Orifice, Nozzle & Diffuser Flow Calculator — Compressible and Incompressible Flow Through Restrictions and Area Changes

For a gas, the liquid formula above is replaced with the isentropic flow equation for a converging passage, which is what makes choked flow show up correctly (the reference Valcor tool this calculator is modeled after does not do this — it uses the incompressible formula for gases too, which quietly over-predicts flow once the pressure ratio gets low). The downstream-to-upstream pressure ratio decides which branch applies:

For a liquid, only the pressure difference ΔP = P₁ − P₂ matters — raising P₁ by 10 psi or dropping P₂ by 10 psi are physically identical, since density is constant either way. For a gas, especially once it's choked, that stops being true, and it's worth understanding exactly why — it's a genuinely different piece of physics, not a rounding error.

Density is ρ = P/(RT) — it depends on the absolute pressure level, not the drop across the restriction. Raise P₁ from 50 to 100 psia and also raise P₂ to keep ΔP the same, and the gas arriving at the orifice is now roughly twice as dense: the same ΔP pushes twice the mass through, because there's simply twice as much mass packed into every cubic foot approaching the hole. For a compressible fluid, ΔP never tells the whole story by itself the way it does for a liquid.

This is the sharper point, and it's a statement about causality, not just an approximation. Pressure changes propagate through a fluid as sound waves, at the local speed of sound, relative to the fluid. Once the throat is choked, the gas sitting right at the throat is already moving at exactly Mach 1 — the speed of sound. A pressure disturbance created downstream, by lowering P₂ still further, tries to propagate upstream through the throat to "announce" the change — but it's swimming upstream into a flow already moving at its own top speed. It never wins that race. It never reaches the throat. The throat genuinely cannot "hear" what's happening downstream of it anymore.

So raising P₁ always does something, whether choked or not (more ΔP and more density feeding the restriction), while lowering P₂ only does something until the throat goes sonic, at which point it does precisely nothing. Practically: if a choked vent, relief device, or pneumatic line is already choked, opening a bigger downstream path or pulling harder on the far side accomplishes nothing — the only lever left is upstream supply pressure.

Four charts, same 8 sharp-edged orifice sizes discharging to atmosphere (50–200 psig upstream, 5 psi steps), computed analytically from the exact same equations as the calculator above — not digitized from a photo, and not a separate model. Air is choked at every single point on every air chart here (the critical pressure ratio for air is ≈0.528; P₂/P₁ never rises above ≈0.23 across this whole range), so the two air charts are a direct, literal demonstration of card 04's point: air mass flow (and SCFM, which tracks it) keeps climbing in a straight line with absolute upstream pressure, exactly as choked-flow theory predicts, with zero contribution from the fact that P₂ is fixed at atmospheric throughout.

Assumptions: C_d = 0.61, E = 1 (discharging from a large line/tank — the "Tank/plenum" fitting preset above), P₂ = 14.696 psia (atmosphere), water at ~68°F, air at 70°F with k = 1.4 / R = 287 J/(kg·K), SCFM referenced to 14.696 psia / 60°F. Hover any curve for the exact value at each 5 psi increment.

Fluid properties come from live lookups — real CoolProp equation-of-state data for gases and most liquids (via Thermo Land's data feed), or this site's own digitized density-vs-temperature curves for the MIL-spec/aviation liquids CoolProp doesn't carry (via Multi-Fluid Property Charts). Gas density and gamma (k) are the real fluid's values at the entered temperature and pressure, not an ideal-gas assumption — noticeably more accurate near the critical point or at high pressure than a constant-k model. See the calculator's own "gaps" note for which fluids aren't covered by either source.

All four modes are 1-D, steady, adiabatic, and (for gas) isentropic idealizations — friction losses, real nozzle boundary layers, and shock structures inside a C-D nozzle's diverging section aren't modeled. See the Gas Flow Safety Calculator for a complementary, safety-margin-focused take on compressible/choked gas flow.