Venturi Meter Calculator Formula
Understand the math behind the venturi meter calculator. Each variable explained with a worked example.
Formulas Used
Volumetric Flow Rate
flow_rate = cd * a2 * sqrt(2 * dp_pa / (density * (1 - pow(beta, 4)))) * 1000Beta Ratio (D2/D1)
beta_ratio = betaVariables
| Variable | Description | Default |
|---|---|---|
cd | Discharge Coefficient (Cd) | 0.98 |
pipe_dia | Upstream Pipe Diameter (D1)(mm) | 100 |
throat_dia | Throat Diameter (D2)(mm) | 50 |
delta_p | Differential Pressure(kPa) | 15 |
density | Fluid Density(kg/m^3) | 1000 |
a2 | Derived value= pi * pow(throat_dia / 1000, 2) / 4 | calculated |
beta | Derived value= throat_dia / pipe_dia | calculated |
dp_pa | Derived value= delta_p * 1000 | calculated |
How It Works
Venturi Meter Flow Measurement
A Venturi meter uses a converging-diverging section to measure flow with minimal permanent pressure loss.
Formula
Q = Cd A2 sqrt(2 delta_P / (rho (1 - beta^4)))
where A2 is the throat area, beta = D2/D1 is the diameter ratio, and the (1 - beta^4) term accounts for the velocity change between upstream and throat. Cd for Venturi meters is typically 0.95-0.99.
Worked Example
A Venturi with 100 mm upstream and 50 mm throat, 15 kPa differential, water.
- 01beta = 50/100 = 0.5, beta^4 = 0.0625
- 02A2 = pi x 0.05^2 / 4 = 0.001963 m^2
- 03sqrt(2 x 15000 / (1000 x (1 - 0.0625))) = sqrt(30000/937.5) = sqrt(32) = 5.657 m/s
- 04Q = 0.98 x 0.001963 x 5.657 = 0.01088 m^3/s = 10.88 L/s
Frequently Asked Questions
Why is the Venturi Cd higher than for an orifice?
The smooth converging-diverging shape of a Venturi minimises flow separation and turbulence losses, so the actual flow is much closer to the theoretical (ideal) value. Cd is typically 0.95-0.99 vs 0.60-0.65 for orifices.
What is the advantage over an orifice plate?
Venturi meters recover about 80-95% of the differential pressure, resulting in much lower permanent pressure loss. They are preferred in large systems where pumping energy is expensive.
What beta ratio is optimal?
Beta ratios between 0.4 and 0.75 are common. Lower beta gives higher sensitivity but more pressure drop. The optimal choice balances measurement accuracy against allowable permanent loss.
Ready to run the numbers?
Open Venturi Meter Calculator