Calculate flow rate through an orifice plate based on differential pressure and discharge coefficient.
An orifice plate is a calibrated restriction that meters flow rate from the pressure drop across it. This calculator solves flow from differential pressure, discharge coefficient, and orifice area using the Torricelli/Bernoulli form, and the inverse problem of sizing orifice diameter from required flow. It applies to drain orifices, level-control restrictors, and ISO 5167 flow-measurement orifice plates.
Q = C_d × A × √(2 × g × h) for free discharge under gravity head h, or Q = C_d × A × √(2 × ΔP / ρ) for pressure-driven flow with ΔP across the orifice. C_d is the discharge coefficient — 0.61 for sharp-edged orifice in pipe, 0.97 for ISA nozzles, 0.75 for thin-plate concentric orifices in pipe flow. Area A = π × d² / 4 where d is the orifice diameter. The square-root relationship means a 1% flow accuracy requires 2% accurate ΔP. The β ratio β = d / D (orifice to pipe) typically falls in 0.2–0.7; below 0.2 the orifice contribution is dominant, above 0.7 the upstream pipe shape biases C_d.
A process engineer estimating drain time for a vessel from 3 m depth to empty integrates Torricelli over the level, using C_d = 0.61 for a 50 mm sharp-edged orifice, and gets 4.2 hours total drain time.
An instrumentation technician sizing an ISO 5167 orifice for 100 m³/h of water at 4 bar picks β = 0.4 and confirms the calibrated differential is 250 mbar — within the DP-transmitter span.
A pneumatics designer adds a 1.5 mm restrictor to soft-start a clamp; the calculator gives 12 lpm air flow at 4 bar inlet, matching the desired actuator rise-time of 0.8 seconds.
Sharp-edged orifice in pipe: 0.61. ISA flow nozzle: 0.97. Venturi: 0.98. Free-discharge tank orifice (rounded entry): 0.95. Always check the geometry standard before picking.
Liquids are nearly incompressible, so Q = C_d × A × √(2gh) directly. Gas flow above 50% pressure drop is sonic and needs the critical-flow correction. Use the gas formula with expansibility factor Y for ΔP/P > 0.1.
Yes. C_d in ISO 5167 plates depends on β = d/D. Designers ensure at least 20D of straight pipe upstream and 5D downstream so the velocity profile is fully developed.