Orifice flow: equation and checked examples
qm=Cd·Ao·sqrt(2ΔPρ/(1−β⁴)); Q=qm/ρ, β=d/D, Ao=πd²/4. Diameters are converted from mm to m. Results show Q in m³/h and mass flow in kg/h.
🙋 Why are the flow readouts in different units?
🎓 The illustration uses L/s and the cards use m³/h. Multiply L/s by 3.6 to compare them. Changing the bore also changes ReD and Cd, so a separate fixed-Cd animation can disagree with the actual calculator.
Water-pipe calculation example
D=50mm, β=0.60, d=30mm, ΔP=100000Pa, T=20°C: ρ=992.832kg/m³, Cd=0.61013, Q=23.620m³/h (6.561L/s), qm=23450.26kg/h, ReD=165877. β=0.70: Q=34.205m³/h.
Model and scope
Water properties are approximate: at 20°C, density is 992.832kg/m³ and viscosity is 0.001Pa·s, not a validated water-property table. Liquid-water conditions at high temperature are not guaranteed. The animation and result cards share one calculation. Permanent pressure loss in the illustration uses the separate approximation (1−β^1.9)ΔP.
Reader-Harris/Gallagher with corner taps, L1=L2′=0. For D<71.12mm the addition is 0.011(0.75−β)(2.8−D/0.0254), with D in metres. Flange-tap calibration is not modeled.
The nominal limits are D=50–1000mm, d>12.5mm, β=0.1–0.75 and ReD≥5000 (ReD≥16000β² for β>0.56). The UI also permits extrapolation and warns about it. Installation, roughness and straight runs are not checked; ISO compliance and field accuracy are not guaranteed.
With Cd fixed, Q scales with sqrt(ΔP); this tool instead iterates Cd using ReD. Differential-pressure uncertainty gives approximately δQ/Q=0.5δΔP/ΔP when other inputs and Cd are fixed: 5000Pa ±100Pa corresponds to about ±1% flow. Required straight runs depend on upstream fittings and β, not a universal 30D rule.
FAQ
Which equation is used?
qm=Cd·Ao·sqrt(2ΔPρ/(1−β⁴)); Q=qm/ρ, β=d/D, Ao=πd²/4. Diameters are converted from mm to m. Results show Q in m³/h and mass flow in kg/h.
Which pressure taps are modeled?
Reader-Harris/Gallagher with corner taps, L1=L2′=0. For D<71.12mm the addition is 0.011(0.75−β)(2.8−D/0.0254), with D in metres. Flange-tap calibration is not modeled.
Is this accurate for air or steam?
No. The expansibility factor is fixed at ε=1. Air uses an ideal-gas density at 101325Pa; steam uses approximate properties, not a saturation table. Do not use these illustrative gas results for design or billing.
What happens outside the correlation range?
The nominal limits are D=50–1000mm, d>12.5mm, β=0.1–0.75 and ReD≥5000 (ReD≥16000β² for β>0.56). The UI also permits extrapolation and warns about it. Installation, roughness and straight runs are not checked; ISO compliance and field accuracy are not guaranteed.
Reader-Harris/Gallagher: reference implementation and limits
How to Use
Enter internal diameter D in mm and differential pressure in Pa. Set beta=d/D and temperature in °C; select water, air or steam. Results update as inputs change. The illustration uses L/s; result cards use m³/h. There is no gas-pressure, natural-gas or user-viscosity input.
Worked Example
D=50mm, β=0.60, d=30mm, ΔP=100000Pa, T=20°C: ρ=992.832kg/m³, Cd=0.61013, Q=23.620m³/h (6.561L/s), qm=23450.26kg/h, ReD=165877. β=0.70: Q=34.205m³/h.
Practical Notes
Orifice flow calculator using corner-tap Cd iteration. Explore pipe diameter, beta ratio, pressure drop and temperature with checked examples. Approximate properties and epsilon=1; not an ISO compliance or design-accuracy guarantee. Water properties are approximate: at 20°C, density is 992.832kg/m³ and viscosity is 0.001Pa·s, not a validated water-property table. Liquid-water conditions at high temperature are not guaranteed. The animation and result cards share one calculation. Permanent pressure loss in the illustration uses the separate approximation (1−β^1.9)ΔP.