Pipe Rust Volume Formula

I need a mechanically minded engineer who is comfortable turning field data into a clean, reproducible formula that tells me one thing: the volume of rust that exists inside a corroded steel pipe, expressed per metre (or foot) of run.

All the raw information is already on my desk—pipe dimensions, measured wall-thickness loss, historical corrosion-rate records, plus photos and scan data—so you can dive straight into modelling rather than hunting for numbers. Your job is to translate those figures into one or more transparent calculations I can drop into a spreadsheet, Python script, or even a hand-calc sheet.

I’m looking for:

• A clear derivation of the governing equation(s) with assumptions spelled out
• A sample calculation using dummy data so I can see each step
• Guidance on any limits of applicability (for instance, minimum data quality or geometry constraints)

Accuracy matters more than polish; if you lean on solid geometry, differential volume elements, or corrosion-rate conversions, please show the math so I can audit it later. If there’s more than one valid approach, feel free to include alternatives with notes on when each is preferable.

I’ll supply the complete dataset once we agree on scope.