# Bernoulli’s Theorem

According to this theorem, the total energy, (pressure energy, potential energy and kinetic energy) per unit volume or mass of an incompressible and non-viscous fluid in steady flow through a pipe remains constant throughout the flow, provided there is no source or sink of the fluid along the length of the pipe (Fig. 8).

**Fig. 8**

Mathematically, for unit volume of liquid flowing through a pipe.

constant

- Bernoulli’s theorem for unit mass of liquid flowing through a pipe can also be written as:
- Dividing above equation by
*g*, we get

Here

*P*/*ρ*g is called pressure head,*h*is called gravitational head, and v^{2 }/ 2g is called velocity head. From this equation Bernoulli’s theorem can be stated as: in streamline flow of an ideal liquid, the sum of pressure head, gravitational head, and velocity head of every cross section of the liquid is constant.