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Example: Network Analysis by Hardy-Cross Method - With 3 LOOPS

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Index of common pipes in LOOPS

Index of EG in LOOP 1 n1 3 :

Index of GE in LOOP 2 n2 1 :

Index of GF in LOOP 1 n3 4 :

Index of FG in LOOP 3 n4 2 :

Flows at Nodes QJ 303.56 152.78 - 114.58 - 36.2 - 41 mat L s / * :

Continuity of the whole network. Sum of Nodal flows should be zero QJ sum 0

Friction Factor f 0.02 :

Hazen William 'n' n 1.85 :

Flows in LOOPS should be balanced first to start with. Otherwise, will yield wrong answers

Assumed Flows forContinuity in LOOP 1 Q1 103.56 - 20040 53.56 - 41 mat L s / * :

Assumed Flows forContinuity in LOOP 2 Q2 40 - 160 7.22 7.22 41 mat L s / * :

Assumed Flows forContinuity in LOOP 3 Q3 50 - 53.56 100.78 13.8 - 41 mat L s / * :

1

3

5

2

8

4

3

9

6

4

10

7

Friction Factor f 0.02 :

Flows in LOOPS Sign Convention
1. Clockwise: +ve
2. Anticlockwise: -ve

Lengths LOOP 1 L1 100020001000200041 mat m * :

Dia. LOOP 1 D1 0.4 0.45 0.30 0.30 41 mat m * :

Lengths LOOP 2 L2 10002000500220041 mat m * :

Dia. LOOP 2 D2 0.3 0.3 0.25 0.25 41 mat m * :

Lengths LOOP 3 L3 10002000750220041 mat m * :

Dia. LOOP 3 D3 0.4 0.3 0.3 0.3 41 mat m * :

METHOD 1: Hardy Cross Method using Successive Steps of Corrections

PROGRAM 1 starts with assumed flow for both LOOPS

Program 1: Using Vectorize Function. Find 'Corrected Flow' for the 3 LOOPS Q# L# D# Calc_ΔQ# k# 8 f * L# * g.e D# (5^* π 2^* / vectorize : HL# k# Q# * Q# abs (n 1 -^* vectorize : δHL# HL# Q# / abs vectorize : ΔQ# HL# sum n δHL# sum (* / - : 41 line :

<---------- K values for all pipes

<---------- Head Loss for all pipes

<---------- Net Head Loss

<---------- Corrections for 3 LOOPS .
To be minimized with successive steps

1st correction (Starts with assumed flows in both LOOPS)

ΔQQ Q1 Q2 Q3 31 mat L1 L2 L3 31 mat D1 D2 D3 31 mat Calc_ΔQ# vectorize : L s / 5.73 - 60.28 - 27.75 - 31 mat

ΔQQ 1 el L s / 5.73 -

ΔQQ 2 el L s / 60.28 -

ΔQQ 3 el L s / 27.75 -

1st Corrected flows in LOOP 1 QQ1.cor1 Q1 ΔQQ 1 el + : L s / 109.29 - 194.27 34.27 59.29 - 41 mat

1st Corrected flows in LOOP 2 QQ2.cor1 Q2 ΔQQ 2 el + : L s / 100.28 - 99.72 53.06 - 53.06 - 41 mat

1st Corrected flows in LOOP 3 QQ3.cor1 Q3 ΔQQ 3 el + : L s / 77.75 - 25.81 73.03 41.55 - 41 mat

Now Apply 1st Correction for Pipe GE common to loops 1 & 2

Adjusted flow for Pipe EG in LOOP 1 ΔHL1 QQ1.cor1 3 el ΔQQ 2 el - : L s / 94.55

Adjusted flow for Pipe GE in LOOP 2 QQ2.cor1 1 el ΔHL1 :

QQ1.cor1 3 el L s / 34.265

QQ1.cor1 3 el ΔHL1 :

QQ1.cor1 L s / 109.29 - 194.27 94.55 59.29 - 41 mat

QQ2.cor1 L s / 94.55 99.72 53.06 - 53.06 - 41 mat

Now Apply 1st Correction for Pipe GE common to loops 1 & 3

Adjusted flow for Pipe GF in LOOP 1 ΔHL2 QQ3.cor1 4 el ΔQQ 3 el - : L s / 13.8 -

QQ3.cor1 2 el ΔHL2 - :

QQ1.cor1 4 el ΔHL2 :

QQ3.cor1 2 el L s / 13.8

QQ1.cor1 L s / 109.29 - 194.27 94.55 13.8 - 41 mat

QQ2.cor1 L s / 94.55 99.72 53.06 - 53.06 - 41 mat

QQ3.cor1 L s / 77.75 - 13.8 73.03 41.55 - 41 mat

2nd correction (Starts with flows in correction 1)

ΔQQ2 QQ1.cor1 QQ2.cor1 QQ3.cor1 31 mat L1 L2 L3 31 mat D1 D2 D3 31 mat Calc_ΔQ# vectorize : L s / 38.88 - 6.38 - 2.77 31 mat

2nd Corrected flows in LOOP 1 QQ1.cor2 QQ1.cor1 ΔQQ2 1 el + : L s / 148.17 - 155.39 55.67 52.68 - 41 mat

2nd Corrected flows in LOOP 2 QQ2.cor2 QQ2.cor1 ΔQQ2 2 el + : L s / 88.16 93.34 59.44 - 59.44 - 41 mat

2nd Corrected flows in LOOP 3 QQ3.cor2 QQ3.cor1 ΔQQ2 3 el + : L s / 74.98 - 16.57 75.8 38.78 - 41 mat

Now Apply 2nd Correction for Pipe GE common to loops 1 & 2

Adjusted flow for Pipe EG in LOOP 1 ΔHL3 QQ1.cor2 3 el ΔQQ2 2 el - : L s / 62.05

Adjusted flow for Pipe GE in LOOP 2 QQ2.cor2 1 el ΔHL3 - :

QQ1.cor2 3 el L s / 55.67

QQ1.cor2 3 el ΔHL3 :

QQ1.cor2 L s / 148.17 - 155.39 62.05 52.68 - 41 mat

QQ2.cor2 L s / 62.05 - 93.34 59.44 - 59.44 - 41 mat

QQ3.cor2 L s / 74.98 - 16.57 75.8 38.78 - 41 mat

Now Apply 2nd Correction for Pipe GE common to loops 1 & 3

Adjusted flow for Pipe GF in LOOP 1 ΔHL4 QQ3.cor2 4 el ΔQQ2 3 el - : L s / 41.55 -

QQ3.cor2 2 el ΔHL4 - :

QQ3.cor2 2 el L s / 41.5465

QQ1.cor2 4 el ΔHL4 :

QQ1.cor2 L s / 148.17 - 155.39 62.05 41.55 - 41 mat

QQ2.cor2 L s / 62.05 - 93.34 59.44 - 59.44 - 41 mat

QQ3.cor2 L s / 74.98 - 41.55 75.8 38.78 - 41 mat

3rd correction (Starts with flows in correction 1)

ΔQQ3 QQ1.cor2 QQ2.cor2 QQ3.cor2 31 mat L1 L2 L3 31 mat D1 D2 D3 31 mat Calc_ΔQ# vectorize : L s / 2.87 - 9.59 6.43 - 31 mat

Similarlr, continue as above

PROGRAM 2: Calculates 'Corrected Flows' & 'Corrections' CALLS PROGRAM 1 q1 q2 q3 Calc_All_Δ Δq q1 q2 q3 31 mat L1 L2 L3 31 mat D1 D2 D3 31 mat Calc_ΔQ# vectorize : q1.cor q1 Δq 1 el + : q2.cor q2 Δq 2 el + : q3.cor q3 Δq 3 el + : Δcd1 q1.cor n1 el Δq 2 el - : q1.cor n1 el Δcd1 : q2.cor n2 el Δcd1 - : -------------------- Δcd2 q3.cor n3 el Δq 3 el - : q1.cor n3 el Δcd2 : q3.cor n4 el Δcd2 - : Δq.cor q1.cor q2.cor q3.cor 31 mat L1 L2 L3 31 mat D1 D2 D3 31 mat Calc_ΔQ# vectorize : q1.cor q2.cor q3.cor 31 mat Δq.cor 12 mat 131 line :

n1 3

n2 1

n3 4

n4 2

Corrections at start Q1 Q2 Q3 31 mat L1 L2 L3 31 mat D1 D2 D3 31 mat Calc_ΔQ# vectorize L s / 5.735 - 60.2804 - 27.7465 - 31 mat

After 1st correction X1 Q1 Q2 Q3 Calc_All_Δ : L s / 109.295 - 194.265 94.5454 13.8 - 41 mat 94.5454 - 99.7196 53.0604 - 53.0604 - 41 mat 77.7465 - 13.8 73.0335 41.5465 - 41 mat 31 mat 38.8794 - 7.8059 2.7664 31 mat 12 mat

QQ1.cor1 L s / 109.295 - 194.265 94.5454 13.8 - 41 mat

QQ2.cor1 L s / 94.5454 99.7196 53.0604 - 53.0604 - 41 mat

QQ3.cor1 L s / 77.7465 - 13.8 73.0335 41.5465 - 41 mat

After 2nd correction X2 X1 1 el 1 el X1 1 el 2 el X1 1 el 3 el Calc_All_Δ : L s / 148.1743 - 155.3857 47.8601 41.5465 - 41 mat 47.8601 - 107.5255 45.2545 - 45.2545 - 41 mat 74.9801 - 41.5465 75.7999 38.7801 - 41 mat 31 mat 0.8354 4.2791 - 6.4306 - 31 mat 12 mat

QQ1.cor2 L s / 148.1743 - 155.3857 62.0474 41.5465 - 41 mat

QQ2.cor2 L s / 62.0474 - 93.3383 59.4417 - 59.4417 - 41 mat

QQ3.cor2 L s / 74.9801 - 41.5465 75.7999 38.7801 - 41 mat

After 3rd correction X3 X2 1 el 1 el X2 1 el 2 el X2 1 el 3 el Calc_All_Δ : L s / 147.3389 - 156.2211 52.9747 38.7801 - 41 mat 52.9747 - 103.2464 49.5336 - 49.5336 - 41 mat 81.4108 - 38.7801 69.3692 45.2108 - 41 mat 31 mat 1.9015 - 0.1582 1.1582 - 31 mat 12 mat

METHOD 2: Hardy Cross Method: For Any Given Number of Iterations

PROGRAM 3: Repeated Iteration Method. CALLS PROGRAM 2 q1 q2 q3 iter Q j 1 iter range j 1 ≡ P j el q1 q2 q3 Calc_All_Δ : P j el P j 1 - el 1 el 1 el P j 1 - el 1 el 2 el P j 1 - el 1 el 3 el Calc_All_Δ : if 11 line for P iter el 21 line :

With 10 iterations Q1 Q2 Q3 10 Q L s / 140.68 - 162.88 58.93 53.02 - 41 mat 58.93 - 103.95 48.83 - 48.83 - 41 mat 89.82 - 53.02 60.96 53.62 - 41 mat 31 mat 0.84 0.1 0.5 - 31 mat 12 mat

With 20 iterations Q1 Q2 Q3 20 Q L s / 136.6 - 166.96 62.51 55.92 - 41 mat 62.51 - 104.45 48.33 - 48.33 - 41 mat 92.2 - 55.92 58.58 56 - 41 mat 31 mat 0.12 0.02 0.07 - 31 mat 12 mat

With 25 iterations Q1 Q2 Q3 25 Q L s / 136.17 - 167.39 62.89 56.22 - 41 mat 62.89 - 104.5 48.28 - 48.28 - 41 mat 92.45 - 56.22 58.33 56.25 - 41 mat 31 mat 0.05 0.01 0.03 - 31 mat 12 mat

With 30 iterations Q1 Q2 Q3 30 Q L s / 136 - 167.56 63.03 56.34 - 41 mat 63.03 - 104.52 48.26 - 48.26 - 41 mat 92.55 - 56.34 58.23 56.35 - 41 mat 31 mat 0.02 0 0.01 - 31 mat 12 mat

With 35 iterations Q1 Q2 Q3 35 Q L s / 135.94 - 167.62 63.09 56.38 - 41 mat 63.09 - 104.53 48.25 - 48.25 - 41 mat 92.59 - 56.38 58.19 56.39 - 41 mat 31 mat 0.01 0031 mat 12 mat

With 40 iterations Q1 Q2 Q3 40 Q L s / 135.91 - 167.65 63.11 56.4 - 41 mat 63.11 - 104.54 48.24 - 48.24 - 41 mat 92.6 - 56.4 58.18 56.4 - 41 mat 31 mat 00031 mat 12 mat

METHOD 3: Hardy Cross Method: Using While Loop

PROGRAM 4: Using 'While' loop : CALLS PROHRAM 2 q1 q2 q3 Z A q1 q2 q3 Calc_All_Δ : ΔQ A 2 el : qq1 A 1 el 1 el : qq2 A 1 el 2 el : qq3 A 1 el 3 el : Δ 0.001 L s / * : ΔQ 1 el abs Δ ≥ (ΔQ 2 el abs Δ ≥ (& (ΔQ 3 el abs Δ ≥ (& B qq1 qq2 qq3 Calc_All_Δ : qq1 B 1 el 1 el : qq2 B 1 el 2 el : qq3 B 1 el 3 el : ΔQ B 2 el : 51 line while B 81 line :

Using "while" LOOP - PROGRAM 4 Q1 Q2 Q3 Z L s / 135.94 - 167.62 63.09 56.38 - 41 mat 63.09 - 104.53 48.25 - 48.25 - 41 mat 92.59 - 56.38 58.19 56.39 - 41 mat 31 mat 0.01 0031 mat 12 mat

Using 35 iterations - PROGRAM 3 Q1 Q2 Q3 35 Q L s / 135.94 - 167.62 63.09 56.38 - 41 mat 63.09 - 104.53 48.25 - 48.25 - 41 mat 92.59 - 56.38 58.19 56.39 - 41 mat 31 mat 0.01 0031 mat 12 mat

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