Illustrations of Bernoullis equation:

You may note from Figure that mass m moves through a vertical distance (h₂ - h₁) in going from the point A to B. Therefore, work must be done on the liquid to move it from A to B against the gravitational force. The net work done on the system by the gravitational force can be written as:

- mg (h₂ - h₁)

According to the work-energy principle, the change in kinetic energy of the system is equal to the net work done on the system by external forces. So, from we can write:

1/2 m (v₂²  - v₁² ) = ( p₁- p₂ ) m/ ρ + [- mg (h₂- h₁ )]

or,  p₁/ ρ  + gh₁ +  v₁²/2 =  p₂/ ρ  + gh₂ +v₂²/2

Eq. (1.13) is called Bernoulli's equation. It could also be written as:

 p/ ρ + gh + v²/v     = constant.

Multiplying both sides by ρ, we get:

p + ρ gh + 1/2 ρv² = constant.

We have written Bernoulli's equation in the form represented by Eq. to show that it (Bernoulli's equation) is a statement of the fact that the available energy per unit volume of a fluid remains constant along any given tube of flow. This follows from the fact each term in Eq. has the dimensions of energy. The term1/2 ρ v² is the kinetic energy per unit volume; the term ρ gh is the gravitational potential energy per unit volume; and p represents the flow energy per unit volume. Therefore, in other words, Bernoulli's equation represents the fact that the various forms of available energy (kinetic, potential and flow or pressure energy) can be transformed from one to another; the total available energy remains constant. Now let us elaborates a few illustrations of Bernoulli's equation.