Air hose and line sizing.
A tool that will not do its job is often being starved by the hose feeding it. Enter the air the tool needs and the run it is on, and see what the line costs you - and what a different bore would do instead.
What this assumes
- The loss is calculated from first principles - Darcy-Weisbach with a Swamee-Jain friction factor - rather than from a tabulated formula, so every quantity in it is a stated physical value rather than a constant that is easy to reproduce wrongly.
- Free air is air measured at atmospheric pressure, which is how a compressor is rated. Compressed into the line it takes up less room, and the calculation accounts for that.
- A hose wall roughness of 0.03 mm is assumed, which suits smooth-bore rubber. A coiled, corrugated or aged hose is worse.
- This is the straight hose only. Couplers, quick-release fittings, filters, regulators and bends each add loss of their own, and a poor quick-coupler can cost more than the hose does.
- Air density is treated as constant along the run. That holds while the loss is a modest share of the supply pressure, and the result says so when it is not.