It describes that the total energy (pressure energy, potential energy and kinetic energy) of an incompressible and non-viscous fluid in steady flow by a pipe remains constant throughout the flow, provided there is no source or sink of the fluid along the length of the pipe.

This statement is related on the consideration that there is no loss of power because of friction.

Mathematically, for unit volume of fluid going by a pipe.

Proof. To prove Bernoulli’s theorem, we have the given assumptions:
1.    The liquid is incompressible.   
2.     The liquid is non–viscous. 
3.     The flow is steady and the velocity of the liquid is less than the critical velocity for the liquid.