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Formulas

Bernoulli's Principle

States that for an inviscid flow of a non-conducting fluid, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.

Physics
Subject
Fluid Mechanics
Sub Subject
Fluid Dynamics
Chapter
Conservation of Energy in Fluids
Topic

Bernoulli's Principle

📊 advanced
$$P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$$
States that for an inviscid flow of a non-conducting fluid, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.
Variables & Units
$P$
Static pressure
Unit: Pascal ($Pa$)
$\rho$
Fluid density
Unit: $kg/m^3$
$v$
Flow velocity
Unit: $m/s$
$g$
Acceleration due to gravity
Unit: $9.81 m/s^2$
$h$
Elevation head
Unit: Meter ($m$)
Key Information
📐 Derived From
Conservation of energy for a flowing fluid.
💡 Example
Explaining the lift on an airplane wing.
🔧 Applications
Aerodynamics, plumbing, and carburetors.
⚠️ Constraints
Applies to incompressible, non-viscous, laminar flow.

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