# Bernoulli's Equation Calculator

Calculate fluid pressure using Bernoulli's equation: P + ½ρv² + ρgh = constant. Solve for pressure at a second point given velocities.

## What this calculates

Bernoulli's equation describes the conservation of energy in a flowing fluid. For an ideal, incompressible, non-viscous fluid: P + ½ρv² + ρgh = constant along a streamline. This calculator finds the pressure at a second point given the conditions at a first point, useful for pipe flow, airfoil lift, and venturi effects.

## Inputs

- **Pressure at Point 1 (P₁)** (Pa) — min 0
- **Velocity at Point 1 (v₁)** (m/s) — min 0
- **Height at Point 1 (h₁)** (m)
- **Velocity at Point 2 (v₂)** (m/s) — min 0
- **Height at Point 2 (h₂)** (m)
- **Fluid Density (ρ)** (kg/m³) — min 0 — Water: 1000, Air: 1.225, Oil: ~900

## Outputs

- **Pressure at Point 2 (P₂)** (Pa) — Calculated pressure at point 2
- **Pressure at Point 2** (kPa) — Pressure in kilopascals
- **Pressure Difference (ΔP)** (Pa) — P₁ - P₂

## Frequently Asked Questions

**Q: What is Bernoulli's principle?**

A: Bernoulli's principle states that in a flowing fluid, an increase in velocity occurs simultaneously with a decrease in pressure or potential energy. It is a statement of energy conservation for flowing fluids. The full equation P + ½ρv² + ρgh = constant sums the pressure energy, kinetic energy, and potential energy per unit volume.

**Q: How does Bernoulli's equation explain airplane lift?**

A: An airplane wing (airfoil) is shaped so air flows faster over the top than the bottom. By Bernoulli's principle, faster flow means lower pressure on top. The pressure difference between the bottom (higher pressure) and top (lower pressure) creates an upward force called lift. However, angle of attack and Newton's third law also contribute significantly.

**Q: What is the venturi effect?**

A: The venturi effect occurs when fluid flows through a constricted section of pipe. The velocity increases in the narrow section, and by Bernoulli's principle, the pressure decreases. This is used in venturi meters to measure flow rate, in carburetors to mix fuel with air, and in aspirators to create suction.

**Q: What are the limitations of Bernoulli's equation?**

A: Bernoulli's equation assumes the fluid is ideal: incompressible, non-viscous, and in steady flow along a streamline. It fails for compressible flows (high-speed gas), viscous fluids (like honey), turbulent flow, or flow with energy addition/removal (pumps, turbines). For real engineering, corrections for friction and compressibility are needed.

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Source: https://vastcalc.com/calculators/physics/bernoulli
Category: Physics
Last updated: 2026-04-21