Gas (Compressible) Differential-Pressure Flow Meter
Compressible-gas flow through an orifice plate, from the differential pressure across it.
Example
You enter
- Pipe inside diameter (in) 4
- Bore / throat diameter (in) 2
- Upstream static pressure (psia, absolute = psig + 14.7) 100
- Differential pressure (psi; 1 psi = 27.68 in w.c.) 1
- Upstream temperature (F) 60
- Gas specific gravity (air 1.0, nat gas ~0.6) 1
- Isentropic exponent kappa (air 1.4, nat gas 1.3) 1.4
- Discharge coefficient Cd (when entered; orifice 0.61) 0.61
You get
- Expansion factor Y (eps) 0.9973
- Standard flow 747.6 scfm
- Mass flow (lb/min) 57.06
- Beta ratio 0.5
Checked against published worked examples from: SunCam (H. Bengtson).
Details, formula, and sources
ScopeA gas expands and thins across the restriction, so the incompressible equation is multiplied by the ISO 5167-2 expansibility factor eps = 1 - (0.351 + 0.256 beta^4 + 0.93 beta^8)(1 - (p2/p1)^(1/kappa)), which falls below 1 as the pressure ratio drops; qm = (Cd/sqrt(1-beta^4)) eps (pi/4) d^2 sqrt(2 gc dP rho1) with rho1 the upstream density from the ideal-gas law. Air (SG 1, kappa 1.4) in a 2 in orifice in a 4 in line at 100 psia, 60 F, 1 psi dP reads eps 0.997 and about 748 scfm; raise dP to 10 psi and eps falls to 0.973. Enter the UPSTREAM ABSOLUTE pressure (psia = psig + 14.7) and dP in psi (1 psi = 27.68 in w.c.); kappa ~1.4 air, 1.3 natural gas, 1.13 propane. Reports the expansion factor, mass flow, and actual/standard (scfm) volumetric flow. Orifice-plate form, valid for p2/p1 >= 0.75; a precise Cd and the venturi/nozzle form come from ISO 5167 / the meter calibration. A field/sizing estimate; the calibrated meter governs.
Formula or tableeps = 1 - (0.351 + 0.256 beta^4 + 0.93 beta^8)(1 - (p2/p1)^(1/kappa)); qm = (Cd/sqrt(1-beta^4)) eps (pi/4) d^2 sqrt(2 gc dP rho1); rho1 = p1 MW/(R T), MW = 28.97 SG; scfm at 14.696 psia, 60 F.
Source and editionThe ISO 5167-2 orifice-plate expansibility (expansion) factor and the compressible-flow mass-flow equation, cited by name; the underlying flow physics is public and the meter's calibration governs the precise discharge coefficient.
Free accessThe expansibility-factor correlation and the compressible orifice-flow equation are the published ISO 5167-2 form; the discharge coefficient (0.61 orifice) is editable and the meter's own calibration governs, and the gas properties (specific gravity, isentropic exponent) are standard.
What governsEstimate. AHJ and licensed professional govern.
API field namespipe_id_in, bore_in, p1_psia, dp_psi, temp_f, gas_sg, kappa, cd, expansion_factor, scfm, mass_flow_lb_min, beta_ratio
- Discharge coefficient entered (0.61 typical), or for a square-edge orifice (added 2026-10-09) computed by the ISO 5167-2 Reader-Harris/Gallagher equation for flange, corner, or D and D/2 taps, iterated with Re = 4 qm/(pi D mu)ISO 5167-2; orifice-discharge-coefficient
- Expansibility factor eps = 1 - (0.351 + 0.256 beta^4 + 0.93 beta^8)(1 - (p2/p1)^(1/kappa)); orifice plate, p2/p1 >= 0.75ISO 5167-2
- Mass flow qm = (Cd/sqrt(1 - beta^4)) eps (pi/4) d^2 sqrt(2 gc dP rho1)ISO 5167-2 / Bernoulli
- Upstream density rho1 = p1 MW/(R T) ideal gas, MW = 28.97 x SG; scfm at 14.696 psia, 60 Fideal-gas law
- Scope orifice-plate expansion form; Cd editable and the calibrated meter governsscope of this tile