Gas Pipeline Pressure Drop Calculator (Isothermal)
Find the pressure at the end of a long gas pipe for a given mass flow, using the isothermal compressible flow equation with the Darcy friction factor from Colebrook. Suitable for fuel gas, nitrogen and compressed air headers.
- G = ṁ ÷ A = 50.69 kg/s·m²; Re = G D ÷ µ = 471,400; f (Colebrook) = 0.01733
- p₁² − p₂² = G² Z R T ÷ M × [f L ÷ D + 2 ln(p₁ ÷ p₂)], solved for p₂
- p₂ = 7.4222 bar a
Isothermal Compressible Flow
G = ṁ ÷ A, Re = G × D ÷ µ, f from Colebrook White
p₁ and p₂ are absolute inlet and outlet pressures, G the mass flux, Z the compressibility, R = 8314 J/kmol·K, T absolute temperature, M the molecular weight, f the Darcy friction factor, L the length and D the inside diameter. The isothermal assumption suits long buried or insulated lines where gas stays near ambient temperature. Fittings can be added as equivalent length.
Worked example
1500 kg/h of natural gas (M 18) at 8 bar a through 1.5 km of 4" Sch 40 (102.3 mm) arrives at about 7.42 bar a, a drop of about 0.58 bar. In a 3" line the same flow would arrive at only about 5.3 bar a.
Frequently Asked Questions
When do I need the compressible flow equation?
When the pressure drop is more than about 10 % of the inlet absolute pressure. Below that, the incompressible Darcy equation with average density is adequate.
Why isothermal?
Long pipelines exchange heat with the surroundings and stay near ground or ambient temperature, which is closer to isothermal than adiabatic.
Can the line choke?
Yes. If the flow is too high for the pipe, the pressure falls toward a limit where the gas reaches its maximum velocity and no more flow is possible.
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