🌊 Fluid Mechanics & Hydrodynamics
Bernoulli's Principle & Venturi Flow Calculator
Compute fluid velocity changes ($v_1, v_2$), pressure drop ($\Delta P$), and volumetric discharge rate ($Q$) through pipe constrictions and Venturi flowmeters.
💧 Water (1,000 kg/m³)
🌊 Seawater (1,025 kg/m³)
🛢️ Oil (850 kg/m³)
💨 Air (1.225 kg/m³)
Venturi Tube Geometry
mm
mm
kg/m³
Volumetric Flow Rate (Q)
14.28 L/s
Inlet Velocity ($v_1$)
1.82 m/s
Throat Velocity ($v_2$)
7.27 m/s
Area Ratio ($A_1/A_2$)
4.00×
💡 Venturi Effect Principle:
As the fluid enters the 50 mm constriction, velocity accelerates by 4.0×, causing static pressure to drop by 25.0 kPa according to Bernoulli's conservation of mechanical energy.
Derivation of the Venturi Flow Equation
Combining Bernoulli's equation with the mass continuity equation ($A_1 v_1 = A_2 v_2$):
$$v_2 = \sqrt{\frac{2 \Delta P}{\rho \left(1 - \frac{A_2^2}{A_1^2}\right)}}, \quad Q = A_2 v_2 = A_1 A_2 \sqrt{\frac{2 \Delta P}{\rho (A_1^2 - A_2^2)}}$$
- Incompressible Continuity: $Q = A_1 v_1 = A_2 v_2$.
- Bernoulli Equation: $P_1 + \frac{1}{2}\rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho g h_2 = \text{Constant}$.