Generations of low- and medium-pressure networks were sized with this correlation. Where it comes from, where it holds, and what happens at its boundaries.
The Renouard formula is the classic empirical correlation of Italian and Spanish practice for pressure losses in gas networks. In its medium-pressure form:
with absolute pressures in bar, s the gas relative density, L in km, Q in Sm³/h and D in mm (a linearised variant exists for low pressure). Its success is deserved: no iterations, no friction factor to solve — a single line of arithmetic, perfect for the age of the slide rule and the lookup table.
That simplicity has a price, declared from the start: the correlation models smooth pipes in turbulent flow, with the friction «baked into» the non-integer exponents, and it is valid for Q/D ≤ 150 (flow in Sm³/h, diameter in mm). The constraint is not red tape: beyond that ratio the real flow regime drifts away from the one the exponents were fitted on, and the formula underestimates the drops — that is, it turns non-conservative exactly where prudence would matter.
Comparing Renouard with the general flow equation — Colebrook-White friction computed on the pipe's real roughness — at the Reynolds numbers typical of distribution, the picture is:
These deviations are not an opinion: they are measured and published, case by case, in the Gasnetics validation dossier, and pinned by the engine's regression tests.
The general equation of steady isothermal compressible flow,
with f from Colebrook-White on the real roughness and z from the mixture's compressibility, holds from low pressure to transmission mains with the same explicit assumptions. The Q/D constraint lapses (the physics is valid at any load) and the design guard remains the velocity limits. It requires an iteration for f and z — trivial work for a computer, unthinkable for a slide rule: the historical reason Renouard existed, and the technical reason it is no longer needed.
The medium-pressure form holds for smooth pipes in turbulent flow with Q/D ≤ 150 (flow in Sm³/h, diameter in mm). Outside that domain the correlation underestimates the pressure drops, markedly so: that is why the constraint existed.
Compared with the general flow equation with Colebrook-White friction at the Reynolds numbers typical of distribution, inside its domain Renouard turns out 15–19% more conservative: its coefficient embeds historic margins and roundings.
It is a correlation consolidated by practice and remains legitimate inside its domain; its margin however is implicit and undeclared, and outside the domain it becomes non-conservative. A general law with friction on the real roughness gives the same physical result across the whole pressure range, with explicit assumptions.