Hong Life CalculatorsUnderstanding the Venturi meter flow calculator — concept and principle
A Venturi meter measures flow in a closed pipe by narrowing it smoothly to a throat and measuring the pressure difference between the full pipe and the throat. From the two diameters, the measured pressure difference, the fluid density and a discharge coefficient, the calculator returns the volumetric flow in L/s and the mean velocity in the throat. It is used in water supply, process plants and laboratories because the device has no moving parts and recovers most of its pressure loss.
How it is calculated
- Areas: A₁ = πD²/4 for the pipe and A₂ = πd²/4 for the throat (mm converted to m).
- Q = C_d · A₂ · √(2Δp ÷ (ρ(1 − (A₂/A₁)²))), with Δp in Pa and ρ in kg/m³, giving Q in m³/s, then × 1000 for L/s.
- Throat velocity = Q ÷ A₂.
- (A₂/A₁)² equals β⁴, where β = d/D is the diameter ratio.
The principle
Between the inlet and the throat the flow speeds up, as the continuity equation requires (A₁v₁ = A₂v₂), and by Bernoulli's equation the pressure must drop. Combining the two gives an ideal throat velocity of √(2Δp ÷ (ρ(1 − β⁴))). The term 1 − β⁴ corrects for the fact that the fluid was already moving in the pipe. Real flow has friction and a non-uniform velocity profile, so the ideal value is multiplied by the discharge coefficient C_d. For well-made classical Venturi tubes C_d is close to 1 (about 0.98–0.995 in ISO 5167-4, depending on construction).
Worked example
- Inputs: D = 100 mm, d = 50 mm, Δp = 10 kPa, ρ = 1000 kg/m³, C_d = 0.98.
- A₁ = 0.0078540 m², A₂ = 0.0019635 m², so (A₂/A₁)² = 0.25² = 0.0625.
- Ideal throat velocity: √(2 × 10,000 ÷ (1000 × 0.9375)) = √21.333 = 4.6188 m/s.
- Actual throat velocity: 0.98 × 4.6188 = 4.526 m/s (shown as 4.52642611).
- Q = 0.0019635 × 4.5264 = 0.0088876 m³/s = 8.888 L/s (shown as 8.887616885).
| Discharge coefficient | Flow (L/s) |
|---|---|
| 0.245 | 2.221904221 |
| 0.49 | 4.443808442 |
| 0.735 | 6.665712664 |
| 0.98 | 8.887616885 |
| 1.23 | 11.10952111 |
| 1.47 | 13.33142533 |
| 1.96 | 17.77523377 |
How to read the result
Flow is proportional to the square root of Δp, so doubling the flow requires four times the pressure difference. This limits the useful range of one meter (turndown): at a tenth of full flow the pressure signal is only a hundredth as large and becomes hard to read accurately. Choose the throat so that normal flow gives a clearly measurable Δp.
Common mistakes
- Entering the permanent pressure loss instead of the inlet-to-throat difference.
- Using gauge readings in bar or mmH₂O without converting to kPa.
- Treating a sharp orifice plate as a Venturi; orifice C_d is around 0.6, not 0.98.
- Using it for gases with a large pressure drop, where an expansibility factor is needed.
Frequently asked questions
Why is a Venturi more efficient than an orifice plate?
The gradual diverging cone lets the fluid slow down smoothly, so most of the pressure is recovered; an orifice loses much more energy in turbulence.
What β ratio is typical?
ISO 5167-4 covers classical Venturi tubes with β between 0.3 and 0.75.
Can I find Δp from a known flow?
Rearrange: Δp = ρ(1 − β⁴) ÷ 2 × (Q ÷ (C_d A₂))².
Sources: ISO 5167-4, Measurement of fluid flow by means of pressure differential devices — Part 4: Venturi tubes · F. M. White, Fluid Mechanics, McGraw-Hill (flow meters)