Bernoulli Equation Calculator
Calculate pressure, velocity, and height relationships in fluid flow using Bernoulli's principle
Calculator
Point 1
Point 2
Introduction
Bernoulli's equation describes the relationship between pressure, velocity, and height in fluid flow. It states that the total energy of a fluid particle remains constant along a streamline, assuming incompressible, non-viscous flow with no external work added.
This fundamental principle is essential for understanding aircraft wings, venturi meters, pipe flow, and many other fluid dynamics applications.
How to Use
- Enter pressure at point 1 (Pa) - atmospheric pressure: 101,325 Pa
- Input velocity at point 1 (m/s) - typical range: 0.1-10 m/s
- Specify height at point 1 (m) - relative to reference point
- Enter corresponding values for point 2
- Input fluid density (kg/m³) - for water: 998 kg/m³, air: 1.225 kg/m³
- Click "Calculate" to verify Bernoulli's equation
Formula
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
P = Pressure (Pa)
ρ = Fluid density (kg/m³)
v = Velocity (m/s)
g = Gravitational acceleration (9.81 m/s²)
h = Height (m)
Bernoulli's Equation Formulas
Standard Bernoulli Equation
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
Where P = pressure, ρ = density, v = velocity, g = gravity, h = height
Simplified Form (Horizontal Flow)
P₁ + ½ρv₁² = P₂ + ½ρv₂²
When height difference is negligible (h₁ = h₂)
Velocity from Pressure
v = √(2ΔP ÷ ρ)
For calculating velocity from pressure difference
Use Cases
Aerospace Engineering
- Aircraft wing design and lift calculation
- Wind tunnel testing and analysis
- Rocket propulsion systems
- Helicopter rotor aerodynamics
Civil Engineering
- Pipe flow analysis and design
- Venturi meter calculations
- Water distribution systems
- Hydroelectric power plants
Understanding Your Results
Pressure Terms
Static pressure represents the fluid's potential energy. Higher pressure at one point drives flow toward lower pressure regions.
Velocity Terms
Dynamic pressure (½ρv²) represents kinetic energy. Faster flow means lower static pressure due to energy conservation.
Height Terms
Gravitational potential energy (ρgh) becomes significant in vertical flows. Higher elevation points have more potential energy.
Frequently Asked Questions
What are the assumptions in Bernoulli's equation?
The equation assumes incompressible flow, non-viscous fluid, steady flow, and no external work added to the system. Real fluids may deviate from these ideal conditions.
How does Bernoulli's principle explain lift?
Air flowing over an airfoil moves faster over the top surface, creating lower pressure. The pressure difference between upper and lower surfaces generates lift force.
What is the continuity equation?
The continuity equation (A₁v₁ = A₂v₂) states that the volume flow rate remains constant in a closed system, relating velocity changes to cross-sectional area changes.
Related Calculators
Conclusion
Bernoulli's equation is a cornerstone of fluid mechanics that describes the conservation of energy in fluid flow. Understanding this principle enables engineers to design efficient systems, predict fluid behavior, and solve complex problems in various engineering fields.
From aircraft design to pipeline engineering, Bernoulli's principle continues to be fundamental in modern engineering applications, demonstrating the elegant relationship between pressure, velocity, and height in fluid systems.