State and prove Bernoulli's theorem.
Statement: For the streamline flow of non-viscous and incompressible liquid, the sum of potential energy, kinetic energy and pressure energy is constant.
Proof: Let us consider the ideal liquid of density ρ flowing through the pipe LM of varying cross-section. Let P1 and P2 be the pressures at ends L and M and A1 and A2 be the areas of cross-sections at ends L and M respectively. Let the liquid enter with velocity V1 and leave with velocity v2. Let A1 > A2. By equation of continuity,
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