How a Venturi meter measures flow
A Venturi tube is a section of pipe that narrows through a converging cone to a short throat, then widens again through a longer diverging cone. Named after the Italian physicist Giovanni Battista Venturi and turned into a practical water meter by Clemens Herschel in 1887, it is still used for water, wastewater, gas and process flows.
As the fluid enters the throat, it speeds up to keep the same flow rate through a smaller area. By Bernoulli’s principle, its pressure falls. Two pressure taps, one upstream and one at the throat, measure that difference Δp, which grows with the square of the flow.
The equation
Combining continuity and Bernoulli’s equation for an incompressible fluid gives the throat velocity and the flow rate:
v₂ = √(2Δp ÷ (ρ(1 − β⁴)))
Q = Cd × A₂ × v₂
where:
- β is the diameter ratio d₂ ÷ d₁;
- A₂ is the throat area, π d₂² ÷ 4;
- ρ is the fluid density (1000 kg/m³ for water);
- Cd is the discharge coefficient.
The inlet velocity is v₁ = v₂ × β².
Example
A 4-inch pipe with a 2-inch throat (β = 0.5) carrying water with a 5 psi pressure difference gives a throat velocity of about 28 ft/s (8.6 m/s). With a discharge coefficient of 0.98, the flow is about 1,020 L/min, or 270 US gallons per minute. The inlet velocity is a quarter of the throat velocity, about 7 ft/s (2.1 m/s).
Choosing the discharge coefficient
| Device | Typical Cd |
|---|---|
| classical Venturi, machined convergent | about 0.995 |
| classical Venturi, cast or welded | about 0.98 to 0.985 |
| flow nozzle | about 0.95 to 0.99 |
| sharp-edged orifice plate | about 0.6 |
The values for standard devices are given in ISO 5167, which also sets the geometry, the diameter ratio (about 0.3 to 0.75 for Venturis) and the straight pipe lengths needed upstream.
Limits
- The formula assumes an incompressible fluid. For gases with a pressure drop above a few percent of the line pressure, an expansibility factor is needed.
- The flow must be fully turbulent and well developed; bends and valves just upstream distort the reading.
- Because Δp varies with the square of the flow, the meter loses accuracy at low flows.