Venturi Flow Rate Calculator

How does a venturi measure flow?

A venturi meter is a device that gently narrows the pipe section and widens it again. In the narrow section (the throat) the flow speeds up and, by the Bernoulli equation, the pressure falls. The pressure difference between inlet and throat is measured and the flow rate follows from it: Q = Cd × A2 × √(2 × Δp / (ρ × (1 − β⁴))), where A2 is the throat area, β the ratio of throat to pipe diameter and Cd the discharge coefficient.

Where the formula comes from

Continuity links the velocities at the two sections: v1 × A1 = v2 × A2. The Bernoulli equation links the pressure difference to the squares of the velocities: p1 − p2 = ρ × (v2² − v1²) / 2. Combining the two gives the relation above. The small friction loss in real flow is covered by Cd.

Example

A 100 mm pipe has a 50 mm throat and the pressure difference read for water is 20 kPa. Then β = 0.5 and 1 − β⁴ = 0.9375. The theoretical throat velocity is √(40 000 / 937.5) = 6.53 m/s. With Cd = 0.98 the flow rate is 0.98 × 0.001963 × 6.53 = 0.01257 m³/s, or 12.6 litres per second.

Limits

The calculation is for incompressible flow in a full pipe. The discharge coefficient is specific to the meter and the 0.98 offered is approximate. Gas metering needs an expansibility factor and custody transfer needs ISO 5167. The result is invalid if the throat cavitates.