Point 1 (Known Values)
Point 2 (Enter Known Values)
P + ½ρv² + ρgh = constant
P = Static pressure (Pa or psi)
ρ = Fluid density (kg/m³ or lb/ft³)
v = Fluid velocity (m/s or ft/s)
g = Gravitational acceleration (m/s²)
h = Height/elevation (m or ft)
Bernoulli's principle states that for an ideal fluid flowing along a streamline, the sum of pressure energy, kinetic energy, and potential energy remains constant. This fundamental principle of fluid dynamics was formulated by Swiss mathematician Daniel Bernoulli in his book Hydrodynamica (1738) and forms the basis for understanding fluid behavior in pipes, aircraft wings, and many other applications.
The equation describes the conservation of mechanical energy in a flowing fluid. When fluid velocity increases (such as in a constricted pipe section), the static pressure must decrease to maintain energy conservation. This inverse relationship between velocity and pressure is the key insight that explains phenomena from airplane lift to the curve of a baseball.
Venturi Effect
Used in carburetors, vacuum pumps, and flow measurement devices where fluid velocity changes through a constricted section create pressure differences.
Airplane Wings
Air flows faster over the curved top surface of a wing, creating lower pressure above than below, generating lift force.
Pipe Flow Analysis
Engineers use Bernoulli's equation to design water supply systems, calculate pressure drops, and size pumps for fluid transport.
Medical Devices
Blood flow analysis, respiratory equipment, and nebulizers all rely on Bernoulli's principle for their operation.
Disclaimer: Bernoulli equation calculations assume ideal, incompressible, non-viscous fluid flow along a streamline. Actual behavior may vary due to friction, turbulence, compressibility effects, and energy losses. Consult fluid mechanics references and professional engineers for precise analysis in critical applications.