P + ½ρv² = const • Venturi Effect • Continuity Equation — Simulate • Explore • Practice • Quiz
Bernoulli’s Principle is one of the most important concepts in fluid mechanics. It states that for an ideal, incompressible fluid in steady flow, the sum of static pressure, dynamic pressure (½ρv²), and hydrostatic pressure (ρgh) remains constant along a streamline. In practical terms: where fluid flows faster, pressure drops. This relationship is expressed as P + ½ρv² + ρgh = constant.
When fluid flows through a pipe that narrows (a Venturi tube), the continuity equation A₁v₁ = A₂v₂ tells us the fluid must speed up in the constriction to maintain the same flow rate. By Bernoulli’s principle, this increased velocity causes a pressure drop at the throat. The pressure difference is ΔP = ½ρ(v₂² − v₁²). This Venturi effect is the basis for flow measurement devices, carburettors, atomisers, and many other engineering applications.
Bernoulli’s principle explains airplane lift (faster air above the wing creates lower pressure), Pitot tubes (measuring airspeed from pressure difference), Venturi meters (measuring flow rate in pipes), and spray guns (using low pressure to draw liquid upward). Understanding these applications is essential for mechanical, aerospace, and civil engineering students.
In Simulate mode, adjust the flow velocity and pipe diameters to watch the Venturi tube respond in real time. Animated streamlines show velocity changes; pressure bars compare wide-section and throat pressures. Use presets like Water Pipe, Venturi Meter, Fire Nozzle, or Garden Hose. Switch to Explore mode to study 12 concepts across Fundamentals, Applications, and Calculations. Practice mode generates random fluid mechanics problems, and Quiz tests your knowledge with 5 questions per session.
This simulator is designed for mechanical and aerospace engineering students, fluid mechanics trainees, physics students studying fluid dynamics, and instructors teaching Bernoulli’s equation, the Venturi effect, or pipe flow analysis. It provides visual, hands-on understanding without requiring laboratory equipment.