Venturi Meter Flow Rate Calculator
Flow rate through a Venturi meter or Venturi tube from inlet and throat diameters, measured differential pressure, fluid density and discharge coefficient — volume and mass flow and both velocities.
How it works
Q = Cd × A₂ × √(2·Δp ÷ (ρ·(1 − β⁴))) · β = d ÷ D · A₂ = π·d² ÷ 4 · v₂ = Q ÷ A₂, v₁ = Q ÷ A₁ · mass flow = ρ × Q
A Venturi meter narrows the pipe to a throat and back again. By Bernoulli’s equation and continuity, the fluid speeds up in the throat and its pressure drops; measuring that pressure difference gives the flow rate. The discharge coefficient corrects for friction and is close to 1 for a well-made Venturi, and the gradual outlet cone recovers most of the pressure, so a Venturi wastes far less energy than an orifice plate. For gases the formula holds when the pressure drop is small compared with the line pressure; otherwise include the expansibility factor from ISO 5167.
Worked example
A Venturi with a 100 mm inlet and a 50 mm throat (β = 0.5) reads 20 kPa of differential pressure on water (998 kg/m³). With Cd = 0.98 the throat velocity is 0.98 × √(2 × 20,000 ÷ (998 × 0.9375)) = 6.41 m/s and the flow rate is 0.001963 m² × 6.41 = 45.29 m³/h (12.58 L/s, 12.56 kg/s). The inlet velocity is 1.60 m/s.
Sources: Engineering ToolBox — Venturi meters · Wikipedia — Venturi effect (Venturi meter)
Frequently asked questions
How does a Venturi meter measure flow?
The narrower throat raises the velocity and lowers the pressure. The flow rate is proportional to the square root of that pressure difference, so a differential-pressure gauge across the inlet and throat taps reads the flow.
What discharge coefficient should I use?
ISO 5167-4 gives 0.995 for machined classical Venturi tubes, 0.984 for as-cast and 0.985 for welded sheet-iron types, within their Reynolds number ranges. Homemade or 3D-printed venturis may be lower — calibrate if accuracy matters.
What is the difference between a Venturi and an orifice plate?
Both use the same equation, but an orifice plate has Cd ≈ 0.6 and loses most of the pressure drop permanently, while a Venturi has Cd ≈ 0.98 and recovers about 85–90% of it. The orifice is cheaper and shorter.
Can I use this for air?
Yes, if the pressure drop is small (a few percent of the absolute line pressure) — enter the air density at line conditions. For larger drops the gas expands in the throat and needs an expansibility correction.
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This calculator is for educational purposes. Double-check important results before acting on them.