In 1738, Daniel Bernoulli proposed a theorem for the streamline flow of a liquid based on the law of conservation of energy. According to Bernoulli’s theorem, for the streamline flow of a non-viscous and in compressible liquid, the sum of the pressure energy, kinetic energy and potential energy per unit mass is a constant.

**P/ρ + v ^{2}/2 + gh = constant**

**This equation is known as Bernoulli’s equation.**

Consider streamline flow of a liquid of density ρ through a pipe AB of varying cross section. Let P_{1} and P_{2} be the pressures and a_{1} and a_{2}, the cross sectional areas at A and B respectively. The liquid enters A normally with a velocity v_{1} and leaves B normally with a velocity v_{2}. The liquid is accelerated against the force of gravity while flowing from A to B, because the height of B is greater than that of A from the ground level. Therefore P_{1} is greater than P_{2}. This is maintained by an external force.