Current location - Training Enrollment Network - Mathematics courses - What is the geometric meaning of Bernoulli equation?
What is the geometric meaning of Bernoulli equation?
The physical meaning of Bernoulli equation is that the mechanical energy of fluid passing through the flow section remains unchanged along the flow path. Geometrically, the total head is constant along the direction of water flow. As the speed increases, the pressure decreases. When the speed decreases, the pressure increases. On the other hand, Bernoulli equation says that the work done by pressure on fluid is equal to the change of kinetic energy of fluid. Give you an incompressible and inviscid fluid flow field, and you can find out the pressure field of that flow field.

Relevant theoretical explanation

This theory was put forward by Swiss mathematician daniel bernoulli in 1738, and it was called Bernoulli principle at that time. Later generations call the integration of Euler equation along streamline when it flows stably in gravity field as Bernoulli integral, and the energy equation of steady adiabatic flow of inviscid fluid in gravity field as Bernoulli theorem. These are collectively called Bernoulli equations and are one of the basic equations of fluid dynamics.

Bernoulli equation is essentially the expression of the law of conservation of energy when ideal fluid flows stably, and it is the basic law of fluid mechanics. The conservation of mechanical energy of fluid points on streamline is the physical meaning of Bernoulli equation.