Bernoulli Equation Calculator
Calculate pressure, velocity, and height changes in fluid flow using Bernoulli's principle
Bernoulli Equation Calculator
Choose which parameter to calculate using Bernoulli's equation
Fluid Properties
Water: 1000 kg/m³, Air: 1.225 kg/m³
Earth: 9.80665 m/s², Moon: 1.62 m/s²
Position 1 (Initial Point)
Position 2 (Final Point)
Flow Rate Analysis (Optional)
Bernoulli Equation Results
Calculated Value
Pressure Change
Energy Conservation Check
Bernoulli's Equation: p₁ + ½ρv₁² + ρgh₁ = p₂ + ½ρv₂² + ρgh₂
Where: p = pressure, ρ = density, v = velocity, g = gravity, h = height
Flow Rate: Q = A × v = π(d/2)² × v
Flow Analysis
Example Calculation - Water Flow in Pipe
Given Parameters
Fluid: Water (ρ = 1000 kg/m³)
Position 1: p₁ = 1000 Pa, h₁ = 3 m, v₁ = 2 m/s
Position 2: p₂ = 1200 Pa, h₂ = 3 m, v₂ = ?
Gravity: g = 9.80665 m/s²
Calculation Steps
Step 1: Apply Bernoulli's equation
p₁ + ½ρv₁² + ρgh₁ = p₂ + ½ρv₂² + ρgh₂
Step 2: Substitute known values
1000 + ½(1000)(2²) + (1000)(9.807)(3) = 1200 + ½(1000)v₂² + (1000)(9.807)(3)
Step 3: Simplify and solve for v₂
1000 + 2000 + 29420 = 1200 + 500v₂² + 29420
32420 = 30620 + 500v₂² → v₂² = 3.6 → v₂ = 1.897 m/s
Common Fluid Densities
Applications
Airplane Wings: Explaining lift generation
Water Systems: Pump design and pipe flow
Venturi Effect: Flow measurement devices
Magnus Effect: Ball trajectory in sports
Aerodynamics: Car and aircraft design
Understanding Bernoulli's Equation
What is Bernoulli's Principle?
Bernoulli's principle states that for an incompressible, steady flow of fluid, the total mechanical energy remains constant along a streamline. This means that as the speed of a fluid increases, its pressure decreases, and vice versa.
Key Assumptions
- •Fluid is incompressible (constant density)
- •Flow is steady (no time-dependent changes)
- •Fluid is inviscid (no viscosity effects)
- •Flow is along a streamline
Bernoulli's Equation
p + ½ρv² + ρgh = constant
- p: Static pressure (Pa)
- ρ: Fluid density (kg/m³)
- v: Flow velocity (m/s)
- g: Gravitational acceleration (m/s²)
- h: Height above reference level (m)
Energy Terms
- p: Pressure energy per unit volume
- ½ρv²: Kinetic energy per unit volume
- ρgh: Potential energy per unit volume
Note: Energy conservation applies along streamlines, not across them
Real-World Applications
Venturi Effect
Flow Constriction
When fluid flows through a constricted section, velocity increases and pressure decreases. Used in carburetors, flow meters, and aspirators.
Airplane Lift
Wing Design
Curved wing shape causes faster airflow over the top surface, creating lower pressure and generating lift force.