Bernoulli's Principle
Bernoulli's principle is a basic principle in fluid mechanics, proposed by Swiss mathematician and physicist Daniel Bernoulli in 1738. This principle describes the relationship between the velocity, pressure and height of a flowing fluid.
The core content of Bernoulli's principle is: in the steady flow of a fluid, where the fluid velocity increases, the pressure will decrease; conversely, where the fluid velocity decreases, the pressure will increase. This can be expressed using the Bernoulli equation:
[ P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant} ]
Where:
- ( P ) is the static pressure of the fluid
- ( \rho ) is the density of the fluid
- ( v ) is the velocity of the fluid
- ( g ) is the acceleration due to gravity
- ( h ) is the height (or potential energy) of the fluid
Bernoulli's principle plays an important role in many engineering and physical applications, such as:
- Lift of an aircraft wing: The airflow velocity on the upper surface of the wing is greater than the airflow velocity on the lower surface, resulting in a lower pressure on the upper surface than on the lower surface, thereby generating lift.
- Venturi effect: When a fluid passes through a converging pipe, the flow velocity increases and the pressure decreases, which is used in many flow meters and ejectors.
- Karman vortex street phenomenon: vortex structure formed when fluid bypasses obstacles, used in fluid mechanics research and practical applications, such as bridge design and wind power generation.
Bernoulli's principle reveals the energy conversion relationship of fluid in different regions, which is of great significance for understanding fluid behavior and designing related engineering equipment.