Bernoulli Equation Calculator
Point 1 (Initial)
Point 2 (Final)
What is the Bernoulli Equation?
The Bernoulli equation is a fundamental principle in fluid dynamics that describes the relationship between pressure, velocity, and elevation in a moving fluid (liquid or gas). Named after Daniel Bernoulli, it is essentially a statement of the principle of conservation of energy for flowing fluids.
The formula states that for an inviscid (frictionless), incompressible fluid in steady flow, the sum of the static pressure, the dynamic pressure (kinetic energy per unit volume), and the hydrostatic pressure (potential energy per unit volume) remains constant along a streamline.
The Bernoulli Formula
The equation is mathematically represented as:
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
- P: Static pressure of the fluid
- ρ (rho): Density of the fluid
- v: Flow velocity
- g: Acceleration due to gravity (9.81 m/s²)
- h: Elevation above a reference point
How to Use This Calculator
This Bernoulli calculator helps you solve for the unknown pressure at a second point (P₂) when you know the conditions at an initial point (P₁, v₁, h₁) and the velocity and height at the destination. Simply enter the fluid density, the parameters for Point 1, and the velocity/height for Point 2. Click "Calculate" to see the resulting pressure in Pascals.
Real-World Applications
Bernoulli's principle is why airplanes fly; the shape of the wing (airfoil) causes air to move faster over the top than underneath, creating lower pressure on top and generating lift. It also explains the Venturi effect used in carburetors and industrial flow meters, as well as why a shower curtain pulls inward when the water is running.
Frequently Asked Questions
Does this apply to all fluids? It works best for low-viscosity, incompressible liquids and gases at low Mach numbers. For highly viscous fluids like honey or compressible high-speed air, modified equations are required.
What units should I use? Our calculator uses standard SI units: Pascals (Pa) for pressure, meters per second (m/s) for velocity, and kilograms per cubic meter (kg/m³) for density.