Here's the "SCADA Leak Detection method.
I will describe the graphic method, you can do the same analytically if you like. With a 5 mile 60", the analytic solution will be better, because otherwise you will be graphically trying to find the intersecting point of two relatively flat lines and its easy to err.
[COLOR=black yellow]At both the beginning and end of the pipeline you must know the flow and the pressure.[/color]
You figure you have a leak, when the two flowrates do not match, now you must estimate where it is.
The accuracy of the solution depends on the accuracy of your flowrate measurements and any transient pressures in the line will give a lot of "noise" to the data that must be filtered out.
Make a profile drawing of the pipeline to scale.
Calculate the total head at the beginning of the pipeline. Here I will assume it equals 300 feet, or around 130 psig if you have water in the line.
Calculate the head loss using a good head loss equation, (Hazen-Williams, Colebrook, or Churchill, etc.) for your pipeline. I assume here that it equals 10 feet/mile of pipeline.
Go to the pipeline profile plot and put a point 300 feet (or whatever your beginning head equals) above the beginning of the pipeline.
From that point draw a line towards the end of the pipeline with a slope equal to your beginning head loss/mile.
Take the outlet head and the flowrate at the end of your pipeline and calculate the head loss/mile there. Here I assume head is 240 feet and head loss/mile is 9 feet/mile.
Go to the plot and put a point 240 feet above the end of the pipeline and draw a line towards the beginning of the pipeline with an upward slope to the left of 9 feet/mile.
Your leak will be located (theoretically) at the intersection of the two head loss lines.
/300 ft
* leak at intersection
| * /
| *O* lne from pipeline end
| | * * <- 9ft/mi
| V * * 240 ft
| | -10ft/mi->* *
| | line from * |
| | beginning of pl * |
+------V-------+-------+-------+--------+
0mi 1mi 2mi 3mi 4mi 5mi
\
leak located at 1 mile
Going the Big Inch!