The Bernoulli equation is a fundamental equation in fluid mechanics that describes the relationship between the pressure, velocity, and elevation of a fluid in steady-state flow. It is named after Swiss mathematician and physicist Daniel Bernoulli, who first derived the equation in the 18th century.
The Bernoulli equation is expressed as:
P + 1/2ρv^2 + ρgh = constant
where P is the pressure, ρ is the density, v is the velocity, g is the acceleration due to gravity, h is the elevation, and the constant on the right-hand side represents the total energy per unit weight of fluid.
The Bernoulli equation states that the total energy of a fluid at any point in a pipe or channel is constant along a streamline. This means that as the fluid moves through a pipe or channel, its pressure, velocity, and elevation may change, but the total energy remains constant.
The Bernoulli equation is commonly used in the design of fluid systems, such as pipes, ducts, and channels, and it has many practical applications in engineering, such as the design of aircraft wings, turbines, and pumps.
It should be noted that the Bernoulli equation assumes ideal fluid behavior, meaning that it assumes the fluid is incompressible, inviscid, and irrotational. While these assumptions may not hold true in all fluid systems, the Bernoulli equation provides a useful starting point for analyzing fluid flow in many practical situations.More about Digital Content