A simple pipe-run estimate
The Atlas Copco empirical equation is Δp = 450 × q1.85 × L ÷ (d5 × p). It gives loss in bar when q is FAD in L/s, L is total equivalent length in metres, d is internal diameter in mm and p is inlet absolute pressure in bar.
This calculator fixes atmospheric pressure at 1.01325 bar and adds it to your gauge input. Flow must be free air delivery, not the smaller volume moving through the pressurised line. Add only fittings equivalent lengths you already know; the calculator supplies no elbow multipliers.
Worked example: an 80 mm pipe
At 140 L/s FAD, 33.4 m total length, 80 mm internal diameter and 8 bar absolute inlet pressure, the estimated loss is about 0.005355 bar. With the fixed atmosphere assumption, the inlet is 6.98675 bar gauge and the downstream estimate is about 6.98140 bar gauge.
Where this estimate stops
Use this for an approximate normal workshop compressed-air pipe run. It does not model roughness, temperature, unusual gases, hoses, filters, dryers or ring networks. A zero-flow result has zero friction loss in this equation; it does not describe pressure losses elsewhere.
The calculator withholds results above 10% of initial absolute pressure or where the outlet would be below zero gauge pressure. This is a conservative calculator guardrail, not a published validity limit for the equation. Separately, a loss above 0.1 bar triggers a warning against the manual’s guideline for the complete fixed pipe installation; this is not a legal or universal pass/fail threshold. Consider a larger bore or an engineering assessment. Recalculate with another known internal diameter to compare the same run.
Air velocity at the pipe’s upstream end
Convert FAD to m³/s, then multiply by reference absolute pressure ÷ inlet absolute pressure to estimate the actual inlet volume flow. Divide by the pipe area π × internal diameter² ÷ 4 in m² for inlet velocity in m/s. Inlet absolute pressure is your gauge input plus the fixed 1.01325 bar atmosphere.
This is an ideal-air continuity extension: inlet and reference air temperatures are equal and compressibility-factor differences are neglected. The inlet means the pipe’s upstream end, not the compressor intake. It is not an average or outlet velocity. Hotter air than the reference or pressure loss along a pipe can make actual velocity higher. It supplies no universal velocity threshold or design approval; the pressure-loss inputs are unused in this mode.
Worked example: air velocity at the pipe’s upstream end
At 6,000 L/min FAD (100 L/s), 50 mm bore, 6.98675 bar gauge (8 bar absolute) and 1.01325 bar absolute flow reference, the actual inlet flow is 0.012665625 m³/s. Dividing by the bore area gives 6.450549844 m/s.