Bernoulli equation

Bernoulli equation

Bernoulli's equation describes the principle of energy conservation for flowing fluids. It is a fundamental equation in fluid dynamics that relates the pressure, velocity, and elevation in a flowing fluid. The equation is named after Daniel Bernoulli, a Swiss mathematician and physicist who first formulated it in the 18th century.

Formulation

Bernoulli's equation can be written in various forms, but the most common form is:

P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant}

where:

• P is the fluid pressure,
• \rho is the fluid density,
• v is the fluid velocity,
• g is the acceleration due to gravity, and
• h is the height above a reference point.

This equation assumes that the fluid flow is steady, incompressible, and along a streamline.

Applications

Bernoulli's equation is used in various fields such as aerodynamics, hydrodynamics, and engineering to analyze fluid behavior in different scenarios. It explains phenomena such as the lift force on airplane wings, the operation of Venturi meters, and the behavior of fluids in pipes and open channels.

Limitations

While Bernoulli's equation is a powerful tool in fluid dynamics, it has limitations. It does not apply to viscous flows or flows with significant heat transfer. Additionally, it assumes that the flow is steady and that the fluid is incompressible, which may not be the case in all real-world scenarios.

See Also

• Fluid dynamics
• Hydrostatics
• Venturi effect
• Daniel Bernoulli