Bernoulli Equation Calculator
Understand fluid dynamics. Use pressure, speed, and height at one point in a flow to find conditions at another, assuming ideal fluid behavior.
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
Air: 1.225, Water: 1000
About Bernoulli's Equation:
Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure. This principle applies to incompressible, non-viscous fluid flow.
How the Bernoulli Equation Calculator Works
Select what you want to calculate: pressure, velocity, or height at point 2. Enter the known values for both points along the streamline: pressure, velocity, height, and fluid density.
The calculator applies Bernoulli's equation: P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂. This expresses conservation of energy for ideal fluid flow. The calculator rearranges to solve for your unknown variable.
Results display with proper units and show the calculation steps. A diagram illustrates the two points along the flow path. The calculator also shows the pressure, kinetic, and potential energy terms separately.
When You'd Actually Use This
Pipe flow analysis
Calculate pressure changes in pipes of varying diameter. As water speeds up in narrow sections, pressure drops - important for pipe design.
Airplane wing lift estimation
Understand how wing shape creates lift. Faster airflow over the curved top creates lower pressure, generating upward force.
Venturi meter calculations
Design flow measurement devices. Pressure difference in a constriction reveals flow rate. Used in carburetors and industrial flow meters.
Water tower pressure analysis
Calculate water pressure at different elevations. Higher towers provide more pressure to distribution systems through gravitational head.
Spray bottle and atomizer design
Understand how fast air creates low pressure to draw liquid up. Bernoulli effect enables spray bottles, paint sprayers, and perfume atomizers.
Fire hose nozzle calculations
Determine exit velocity from nozzle pressure. Firefighters need to know how nozzle settings affect water stream reach and impact.
What to Know Before Using
Bernoulli applies to ideal fluids.Assumes no viscosity, incompressible flow, steady state. Real fluids have friction losses. Use for approximate calculations or add loss terms.
Points must be on the same streamline.Bernoulli's equation applies along a flow path. Don't compare points in separate, unconnected flow streams.
Pressure-speed tradeoff is key.Higher velocity means lower pressure (and vice versa) when height is constant. This inverse relationship drives many fluid phenomena.
Units must be consistent.Use SI units: Pascals for pressure, m/s for velocity, meters for height, kg/m³ for density. The calculator handles conversions.
Pro tip: For horizontal flow (h₁ = h₂), Bernoulli simplifies to P₁ + ½ρv₁² = P₂ + ½ρv₂². This shows directly that pressure drops where velocity increases - the key to understanding many fluid devices.
Common Questions
Why does faster flow mean lower pressure?
Energy is conserved. Kinetic energy (½ρv²) increases, so pressure energy must decrease. Think of pressure as stored energy available to accelerate fluid.
Can I use this for gases?
Yes, for low-speed gas flow where density changes are small (Mach < 0.3). For high-speed compressible flow, use compressible flow equations.
What about friction losses?
Real pipes have friction. Add a head loss term: P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂ + losses. Use Darcy-Weisbach equation for losses.
Does this work for turbulent flow?
Bernoulli applies to individual streamlines even in turbulent flow, but you need time-averaged values. For engineering, use with loss coefficients.
What's dynamic pressure?
Dynamic pressure is ½ρv² - the kinetic energy per unit volume. Total pressure = static pressure + dynamic pressure (for horizontal flow).
How does this relate to continuity equation?
Continuity (A₁v₁ = A₂v₂) gives velocity changes from area changes. Bernoulli then gives pressure changes from velocity changes. Use both together.
Why do shower curtains billow inward?
Fast-moving water creates fast air flow inside the shower. Lower pressure inside pulls the curtain inward. Classic Bernoulli effect demonstration.
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