**Equation of continuity**

In a in compressible and non viscous fluid the mass of the
fluid that enters at a given point per second is equal to the mass of the point
that leaves in the same time.This concept is valid only when the fluid density is constant
and it is not experiencing any viscous forces opposite its motion.

It can be mathematically proved that as per this concept the
area of the cross-section of the fluid flow is inversely proportional to its
velocity. If the area of cross-section is more velocity is less and vice versa.

It can be quite easily observed in daily life also. If the
opening of a water tap is completely opened, water comes out with a certain
velocity. If half of its opening is closed with the finger we can quite easily
noticed that water is coming with better velocity.

**Bernoulli’s Theorem**

In a in compressible, non viscous, a rotational and streamlined
fluid flow of the some of potential energy, kinetic energy and pressure energy
per unit mass is always constant.This fundamental concept is valid only when the fluid is

1.Having a constant density,

2. No opposition appositive to its motion,

3.The fluid particles are having only translatory motion and
no rotatory motion,

4. All particles of the fluid are having the same velocity is
when they are passing a particular point.

This is nothing but law of conservation of energy. Being a
fluid it has not only potential and kinetic energy, it is also having pressure
energy. The total of all the energies is always constant. If any one energy
increases is obvious that the other energy decreases so that the total energy always
remains constant. It is similar to law of conservation of energy that the energy
is neither created, nor destroyed it just converts from one form to another
form.

We can prove this theory basing on the concept of work energy
theorem. It simply states that the work done is equal to changing its energy.We have further derived it in the following diagram that
changing kinetic energy is equal to sum of difference in potential energies and
pressure energies.

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