Gas Flow Equations & Engineering Reference
| Equation | Formula |
|---|---|
| Weymouth | Q = 433.5·E·(Tb/Pb)·√[(P₁²−P₂²)/(G·Tf·L·Z)]·D2.667 |
| Panhandle A | Q = 435.87·E·(Tb/Pb)1.0788·[(P₁²−P₂²)/(G0.8539·Tf·L·Z)]0.5394·D2.6182 |
| Panhandle B | Q = 737·E·(Tb/Pb)1.02·[(P₁²−P₂²)/(G0.961·Tf·L·Z)]0.51·D2.53 |
| IGT | Q = 136.9·E·(Tb/Pb)·[(P₁²−P₂²)/(G0.8·μ0.2·Tf·L)]0.555·D2.667 |
Q = flow rate (scfd), D = internal diameter (inch), L = length (miles), P₁/P₂ = inlet/outlet absolute pressure (psia), G = specific gravity, Tf = average flowing temperature (°R), Z = compressibility factor, E = efficiency factor, μ = gas viscosity (cP, IGT only). Tb=520°R, Pb=14.696 psia (standard base conditions, matches the published validation examples).
Why four different equations for the same physical pipe
Each equation is an empirical fit to a specific flow regime and pipe scale, developed decades apart from different field data sets. Weymouth (1912) fits distribution-scale pipe in fully turbulent flow. Panhandle A (1940s) and its 1956 revision Panhandle B fit large-diameter transmission pipe — A for partially turbulent flow, B for fully turbulent. None of them is universally "more correct"; each is most accurate inside the pipe scale and flow regime it was fit to, which is why picking the right one for your application matters more than picking the newest one.
Why the equation-validity warning exists
This calculator runs a General Flow / Colebrook-White calculation in the background as a friction-factor-based cross-check, regardless of which equation you selected. If your selected equation's result diverges from that cross-check by more than 15%, that's usually a sign the pipe you're sizing sits outside the regime the equation was fit to — for example, running Panhandle A on a small-diameter distribution main, or Weymouth on a large fully-turbulent transmission line.
Reading the Reynolds number and Mach number
All four equations assume turbulent flow — a Reynolds number below about 4,000 means the underlying assumption doesn't hold and the result should not be trusted. The Mach number check is a separate concern: above roughly 0.3, the isothermal, near-incompressible assumptions behind these equations start to break down as the flow approaches transonic conditions.
Why elevation isn't corrected for
A rigorous elevation correction changes the pressure-squared term in each equation, not just the pressure values — it needs its own derivation and its own validation case. This calculator accepts an elevation input for your records but does not yet fold it into the math; for pipelines with meaningful elevation change, treat the result here as preliminary.
Weymouth, Panhandle A, and Panhandle B are validated to within 1% against five worked examples from E. Shashi Menon's Gas Pipeline Hydraulics (CRC Press, 2005), independently cross-checked against Pipe Flow Expert's published verification results. The IGT implementation could not be validated against its published example (Menon Ch.2 p.71 Ex.19) during development — see the in-app warning when IGT is selected.
Weymouth for distribution-scale pipe (roughly NPS 12 and below) in fully turbulent flow. Panhandle A for large-diameter, long-distance transmission in partially turbulent flow. Panhandle B for the same scale in fully turbulent flow (Reynolds number 4–40 million). IGT when viscosity is known and significant — but see the validation warning before relying on it.
Each equation is empirically fit to a different flow regime and pipe scale. This calculator's equation-validity warning flags a mismatch whenever your selected equation diverges more than 15% from the General Flow cross-check.
Z corrects the ideal gas law for real-gas behavior at the pipeline's pressure and temperature. Auto-calculated here via the CNGA correlation, matching the method used in this calculator's published validation examples — override manually if you have a lab-derived value.
Elevation is accepted as an input for your records only — v1 does not fold it into the pressure-drop math. Treat results as preliminary for pipelines with significant elevation change.
Use with caution. Weymouth, Panhandle A, and Panhandle B are validated to within 1% of published examples; the IGT implementation could not be validated during development. Cross-check any IGT result against Weymouth or Panhandle.