Orifice Plate Flow & Differential Pressure Calculator (ISO 5167)
Calculate flow rate, differential pressure, and primary element sizing for square-edged concentric orifice plates per ISO 5167-1/2:2003 and ASME MFC-3M: compute discharge coefficient ($C_d$), beta ratio ($\beta$), permanent unrecoverable head loss ($\Delta P_{perm}$), straight-run piping requirements, and vena contracta cavitation index.
Piping & Orifice Geometry
Step-by-Step ISO 5167 / ASME MFC-3M Mathematical Derivation
Orifice plates operate on Bernoulli's principle of conservation of energy: fluid accelerates through the constricted orifice bore ($d$), converting static pressure head into dynamic kinetic energy, forming a minimum flow area downstream termed the vena contracta.
Qv = Qm / ρ
- Beta ratio $\beta = d / D$: --
- Velocity approach $E$: --
- Current Flow: --
+ 0.000521(10^6 β / ReD)^0.7 + Tap Terms
- Tap Type: Flange Taps
- Discharge Coeff $C_d$: --
- Reynolds $Re_D$: --
Pumping Power Waste ∝ Q · ΔP_perm
- Differential $Delta P$: --
- Loss Fraction: --
- Unrecoverable Loss: --
5 Fatal Traps in Orifice Plate Flow Metering
ISO 5167 specifies an upstream orifice edge radius $r_k le 0.0004 d$ (effectively razor sharp, reflecting no visible light beam). If solids, abrasive slurry, or wire-brush cleaning round this leading edge by even 0.05 mm (0.002"), the discharge coefficient $C_d$ increases by 1% to 3%. Because the transmitter measures lower $Delta P$ for the same actual flow, the meter under-reads process volume, leading to massive unaccounted custody transfer loss.
Designing with $eta < 0.20$ generates extreme differential pressures, severe permanent head loss, and high risk of cavitation at the vena contracta. Conversely, specifying $eta > 0.75$ pushes the orifice edge into the pipe wall boundary layer; small pipe wall roughness variations cause erratic flow separation, destroying measurement repeatability. ISO 5167 explicitly states that empirical discharge coefficient uncertainty doubles or triples outside $0.20 le eta le 0.75$.
Unlike Venturi tubes or flow nozzles (which recover 85% to 90% of differential pressure), concentric square-edged orifice plates permanently destroy 40% to 90% of $Delta P$ in turbulent recirculation vortices downstream of the plate. On a 100 inH2O transmitter across a 2,000 GPM pump line, a 65 inH2O permanent head loss equates to 3.5 kW of continuous electrical waste—costing over $3,500/year in parasitic energy that could justify a low-loss Venturi or magnetic meter.
Orifice plates require fully developed, axisymmetric turbulent velocity profiles. Two 90° out-of-plane elbows or a partially throttled control valve upstream generate massive rotational swirl and velocity peaks. Swirl dramatically alters the angle of fluid approach to the orifice plate, skewing flow measurements by up to 10% to 15%. Always provide at least $28D$ to $44D$ of straight upstream pipe, or install an ISO 5167 compliant 19-tube bundle flow conditioner at $13D$ upstream.
When measuring steam or gas containing entrained liquid droplets in horizontal piping, liquid dam up against the upstream face of the orifice plate. This liquid pool distorts the circular conduit area and alters the effective beta ratio. In gas service, always specify a bottom drain hole (weep hole at 6 o'clock) flush with the pipe ID. Conversely, in liquid service with entrained gas, specify an air vent hole at 12 o'clock to prevent air entrapment.