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

4 appVersion 0.99.7739.40423

t.0 0 time :

Assumed pipe flows also shown

Note:: Common Pipes

LOOP 1 has 2 coorections,

LOOP 2 has 1 correction.

LOOP 3 has 1 corrections

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n.13 Δq2 ≡

n.14 Δq3 ≡

n.21 Δq1 ≡

n.31 Δq1 ≡

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

Darcy-Weisbach 'n' n 2 :

Kinematic Viscosity of water ν 1.13 106 -^* m 2^s / * :

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 53.56 50 - 100.78 13.8 - 41 mat L s / * :

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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 * :

Ks: LOOP 1 Ks1 0.00005 0.00005 0.00005 0.00005 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 * :

Ks: LOOP 2 Ks2 0.00005 0.00003 0.00003 0.00003 41 mat m * :

Lengths LOOP 3 L3 20001000750220041 mat m * :

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

Ks: LOOP 3 Ks3 0.00005 0.00003 0.00003 0.00003 41 mat m * :

Ks = Pipe's effective roughness height (m)
Ks/D = Relative roughness (number)

q L# D# ks# Calc_Param V# q π 4 / D# 2^* / (vectorize : Re# V# D# * ν / (abs vectorize : λ 0.0055 12104^* ks# D# / * 106^Re# / + (13 /^+ (* vectorize : h.f 8 λ * L# * q * q abs n 1 -^* g.e D# (5^* π 2^* / vectorize : hf_q h.f q / abs vectorize : dq h.f sum n hf_q sum (* / - : 61 line :

Pipe velocity

Reynold number

Apprx. Colebrook Formula

Head loss

Correction to the LOOP

Loop 1 Correction Z1 Q1 11 mat L1 11 mat D1 11 mat Ks1 11 mat Calc_Param vectorize : L s / 6.162 - 11 mat

Loop 2 Correction Z2 Q2 11 mat L2 11 mat D2 11 mat Ks2 11 mat Calc_Param vectorize : L s / 55.3262 - 11 mat

Loop 3 Correction Z3 Q3 11 mat L3 11 mat D3 11 mat Ks3 11 mat Calc_Param vectorize : L s / 25.3484 - 11 mat

PROGRAM 2: Calculates 'Corrected Flows' & 'Corrections' CALLS PROGRAM 1 q1 q2 q3 Calc_All_Param Find first corrections for all 3 LOOPS Δq q1 q2 q3 31 mat L1 L2 L3 31 mat D1 D2 D3 31 mat Ks1 Ks2 Ks3 31 mat Calc_Param vectorize : Apply first correction to all pipes in 3 LOOPS q1.cor q1 Δq 1 el + : q2.cor q2 Δq 2 el + : q3.cor q3 Δq 3 el + : LOOP1/Pipe3 gets 2nd correction from LOOP2 (Δq2) q1.cor 3 el q1.cor 3 el Δq 2 el - (: LOOP1/Pipe4 gets 2nd correction from LOOP3 (Δq3) q1.cor 4 el q1.cor 4 el Δq 3 el - (: LOOP2/Pipe1 gets 2nd correction from LOOP1 (Δq1) q2.cor 1 el q2.cor 1 el Δq 1 el - (: LOOP3/Pipe1 gets 2nd correction from LOOP1 (Δq1) q3.cor 1 el q3.cor 1 el Δq 1 el - (: q1.cor q2.cor q3.cor 31 mat Δq 12 mat 151 line :

TRIAL 1 Tr1 Q1 Q2 Q3 Calc_All_Param 1 el :

TRIAL 2 Tr2 Tr1 1 el Tr1 2 el Tr1 3 el Calc_All_Param 1 el :

TRIAL 3 Tr3 Tr2 1 el Tr2 2 el Tr2 3 el Calc_All_Param 1 el :

TRIAL 4 Tr4 Tr3 1 el Tr3 2 el Tr3 3 el Calc_All_Param 1 el :

Tr1 L s / 109.722 - 193.838 89.1643 34.3736 - 41 mat 89.1643 - 104.6738 48.1062 - 48.1062 - 41 mat 34.3736 75.3484 - 75.4316 39.1484 - 41 mat 31 mat

Tr2 L s / 133.903 - 169.657 62.201 54.7411 - 41 mat 62.201 - 107.456 45.324 - 45.324 - 41 mat 54.7411 79.1619 - 71.6181 42.9619 - 41 mat 31 mat

Tr3 L s / 135.2682 - 168.2918 63.5978 48.5462 - 41 mat 63.5978 - 104.694 48.086 - 48.086 - 41 mat 48.5462 86.7219 - 64.0581 50.5219 - 41 mat 31 mat

Tr4 L s / 139.2824 - 164.2776 59.8766 51.5065 - 41 mat 59.8766 - 104.401 48.379 - 48.379 - 41 mat 51.5065 87.7759 - 63.0041 51.5759 - 41 mat 31 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_Param : 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_Param : if 11 line for P iter el 21 line :

Using 10 iterations - PROGRAM 3 Q.10 Q1 Q2 Q3 10 Q :

METHOD 3: Hardy Cross Method: Using While Loop

PROGRAM 4: Using 'While' loop : CALLS PROHRAM 2 q1 q2 q3 Z B q1 q2 q3 Calc_All_Param : ΔQ B 2 el : qq1 B 1 el 1 el : qq2 B 1 el 2 el : qq3 B 1 el 3 el : Δ 0.05 L s / * : ΔQ 1 el abs Δ ≥ (ΔQ 2 el abs Δ ≥ (ΔQ 3 el abs Δ ≥ (| (| B qq1 qq2 qq3 Calc_All_Param : -------------------------------- -------------------------------- qq1 B 1 el 1 el : qq2 B 1 el 2 el : qq3 B 1 el 3 el : ΔQ B 2 el : 71 line while B 81 line :

Using "while" LOOP - PROGRAM 4 Accuracy 0.05 L/s Q.W Q1 Q2 Q3 Z :

RESULTS

Using "while" LOOP - PROGRAM 4 Accuracy 0.05 L/s Q.W L s / 141.2318 - 162.3282 58.5899 51.2061 - 41 mat 58.5899 - 103.7384 49.0416 - 49.0416 - 41 mat 51.2061 90.0257 - 60.7543 53.8257 - 41 mat 31 mat 0.0324 - 0.0066 - 0.0238 - 31 mat 12 mat

Using 10 iterations - PROGRAM 3 Q.10 L s / 141.2318 - 162.3282 58.5899 51.2061 - 41 mat 58.5899 - 103.7384 49.0416 - 49.0416 - 41 mat 51.2061 90.0257 - 60.7543 53.8257 - 41 mat 31 mat 0.0324 - 0.0066 - 0.0238 - 31 mat 12 mat

Compare

Q.10 1 el L s / 141.23 - 162.33 58.59 51.21 - 41 mat 58.59 - 103.74 49.04 - 49.04 - 41 mat 51.21 90.03 - 60.75 53.83 - 41 mat 31 mat

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Note:: Common Pipes

LOOP 1 has 2 coorections.

LOOP 2 has 1 correction.,

LOOP 3 has 1 corrections

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Link to Original Excel File

https://drive.google.com/file/d/0B29kBjmISsLMeEdCSVFHcHZBODQ/edit

Link to VIDEO Example

https://www.youtube.com/watch?app=desktop&v=M8f1FNgeq7o&ab_channel=TM%27sChannel