Hardy-Cross Tutorial

Hardy-Cross Pipe Network Tutorial

This program is intended as an introduction to the Hardy-Cross method of analyzing simple pipe networks. The Hardy-Cross method consists of the following procedure:

    - Number each of the various loops

    - Assume a flow direction (clockwise = positive ; counterclockwise = negative)

    and assume an initial flow through each pipe.

    - Calculate the head loss in each loop. Use the same sign convention as above.

    - Check the closure of loop by summing head losses of all pipes in loop.

    - Calculate flow corrections to improve headloss closure.

    - Repeat process until head losses converge to desired accuracy.

Consider the following system:(See Figure A)

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What is the first step? Should you:

Determine flow direction

Number each loop

Assume an initial flow

Balance flows at each junction?

Now...is the second step to:

Calculate head loss

Make an initial guess of roughness factors

Determine equivalent slope for the system

Assume an initial flow and flow direction?

***Step 2 is the assumption of flows and their directions. Take a look at junction A. (See Figure B)

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Using common sense, which of the following holds true?

As you can see, having assumed initial flows and directions (step 2), inflow must equal outflow for each junction, and therefore, (4) is correct.

Now...Step 3 gets a bit more difficult. Head losses are calculated with the Hazen-Williams formula:

Once the head losses are calculated for each pipe, do you remember just what comes next?

Check closure by summing h for each loop

Sum roughness coefficients for all pipes

Calculate correction factor

Re-initialize flows?

To do this, the calculated head losses are summed for each loop.

You're close enough! But...

For our example,

Does the sum of the heads for Loop I =:

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AB - BC - AC

AB + BC - AC

AC + BC + AB

AB + AC - BC


Now try this one:

Does the sum of the heads for Loop II =:

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BD - CD - BC

BD + BC - CD

BD + CD + BC

CD + BD - BC


If the heads do not close to within 1.0, the flows must be adjusted and the head losses recalculated until closure is attained.

The correction used is as follows:

The final flows and directions as calculated for this example with the Hardy-Cross method are found in figure D(Answer diagram).

For an alternate method of solving pipe flow problems, the user is referred to the WDNALIN program.

Presented on the WWW by Rick Clarkson & Jenna Mulligan