Bernoulli's principle is based on the law of conservation of

The Bernoulli's theorem is in one way the principle of conservation of energy for a flowing liquid (or gas). When an incompressible and non-viscous liquid (or gas) flows in stream-lined motion from one place to another, then at every point of its path the total energy per unit volume (pressure energy + kinetic energy + potential energy) is constant.

That is,

            $\mathrm{P} + \frac{1}{2}{\mathrm{\rho v}}^2 + \mathrm{\rho gh} = \mathrm{constant}$

where P is pressure, $\rho$ is density, g is gravity, v is velocity and h is height.