Question

Explain Bernoulli’s Principle.

Answer 1

Hint: A fluid when flows through a path, majorly has three energies associated with it. These are kinetic energy, potential energy and pressure energy. Bernoulli’s theorem gives a connection between these energies for an ideal fluid, which is not viscous and cannot be compressed.

Complete answer:
Bernoulli’s theorem states that the addition of all the energies of a fluid when fluid is in motion is constant. Or in other terms no energy is dissipated through friction between the layers of the fluid. This theorem is for ideal fluids.
\[\dfrac{1}{2}\rho {v^2} + \rho gh + p = \text{constant}\]
Where, $p$ is the pressure exerted by the fluid, $v$ is the velocity, \[\rho \] is the density, $h$ is the height of the fluid containing the container.
\[\dfrac{p}{{\rho g}} + \dfrac{{{v^2}}}{{2g}} + y = cons\tan t\] (per unit weight)
Each term in per unit mass equation has dimensions of length, \[\dfrac{{{v^2}}}{{2g}}\] is the velocity head, \[\dfrac{p}{{\rho g}}\] is pressure head, \[y\] is potential head.

A physical example is when height remains the same and pressure in a region is lower than velocity will increase to keep the term constant. Bernoulli’s principle is very useful in study of liquids having unsteady flow as this can be used as an approximation for variables such as pressure and speed of fluids. Bernoulli’s theorem can also be defined as the conservation of energies associated with a fluid in motion.

Note: Bernoulli’s principle has lots of assumptions: Flow of fluid is steady, fluid is incompressible, it’s net angular momentum is zero at all points in a fluid (irrotational). And fluid is ideal with zero energy lost in friction.