Utility & Power Quality
Loss falls with the fifth power of diameter. One pipe size up cuts it roughly threefold.
— bar
Lost to friction between compressor and machines
Density is taken at the working pressure and held constant along the run, which is the standard incompressible approximation and stays reasonable while the drop is a small fraction of absolute pressure — above roughly 10% it understates the loss and a compressible treatment is needed. Velocity above about 9 m/s in a main is the practical design ceiling regardless of what the pressure drop says, because velocity carries condensate and noise with it. Fittings equivalent length is where most estimates go wrong: a single poorly chosen valve or a run of tight elbows can exceed the straight pipe, and it should be built up item by item rather than guessed.
Textile Compressed Air Pipe Network Pressure Drop Modeler — free, with the formula and a worked example, at Textile School.