Orifice Flow Calculator
Calculate volumetric flow rate through an orifice plate or sharp-edged opening given pressure drop and fluid properties. Widely used for flow metering in industrial pipelines and process plants.
About this calculator
An orifice meter measures flow rate by creating a pressure drop as fluid passes through a restriction. The theoretical flow rate through an orifice is given by: Q = C_d × A × √(2 × ΔP / ρ) / √(1 − β⁴), where C_d is the discharge coefficient (typically 0.61 for sharp-edged orifices), A = π × d² / 4 is the orifice area (m²), ΔP is the measured pressure drop (Pa), ρ is fluid density (kg/m³), and β = d/D is the beta ratio (orifice diameter to pipe diameter). The term 1/√(1 − β⁴) is the velocity of approach factor, which corrects for the fluid velocity upstream of the orifice. The discharge coefficient accounts for real-fluid effects such as the vena contracta and flow separation. This formula is standardized in ISO 5167 and widely used in custody transfer metering.
How to use
Water (ρ = 1000 kg/m³) flows through an orifice plate with d = 0.05 m diameter (β = 50, so β/100 = 0.5) and a measured pressure drop ΔP = 10,000 Pa. The discharge coefficient C_d = 0.61. First, A = π × 0.05² / 4 = 0.001963 m². Velocity of approach factor = 1/√(1 − 0.5⁴) = 1/√(0.9375) = 1.033. Then Q = 0.61 × 0.001963 × √(2 × 10,000 / 1000) × 1.033 = 0.61 × 0.001963 × 4.472 × 1.033 ≈ 0.00552 m³/s. Enter your orifice diameter, pressure drop, fluid density, discharge coefficient, and beta ratio to compute flow rate instantly.
Frequently asked questions
What is the discharge coefficient of an orifice and how is it determined?
The discharge coefficient (C_d) is a dimensionless factor that corrects the theoretical orifice flow equation for real-fluid effects, primarily the vena contracta (the narrowing of the jet downstream of the orifice) and friction losses. For a standard sharp-edged orifice plate per ISO 5167, C_d is approximately 0.60–0.61 at high Reynolds numbers. For rounded-entry or conical orifices, C_d can be as high as 0.98. The coefficient is determined experimentally by calibration against a reference flow meter or gravimetric measurement. Using the wrong C_d is the most common source of orifice metering error.
How does the beta ratio affect orifice meter accuracy and pressure loss?
The beta ratio (β = orifice diameter / pipe diameter) is a key design parameter that balances measurement sensitivity against permanent pressure loss. A small β (e.g., 0.3) produces a large pressure differential for a given flow rate, improving measurement sensitivity and signal-to-noise ratio, but also creates a larger permanent pressure loss that wastes pumping energy. A large β (e.g., 0.7) reduces permanent loss but gives a smaller differential signal, making measurement less precise. ISO 5167 recommends β between 0.2 and 0.75 for reliable performance. Selecting an appropriate β requires balancing metering accuracy against operating energy cost.
When should I use an orifice plate versus other flow meters like a Venturi or flow nozzle?
Orifice plates are the most common choice because they are inexpensive, easy to install between pipe flanges, and straightforward to replace or inspect. However, they have a relatively high permanent pressure loss compared to Venturi meters, which recover most of the pressure downstream through their gradual diffuser section. Venturi meters are preferred when energy costs are high or when the fluid contains solids that might erode a sharp edge. Flow nozzles offer a middle ground, with lower pressure loss than orifices but higher than Venturis. Orifice plates are ideal when low cost, easy maintenance, and moderate accuracy (±1–2%) are the primary requirements.