Dia-Inch for Welding is used for Estimates of Piping & Inch-Meter is used for Erection estimates of Piping.
Welding estimates are based on the length of the weld. With a little bit of minipulation of the terms, you can convert linear-weld-inches (which is circumference of the pipe) to diameter-inches (so if it costs $60/linear-inch then it is $188.50/diameter-inch). This is just a convienient way for welding shops to bid pipeline jobs (i.e. a 10 mile job using double random joints in 12-inch has nearly 900 welds, so at $60/inch or $188.50/diameter inch the job should be bid around $2.04 million since the $/inch number should include their direct and indirect costs plus profit).
Inch-meter (or inch-mile in the states) is the all-in cost of laying pipe (includes the welding above, but it also includes trenching, field wraping welds, buying the pipe, mobilization, ROW, engineering, surveying, and inspection). In the 10 mile job above, if the estimating parameter is $45/in-mile then the all in costs for budget would be $5.4 million.
This number varies widely from company to company and is often very confidential. We use this number for budgetary purposes, NEVER for joint-interest authorization for expenditures.