Isothermal vs Adiabatic Gas Flow in Pipes
Liquids make pipe hydraulics easy: density is constant, so one pressure-drop equation covers everything. Gases don't extend that courtesy. A gas's density depends on its pressure, so as it flows down a pipe and loses pressure it expands and accelerates — and the further it goes, the faster the pressure falls. Model that with a constant-density (incompressible) method and the answer can be wrong by a little or by a lot, and the worst part is that nothing warns you: the calculation still "works".
This guide covers the three modelling levels for gas in pipes — incompressible, isothermal compressible, and adiabatic compressible — what each assumes, when each is valid, and how to choose.
When incompressible is good enough: the 10% rule
Compressibility only matters when the pressure changes enough to change the density. The widely used rule of thumb (Crane TP-410) grades it by the pressure drop as a fraction of inlet absolute pressure:
- ΔP < 10% of P₁ — density barely changes. An incompressible calculation with the gas density at either end is fine.
- ΔP between 10% and 40% of P₁ — incompressible is acceptable if you use the density at the average pressure; a compressible method is better.
- ΔP > 40% of P₁ — use a proper compressible method. Constant-density answers are no longer trustworthy.
Example. A compressed-air header at 7 bar g (≈ 8 bar absolute): incompressible sizing is fine as long as the header loses less than ~0.8 bar end to end — which a well-sized header should. But a blowdown line taking that same air down to atmosphere drops 87% of its absolute pressure, and is firmly in compressible territory.
Note both numbers are absolute pressures. A 0.5 bar drop on a 1 bar g line is a 33% drop of the 1.5 bar absolute inlet — borderline — not a "small" drop on a "1 bar" line.
What goes wrong when you ignore compressibility
As pressure falls along the pipe, the gas expands, so it must speed up to carry the same mass flow. Higher velocity means a steeper friction gradient, which drops the pressure faster, which expands the gas further. The pressure profile curves downward instead of falling linearly, and the error compounds toward the outlet.
An incompressible model misses all of this. It will happily converge and report a tidy answer — there's no error message, because mathematically nothing failed. We've seen this in the wild: a user modelled a compressed-air system on an incompressible solver and got a converged result that implied a 1.5 mm bore was adequate — physically nonsense, but numerically "successful". The result looked fine right up until the comparison with reality.
The fix is structural, not arithmetic: when the pressure ratio is significant, the model itself has to account for expansion. Compressible pipe-flow methods do that by working in terms of P₁² − P₂² rather than P₁ − P₂. In simplified form (long pipe, acceleration term small):
- — absolute pressures at inlet and outlet
- — friction factor, pipe length, bore, flow area
- — mass flow rate; — specific gas constant; — gas temperature
The squared-pressure form is what bends the profile correctly: a given friction loss "costs" more pressure at the low-pressure end of the pipe than at the high-pressure end.
That still leaves one question open — what happens to the gas temperature along the way? The two classical answers give the two compressible models.
The isothermal model: long lines at ambient
The isothermal model assumes the gas stays at constant temperature. That's a good description of most real distribution piping: flow is slow enough, and the pipe long and uninsulated enough, that heat exchange with the surroundings keeps the gas at ambient. It's the standard assumption for natural-gas transmission and distribution (the AGA pipeline equations are isothermal at heart) and for plant compressed-air mains.
Use isothermal when:
- the line is long relative to its diameter (headers, mains, site distribution),
- velocities are moderate (well below sonic),
- the pipe runs at roughly ambient temperature, uninsulated.
The adiabatic model: short, fast, insulated
The adiabatic model assumes no heat exchange — every joule stays in the gas. As the gas expands and accelerates, that energy comes out of its internal energy, so the temperature falls along the pipe (this is Fanno flow in the textbooks). The faster the flow, the stronger the effect.
Use adiabatic when:
- the line is short and the gas moves fast (relief and vent lines, blowdowns, compressor discharge stubs),
- the pipe is insulated, or the transit time is too short for meaningful heat exchange,
- you need the outlet temperature, not just the pressure — e.g. checking for condensation, material limits, or downstream equipment ratings.
The temperature drop matters in its own right: air let down through a large pressure ratio can come out tens of degrees colder, cold enough to freeze moisture or push elastomers out of spec.
Isothermal vs adiabatic: how different are the answers?
For pressure drop on long lines, often less different than you'd expect — a few percent — because most long lines are slow, and at low velocity the two models converge. That's why pipeline engineering settled on isothermal: it's simpler and accurate where pipelines actually operate.
The models diverge where velocity climbs: near-sonic flow, short high-ratio lines, and anywhere temperature itself is the question. There the adiabatic model is the physically faithful one — and the harder one to solve, since temperature becomes an extra unknown at every point along the line.
Choking: the hard ceiling
Both compressible models contain something the incompressible model cannot represent at all: choking. A gas can't be pushed through a pipe or restriction faster than the speed of sound at the throat. Once the flow chokes (at Mach 1 for adiabatic flow), lowering the downstream pressure further changes nothing upstream — the mass flow is capped, no matter how hard the downstream end "pulls".
If your sizing calculation implies a velocity anywhere near sonic, the result is invalid in an incompressible model and choked in a compressible one. Vent, relief, and blowdown lines live in this regime, which is one more reason they need the compressible treatment.
Sanity-check your boundary conditions first
One practical lesson from real users' models: when a compressible simulation refuses to converge, the cause is often not the solver but a non-physical boundary condition. A real case: a compressed-air network specified with a 164:1 pressure ratio between boundaries — the result of a units mix-up, not a real plant condition. No steady-state model can satisfy that through ordinary pipework.
Before debugging anything else, check that boundary pressures are absolute-consistent (gauge vs absolute strikes again — same trap as steam tables), that units are what you think they are, and that the implied end-to-end ratio is something a real system could sustain.
How SimuPipe handles it
SimuPipe implements all three levels as separate solvers: incompressible, isothermal compressible (the P² formulation above, with real-gas density from the Peng-Robinson equation of state for non-ideal gases), and adiabatic compressible (which solves temperature along the network and detects choking at Mach 1). An Auto mode picks the appropriate solver from your fluid and conditions, and the post-run diagnostics flag the classic trap explicitly — running a gas at a significant pressure ratio on the incompressible solver gets a warning rather than a silently wrong answer. The full equations are on the methodology page.
Quick decision guide
- ΔP < 10% of inlet absolute pressure → incompressible is fine (use gas density at operating conditions).
- Longer lines, ambient temperature, moderate velocity → isothermal compressible. The default for gas distribution and compressed-air mains.
- Short / fast / insulated lines, big pressure ratios, or you care about outlet temperature → adiabatic compressible.
- Anything near sonic velocity → compressible only, and expect choking to set the flow.
- Always work the rules in absolute pressure, and sanity-check boundary ratios before trusting (or debugging) any result.
To see the difference instead of taking it on faith: build a small compressed-air network in SimuPipe, run it on the incompressible and isothermal solvers, and compare the pressure profiles — on a high-ratio line, watching the incompressible answer drift from the compressible one is the fastest way to internalise the 10% rule. For the underlying friction calculation shared by all three solvers, see How to Calculate Pressure Drop in Pipes.