Venturi Effect Formula
The Venturi effect: fluid speeds up and pressure drops when flowing through a constriction.
Based on Bernoulli's equation and the continuity equation.
The Formulas
Bernoulli: P&sub1; + ½ρv&sub1;² = P&sub2; + ½ρv&sub2;²
Pressure drop: ΔP = ½ρ(v&sub2;² − v&sub1;²)
The Venturi effect describes what happens when a fluid flows through a pipe that narrows and then widens. As the fluid enters the constriction, it must speed up to maintain the same mass flow rate (continuity equation). The faster-moving fluid has lower static pressure (Bernoulli's equation). This pressure drop is the Venturi effect.
Variables
| Symbol | Meaning | Unit |
|---|---|---|
| A&sub1;, A&sub2; | Cross-sectional areas at wide and narrow sections | m² |
| v&sub1;, v&sub2; | Fluid velocities at wide and narrow sections | m/s |
| P&sub1;, P&sub2; | Static pressures at wide and narrow sections | Pa |
| ρ | Fluid density (water = 1000 kg/m³, air = 1.225 kg/m³) | kg/m³ |
| ΔP | Pressure difference (P&sub1; − P&sub2;) | Pa |
Example 1 — Pipe Narrowing
Water flows at 2 m/s through a 10 cm diameter pipe that narrows to 5 cm diameter. Find the speed and pressure change at the narrowing.
A&sub1; = π(0.05)² = 7.854 × 10−3 m²
A&sub2; = π(0.025)² = 1.963 × 10−3 m²
Continuity: v&sub2; = v&sub1; × A&sub1;/A&sub2; = 2 × (7.854/1.963) = 8 m/s
ΔP = ½ × 1000 × (8² − 2²) = 500 × (64 − 4) = 500 × 60
ΔP = 30,000 Pa = 30 kPa pressure drop in the narrow section
Example 2 — Venturi Meter Flow Rate
A Venturi meter has a 100 mm inlet narrowing to 50 mm throat. The measured pressure drop is 15 kPa. Find the flow rate (water, ρ = 1000 kg/m³). Cd = 0.98.
A&sub1; = π(0.05)² = 7.854 × 10−3 m², A&sub2; = π(0.025)² = 1.963 × 10−3 m²
Q = Cd × A&sub2; × √(2ΔP / (ρ × (1 − (A&sub2;/A&sub1;)²)))
= 0.98 × 1.963 × 10−3 × √(30000 / (1000 × (1 − 0.0625)))
Q ≈ 0.0109 m³/s = 10.9 liters per second
When to Use It
The Venturi effect and its formulas are used when:
- Designing Venturi meters for accurate industrial flow rate measurement
- Understanding carburetor operation in engines (fuel is drawn in by low pressure)
- Analyzing wings and airfoils — faster air over the curved top creates lower pressure (lift)
- Designing ejectors, aspirators, and vacuum generators using fluid entrainment
- Studying blood flow through narrowed arteries (stenosis)