Compressible Gas Flow Calculator

Formula overview

SI: pressures absolute in Pa or bar a, T in K, M in kg/kmol, R = 8 314 J/(kmol·K), D and L in m, ṁ in kg/s. Transmission equations use their own base conditions Tb and Pb.

Isothermal compressible flow (Crane TP-410 / GPSA):

  P1² − P2² = (ṁ/A)² · (Z·R·T/M) · ( f·L/D + 2·ln(P1/P2) )
  Ma = v₂ / √( k·Z·R·T/M )

Transmission form — Weymouth and Panhandle:
  Q = K·E·(Tb/Pb)^a · [ (P1² − P2²) / (G·Tf·L·Z) ]^b · D^c

The solver marches the pipe in 50 steps so density and velocity are
updated as the pressure falls, and adds ΣK·ρV²/2 for the fittings.

Worked example

Natural gas, M = 18 kg/kmol, T = 288 K, k = 1.3, Z = 0.95,
exit velocity 40 m/s

Sonic velocity = √(k·Z·R·T/M)
               = √(1.3 × 0.95 × 8 314 × 288 / 18)
               = √164 300 = 405 m/s
Ma             = 40 / 405 = 0.10

Comfortably subsonic, so the isothermal result is reliable. Once Ma
approaches about 0.3 the compressibility terms dominate, and at Ma = 1
the line is choked and no extra downstream drop increases flow.

Common mistakes

• Using an incompressible pressure drop on a gas line. It is acceptable while the drop stays under about 10% of inlet pressure. Beyond that the density change is real and the incompressible answer is optimistic.
• Working in gauge pressure. Every compressible relation here is written in absolute pressure — the P1² − P2² term is meaningless on a gauge basis, and the error is largest exactly where gas lines run at low pressure.
• Ignoring the exit Mach number. A design that looks fine on pressure drop can be near choking at the outlet, where noise, vibration, and erosion appear long before the flow limit is actually reached.

FAQ