16.52 -0.00015 0.06744-0.00163 -1.96 8.62 -0.00015 0.22744

0.02 55.460.00132 1.19 9.47 0.00000 0.125430.00192 2.31 27.00 0.00000 0.085430.00340 -3.06 56.11 0.00000 0.054570.00036 -0.43 12.49 0.00000 0.03457

0.00 105.07

0.00254 2.29 23.03 -0.00113 0.098220.00397 4.77 80.36 -0.00113 0.058220.00102 -0.92 15.12 -0.00113 0.061780.00484 -5.81 41.28 -0.00113 0.14178

0.33 159.790.00348 3.13 56.70 0.00000 0.055240.00151 1.82 51.55 0.00000 0.035240.00236 -2.12 47.39 0.00000 0.044760.00236 -2.83 63.19 0.00000 0.04476

0.00 218.83So Ho Ho/Qo Q1

0.00238 2.14 12.42 0.00000 0.172370.00078 0.94 17.85 0.00000 0.05256-0.00124 -1.12 16.55 0.00000 0.06744-0.00164 -1.96 8.63 0.00000 0.22744

0.00 55.450.00132 1.19 9.47 0.00000 0.125430.00192 2.31 27.00 0.00000 0.08543

ΔQo

ΔQo

Page 26: PD4. Problema 4. Hardy Cross

0.00340 -3.06 56.11 0.00000 0.054570.00036 -0.43 12.49 0.00000 0.03457

0.00 105.07

0.00254 2.29 23.03 -0.00113 0.098220.00397 4.77 80.36 -0.00113 0.058220.00102 -0.92 15.12 -0.00113 0.061780.00484 -5.81 41.28 -0.00113 0.14178

0.33 159.790.00348 3.13 56.70 0.00000 0.055240.00151 1.82 51.55 0.00000 0.035240.00236 -2.12 47.39 0.00000 0.044760.00236 -2.83 63.19 0.00000 0.04476

0.00 218.83


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