Hardy-Cross Tutorial
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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)

### Pipe AB: L = 2000 ft. Diameter = 8 in.

### Pipe BC: L = 4000 ft. Diameter = 8 in.

### Pipe CD: L = 2000 ft. Diameter = 8 in.

### Pipe BD: L = 2000 ft. Diameter = 6 in.

### Pipe AD: L = 4000 ft. Diameter = 10 in.

### Click here to view figures!

### 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) ### Click here to view figures!

### 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:

### h = L*Q^1.85/17,076*C^1.85*D^4.87

### h = headloss, feet

### L = pipe length, feet

### C = roughness coefficient

### D = pipe diameter, feet

### Q = flow, gallons per minute

### 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.

### If each loop sums to less than one foot, that is:

### If sum of h < 1.0 ft

### You're close enough! But...

### If the sum of the head losses are greater than one foot, then you must calculate and apply a correction factor,q, until head losses total less than one foot. This may mean LOTS of iterations!

### For our example,

### AB - BC - AC

### AB + BC - AC

### AC + BC + AB

### AB + AC - BC

### **REMEMBER THE SIGN CONVENTION**

### Now try this one:

### Does the sum of the heads for Loop II =: ### Click here to view figures!

### BD - CD - BC

### BD + BC - CD

### BD + CD + BC

### CD + BD - BC

### **REMEMBER THE SIGN CONVENTION**

### 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:

### Correction factor q = -H/sigma A

### where: H = sum of the head losses for loop

### A = 1.85*h/Q for a particular loop

### sigma A = sum total of A in loop

### 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