Why square comes in bernoullis equation?

Answer 1

In Bernoulli's equation, the square term arises from the kinetic energy component of fluid flow. The equation, which relates pressure, velocity, and elevation in a flowing fluid, includes the term (\frac{v^2}{2g}), where (v) is the fluid velocity and (g) is the acceleration due to gravity. This term represents the kinetic energy per unit weight of the fluid, highlighting that the energy associated with motion increases with the square of the velocity. Thus, the square emphasizes the non-linear relationship between velocity and kinetic energy in fluid dynamics.