Bernoulli's equation und applications

Bernoulli's equation für fluid Strömung including venturi meters, pitot tubes und Strömung measurement.

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Overview

The Bernoulli equation relates pressure, velocity, and elevation in a steady, incompressible, inviscid flow. It is derived from the conservation of energy principle for fluid flow along a streamline.

Key Formulas

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

The sum of static pressure, dynamic pressure, and hydrostatic pressure is constant along a streamline.

Pressure Form

$P_1 + \frac{1}{2}\rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2}\rho v_2^2 + \rho g h_2$

Between any two points on a streamline.

Variables

Symbol	Description	Unit
$P$	Static pressure	Pa
$\rho$	Fluid density	kg/m³
$v$	Flow velocity	m/s
$g$	Gravitational acceleration	m/s²
$h$	Elevation above reference	m

Bernoulli Equation Calculator

Pressure at Point 1(kPa)

Velocity at Point 1(m/s)

Elevation at Point 1(m)

Velocity at Point 2(m/s)

Elevation at Point 2(m)

Notes

Valid only for incompressible, steady, inviscid flow along a streamline
Real flows have viscous losses — use the extended equation with head loss for pipe flow
For compressible flows (Mach > 0.3), use the compressible Bernoulli equation

Key Facts

Bernoulli's equation is a statement of conservation of energy for fluid flow
The equation explains why airplane wings generate lift (faster flow = lower pressure)
Venturi effect and Pitot tubes are direct applications of Bernoulli's principle

References

Original Source

Quelle: engineeringtoolbox.com