BernoulliPrinzip

BernoulliPrinzip refers to Bernoulli's principle, a fundamental concept in fluid dynamics that describes how pressure, velocity, and height relate in moving fluids. For steady, incompressible, non-viscous flow, along a single streamline the total mechanical energy per unit volume remains constant. This is expressed by P + 1/2 ρ v^2 + ρ g h = constant, where P is static pressure, ρ is density, v is flow speed, g is gravitational acceleration, and h is elevation. The principle follows from conservation of energy and the Euler equations; as speed increases, pressure or height can decrease, and vice versa.

When the flow height is constant, such as in horizontal passages, the relation simplifies to P + 1/2 ρ v^2 = constant along a streamline. The term 1/2 ρ v^2 is called dynamic pressure, representing kinetic energy per unit volume.

Applications of the Bernoulli principle include explaining lift generation on airplane wings, operation of Venturi meters, and behavior of fluids in pipes where velocity changes lead to pressure differences. It also helps describe how openings, nozzles, and diffusers influence pressure and speed.

Limitations and scope are important. The equation assumes steady, incompressible, non-viscous flow with no energy added or dissipated and is applicable along a streamline. Real fluids have viscosity and can be compressible at high speeds or turbulent; external energy sources like pumps or turbines alter the energy balance. Consequently, BernoulliPrinzip provides a useful but approximate model, most accurate for moderate-speed, low-viscosity, incompressible flows.