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.
cd = 0.98pipe_dia = 100throat_dia = 50delta_p = 15density = 1000
- 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
Ready to run the numbers?
Open Venturi Meter Calculator