State Bernoulli's theorem

Statement: For the streamline flow of non-viscous and incompressible liquid, the sum of potential energy, kinetic energy and pressure energy is constant.



Proof: Let us consider the ideal liquid of density ρ flowing through the pipe LM of varying cross-section. Let P₁ and P₂ be the pressures at ends L and M and A₁ and A₂ be the areas of cross-sections at ends L and M respectively. Let the liquid enter with velocity V₁ and leave with velocity v₂. Let A₁ > A₂. By equation of continuity,

Bernoulli’s principle states that The total mechanical energy of the moving fluid comprising the gravitational potential energy of elevation, the energy associated with the fluid pressure and the kinetic energy of the fluid motion, remains constant.

Bernoulli’s equation formula is a relation between pressure, kinetic energy, and gravitational potential energy of a fluid in a container.

The formula for Bernoulli’s principle is given as:

Where,

• p is the pressure exerted by the fluid
• v is the velocity of the fluid
• ρ is the density of the fluid
• h is the height of the container