Statement of Bernoulli's Theorem: When an ideal fluid (i.e incompressible and non-viscous Liquid or Gas) flows in streamlined motion from one place to another, then the total energy per unit volume (i.e Pressure energy + Kinetic Energy + Potential Energy) at each and every of its path is constant. $P+\frac{1}{2}\rho v^{2} + \rho gh= constant$ Derivation of Bernoulli's Theorem Equation: Let us consider that an incompressible and non-viscous liquid is flowing in streamlined motion through a tube $XY$ of the non-uniform cross-section. Now Consider: The Area of cross-section $X$ = $A_{1}$ The Area of cross-section $Y$ = $A_{2}$ The velocity per second (i.e. equal to distance) of fluid at cross-section $X$ = $v_{1}$ The velocity per second (i.e. equal to distance) of fluid at cross-section $Y$ = $v_{2}$ The Pressure of fluid at cross-section $X$ = $P_{1}$ The Pressure of fluid at cross-section $Y$ = $P_{2}$ The height of cross-section $X$ from