Example 2 :

Calculate the head losses and the corrected flows in the various pipes of a distributed network shown in fig. 20.6. The diameters and the lengths of the pipes used are given against each pipe. Make se of Hardy-cross method with Hazen-William's formula. Compute the corrected flows after two corrections.

Solution:

First of all the magnitudes as well as the directions of the possible flows in each pipe are assumed keeping in consideration the law of continuity at each junction (i.e., input equals the output at each junction). These assumed flows aare shown in fig. 20.7. The twon closed loops ie. ABCDA and DCFED are then analysed by Hardy-Cross method.

Flow into Node: +ve
Flow out of Node: -ve

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

For Darcy-Weisbach: n = 2

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

METHOD 1: Hardy Cross Method using Successive Steps of Corrections

PROGRAM 1 starts with assumed flow for both LOOPS

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

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

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

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

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

Now Apply 1st Correction for Pipe CD common to both loops

2nd correction (Starts with flows in correction 1)

Now Apply 2nd Correction for Pipe CD common to both loops

3rd correction (Starts with flows in correction 2)

Now Apply 3rd Correction for Pipe CD common to both loops

OK

Calculated Flows - After 3 Corrections

From Book Example - After 2 Corrections

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

Solution by Repeated Iteration Method using PROGRAM 2

1st column shows FINAL flows in LOOPS 1 & 2. The 2 nd column shows FINAL Corrections after 3 Iterations

Compare

METHOD 3: Hardy Cross Method: Using While Loop

Results from Different Methods

Successive Steps

Method 1
Since only 3 steps are used, results are slightly different from Methods 2 & 3