Venturi Meter Flow Rate Formula
Calculate volumetric flow rate through a Venturi meter from the pressure difference between the throat and inlet.
Used in industrial flow measurement.
The Formula
A Venturi meter measures flow rate by measuring the pressure drop across a constriction. As fluid flows through the narrowed throat, it speeds up and pressure drops (Bernoulli's principle). The flow rate is calculated from this pressure difference. The discharge coefficient C_d accounts for real-fluid losses (viscosity, friction).
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| Q | Volumetric flow rate | m³/s |
| Cd | Discharge coefficient (typically 0.95–0.99 for well-designed meters) | dimensionless |
| A1 | Cross-sectional area at the inlet (large pipe) | m² |
| A2 | Cross-sectional area at the throat (narrow section) | m² |
| ΔP | Pressure difference between inlet and throat (P1 − P2) | Pa |
| ρ | Fluid density | kg/m³ |
Example 1 — Water Flow Rate
A Venturi meter has inlet diameter D1 = 100 mm and throat D2 = 50 mm. Measured ΔP = 10 kPa. Cd = 0.98. Find Q for water (ρ = 1000 kg/m³).
A1 = π(0.05)² = 7.854 × 10−3 m²
A2 = π(0.025)² = 1.963 × 10−3 m²
(A2/A1)² = (1/4)² = 0.0625
Q = 0.98 × 1.963 × 10−3 × √(2 × 10000 / (1000 × 0.9375))
= 0.98 × 1.963 × 10−3 × √(21.33) = 0.98 × 1.963 × 10−3 × 4.619
Q ≈ 8.88 × 10−3 m³/s = 8.88 liters per second = 32 m³/hour
Example 2 — Gas Flow
Natural gas (ρ = 0.8 kg/m³) flows through a 200 mm pipe with 100 mm throat. ΔP = 500 Pa, Cd = 0.97. Find Q.
A1 = π(0.1)² = 0.03142 m², A2 = π(0.05)² = 7.854 × 10−3 m²
Q = 0.97 × 7.854 × 10−3 × √(2 × 500 / (0.8 × 0.9375))
Q ≈ 0.132 m³/s = 476 m³/hour of natural gas
When to Use It
Use the Venturi meter formula when:
- Measuring flow rates of liquids or gases in industrial pipelines
- Monitoring water distribution systems for leak detection
- Fuel flow measurement in aircraft engines and power plants
- Calibrating other flow measurement devices
Advantages of Venturi meters: no moving parts, low pressure loss (flow recovers after the throat), high accuracy. Disadvantages: expensive to install, require long straight pipe sections upstream.