Bernoulli Equation - Pressure-Velocity Trade-off
Bernoulli's equation states that for ideal fluid flow, the sum of pressure, kinetic, and potential energy per volume is constant. This calculator analyzes pressure-velocity relationships, Venturi effects, and streamline flow.
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Faster flow = lower pressure (Venturi) Pitot: v = √(2ΔP/ρ) from stagnation vs static Applies to incompressible, inviscid flow Wing lift: faster flow over top = lower P
Ready to run the numbers?
Why: Bernoulli explains lift on wings, flow in pipes, and Pitot tube airspeed measurement. As velocity increases, pressure decreases—the Venturi effect. Essential for fluid dynamics and aerodynamics.
How: P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂ along a streamline. For horizontal flow, P + ½ρv² = constant. Continuity: A₁v₁ = A₂v₂.
Run the calculator when you are ready.
✈️ Airplane Wing Lift
Calculate lift force from pressure difference on wing surface
🌊 Venturi Flowmeter
Measure flow rate using venturi tube pressure differential
💧 Water Tank Drainage
Calculate exit velocity from tank with water level height
💨 Atomizer (Perfume Spray)
Pressure drop creates high velocity for atomization
🚗 Carburetor Venturi
Fuel-air mixing using venturi effect in carburetor
📡 Pitot Tube (Airspeed)
Measure airspeed using pitot-static system
Input Parameters
Point 1
Point 2
Units
Please provide pressures at both points
For educational and informational purposes only. Verify with a qualified professional.
🔬 Physics Facts
Wing lift: Bernoulli + Newton's 3rd both contribute
— NASA
Venturi used in carburetors and atomizers
— HyperPhysics
Pitot tube measures airspeed from P_total - P_static
— Physics LibreTexts
Ideal flow: no viscosity, incompressible, steady
— Engineering Toolbox
📋 Key Takeaways
- • Bernoulli's principle states that as fluid speed increases, pressure decreases, and vice versa
- • The Bernoulli equation applies to ideal, incompressible, inviscid flow along a streamline
- • Total energy (pressure + kinetic + potential) remains constant along a streamline in ideal flow
- • The Venturi effect demonstrates how constricted flow increases velocity and decreases pressure
- • Pitot tubes measure airspeed by comparing total pressure (static + dynamic) to static pressure
- • Real flows have energy losses due to friction, turbulence, and viscosity
🤔 Did You Know?
Airplane wings generate lift through the Bernoulli effect - faster airflow over the curved top surface creates lower pressure, lifting the aircraft.
Source: NASA
The Venturi effect is used in carburetors, atomizers, and flowmeters - constricting flow increases velocity and decreases pressure to draw in fluids or measure flow rates.
Source: Engineering Toolbox
Daniel Bernoulli published his principle in 1738, but it was actually discovered by his father Johann Bernoulli. The equation revolutionized fluid dynamics and aerodynamics.
Source: MIT OpenCourseWare
⚙️ How It Works
Bernoulli's equation describes the conservation of energy in fluid flow. It states that P + ½ρv² + ρgh = constant along a streamline, where P is static pressure, ½ρv² is dynamic pressure (kinetic energy per unit volume), and ρgh is hydrostatic pressure (potential energy per unit volume). When fluid flows through a constriction (Venturi tube), continuity requires velocity to increase, so pressure must decrease to maintain constant total energy. This principle explains lift on airplane wings, atomizer sprays, and many fluid flow phenomena.
💡 Expert Tips
- • Bernoulli's equation applies only along a single streamline - don't compare points on different streamlines
- • For compressible flow (Mach > 0.3), use the modified Bernoulli equation accounting for density changes
- • Real flows have head losses - add a loss term (h_loss) to the equation for accurate predictions
- • Pitot tubes measure airspeed by comparing total pressure (stagnation) to static pressure
- • Venturi flowmeters use the pressure drop across a constriction to measure flow rate
📊 Pressure-Velocity Relationship Comparison
| Application | Velocity Change | Pressure Change | Result |
|---|---|---|---|
| Airplane Wing | Increases (top) | Decreases | Lift force |
| Venturi Tube | Increases (throat) | Decreases | Flow measurement |
| Atomizer | Increases (air) | Decreases | Liquid spray |
| Pitot Tube | Stagnation (v=0) | Maximum (total) | Airspeed measurement |
❓ Frequently Asked Questions
Q: Why does pressure decrease when velocity increases?
According to Bernoulli's principle, total energy (pressure + kinetic + potential) remains constant along a streamline. When velocity increases, kinetic energy increases, so pressure must decrease to maintain constant total energy.
Q: What is the difference between static and dynamic pressure?
Static pressure (P) is the pressure exerted by the fluid at rest. Dynamic pressure (½ρv²) is the pressure due to fluid motion. Total pressure is the sum of both.
Q: How does a venturi tube work?
A venturi tube has a constricted section (throat). According to continuity, velocity increases in the throat. By Bernoulli's principle, pressure decreases. This pressure drop can be measured to determine flow rate.
Q: What is a pitot tube?
A pitot tube measures total pressure (static + dynamic). By comparing total pressure to static pressure, the dynamic pressure (½ρv²) can be found, allowing calculation of flow velocity. Used in aircraft for airspeed measurement.
Q: Does Bernoulli's equation apply to gases?
Yes, but only for low-speed, incompressible flow. For high-speed gas flow (Mach > 0.3), compressibility effects become significant and the equation must be modified.
Q: What causes energy loss in real flows?
Real flows have friction (viscosity), turbulence, and other losses that convert mechanical energy to heat. The modified Bernoulli equation includes a head loss term: P₁/ρ + ½v₁² + gh₁ = P₂/ρ + ½v₂² + gh₂ + h_loss.
📚 Official Data Sources
⚠️ Disclaimer: This calculator provides theoretical results assuming ideal, incompressible, inviscid flow along a streamline. Real-world flows have energy losses due to friction, turbulence, and viscosity. For compressible flows (Mach > 0.3), use modified equations. For critical applications, consult a fluid dynamics engineer.
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