The law of conservation of energy for perfect fluid flow

It was previously shown, that the Bernoulli equation expresses the conservation of mechanical energy for the flow of a perfect fluid, provided that the body forces are conservative, and the flow irrotational and barotropic. This equation is valid for a unit mass of fluid at any point in the entire field of flow. In the subsequent section we shall consider an arbitrary finite volume of flowing fluid in order to determine the rate of change of its kinetic and internal energy.