Orifice Flow Calculator

The flow rate through an orifice is derived from Bernoulli's equation with a correction factor:

$$Q = C_d \cdot A \cdot \sqrt{\frac{2 \Delta P}{\rho}}$$

where:

• Q — volumetric flow rate (m³/s)
• C_d — discharge coefficient (dimensionless)
• A — orifice area (m²)
• ΔP — pressure difference across the orifice (Pa)
• ρ — fluid density (kg/m³)

The ideal velocity through the orifice (without losses) comes from Torricelli's theorem:

$$v_{ideal} = \sqrt{\frac{2 \Delta P}{\rho}}$$

The discharge coefficient C_d accounts for two effects:

• Velocity coefficient (Cv): friction losses reduce actual velocity below ideal
• Contraction coefficient (Cc): the jet contracts to an area smaller than the orifice (vena contracta)

$$C_d = C_v \times C_c$$

Typical discharge coefficients:

• Sharp-edged orifice: C_d ≈ 0.60–0.65
• Well-rounded nozzle: C_d ≈ 0.95–0.99
• Short tube (L/D ≈ 2–3): C_d ≈ 0.80–0.85
• Borda (re-entrant) inlet: C_d ≈ 0.51

For precise metering applications, C_d is determined by calibration or from standards (ISO 5167) based on the beta ratio (orifice diameter / pipe diameter), Reynolds number, and tap location.

The actual flow rate is the product of the discharge coefficient and ideal flow rate. The difference between ideal and actual values represents energy lost to flow contraction and turbulence at the orifice. A higher C_d means a more efficient orifice design with less energy loss. The calculator shows both ideal and actual velocities so you can assess the orifice efficiency.