Bernoulli Equation & Fluid Flow Calculator
Apply Bernoulli's equation to find pressure, velocity, or height in fluid flow systems — venturi meters, pipes, and aerodynamics.
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Bernoulli Equation Guide
What's the key thing to understand about Bernoulli's Equation?
P + ½ρv² + ρgh = constant. P = static pressure (Pa), ½ρv² = dynamic pressure (Pa), ρgh = hydrostatic pressure (Pa). Between two points in steady, inviscid, incompressible flow: P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂. Key insight: as velocity increases, pressure decreases (and vice versa). Example: pipe narrows from 5cm to 2.5cm diameter. Continuity: A₁v₁ = A₂v₂. Flow at 2 m/s through large section: v₂ = v₁ × (A₁/A₂) = 2 × 4 = 8 m/s. Pressure drop: ΔP = ½ρ(v₂² - v₁²) = ½×1000×(64-4) = 30,000 Pa.
What do I need to know about Torricelli's Theorem?
A special case of Bernoulli: the speed of fluid exiting a small hole in a large tank. v_exit = √(2gh). Where h = height of fluid above the exit hole. Same formula as free-fall velocity — the fluid accelerates as if falling from height h. Example: tank with 5m of water above exit: v = √(2×9.81×5) = √98.1 = 9.9 m/s. This approximation assumes: the exit hole is small compared to the tank. The tank level drops slowly. Viscosity is negligible (reasonable for water through large holes). Real orifices lose some energy to turbulence and viscosity, so the actual exit velocity is typically 95-98% of the theoretical Torricelli value.
What's the key thing to understand about Venturi Meter?
A venturi meter measures flow rate by creating a controlled narrowing. Mass flow rate: Q = A₁A₂√(2ΔP/(ρ(A₁²-A₂²))). Pressure drop ΔP = P₁ - P₂ measured by a manometer or differential pressure sensor. Applications: water supply measurement, natural gas metering, carburettors (the venturi principle draws fuel into the airstream). Aircraft pitot-static tube: measures dynamic pressure ½ρv² from which airspeed is calculated. Pitot tube: total pressure = static + dynamic. Static port: static pressure only, measured perpendicular to the airflow so the moving air doesn't directly hit the sensor.
What's the key thing to understand about Bernoulli and Lift?
Aircraft wings (aerofoils) generate lift through a pressure difference — but the mechanism is more nuanced than the textbook explanation. Common (oversimplified) explanation: air travels faster over the curved top surface → lower pressure → upward lift (Bernoulli). More accurate: lift arises primarily from circulation of airflow around the wing (Kutta-Joukowski theorem). The wing deflects air downward — by Newton's 3rd law, the wing is pushed upward. Bernoulli pressure difference is a real effect contributing to lift, but the popular explanation that faster airflow over the curved top surface alone explains flight is an oversimplification — Newton's third law and the wing's angle of attack matter at least as much.