ベルヌーイの定理

Bernoulli's principle states that when a fluid moves horizontally, pressure and speed have an inverse relationship. As fluid speed increases, pressure decreases, and vice versa. This principle applies to incompressible fluids in laminar, steady flow where gravitational energy density remains constant. Understanding this relationship is fundamental to analyzing horizontal flow systems.

Entrainment occurs when high-speed fluid creates a low-pressure region that draws in another fluid. Bunsen burners use natural gases to entrain air for combustion, while atomizers use air to entrain perfume droplets. This phenomenon directly results from Bernoulli's principle, where pressure drops in high-speed regions, allowing adjacent fluids to rush in and mix.

A manometer has two openings: one directly opposing fluid flow (stagnation point) and one along the flow direction. The pressure difference between these points is proportional to the square of the incoming fluid's speed. This pressure difference causes the liquid inside to reach different heights on each end. By measuring the height difference, you can determine the fluid's speed.

Bernoulli's equation applies to incompressible fluids in laminar, steady flow. For static fluids, kinetic energy density equals zero, reducing the equation to a pressure-height relationship. For horizontal flows, gravitational energy density is constant throughout. These conditions ensure the energy conservation principles underlying Bernoulli's equation remain valid.

When a fluid is static, its kinetic energy density is zero. Bernoulli's equation then reduces to an expression relating pressures at different heights within the incompressible fluid. This simplified form shows how pressure varies with gravitational potential energy, providing the foundation for understanding hydrostatic pressure in stationary fluids.

In horizontal flow, total mechanical energy remains constant according to energy conservation. When fluid speed increases, kinetic energy increases, so pressure energy must decrease to maintain constant total energy. This inverse relationship between speed and pressure is the core principle behind many fluid applications, from carburetors to spray devices.

Bernoulli's equation is a general energy conservation statement for incompressible fluids in laminar, steady flow. Bernoulli's principle is the simplified form applied specifically to horizontal flows where gravitational energy density is constant. This principle directly relates pressure and speed, making it particularly useful for analyzing horizontal flow systems and practical applications.