Bernoulli's theorem is based upon the conservation of

Bernoulli's theorem states that for an incompressible, non-viscous fluid in steady flow, the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant along a streamline.

The equation is given by $P + \dfrac{1}{2}\rho v^2 + \rho gh = \text{constant}$.

This is a direct consequence of the work-energy theorem applied to fluid flow.

Therefore, Bernoulli's theorem is based upon the principle of conservation of energy.