Torricelli’s theorem ( Velocity of efflux ) : Principle , Derivation and sloved examples

According to Torricelli’s theorem -The velocity of efflux of a liquid issuing out of an orifice is the same as it would attain if allowed to fall freely through the vertical height between the liquid surface and orifice .
velocity of efflux v = ( 2gh )1/2

Note – The velocity of efflux is the velocity of escaping liquid relative to the container (but not necessarily relative to ground when the container moves ) .

Kepler’s laws of planetary motion | Definition , Diagrams , Equations ,Facts and Solved Examples .

Johannes Kepler used empirical observations, and sophisticated calculations to arrive at the famous Kepler’s laws of planetary motion, published in 1609 and 1619. What is particularly significant about Kepler’s laws is that they challenged the prevailing world’s view, with the Earth in the center of the universe (a geocentric theory) and the Sun and all the planets and stars orbiting around it, just as the Moon does .

Variation of pressure with Depth in a fluid

We know that in an statics fluid pressure in horizontal direction will be constant because  of equi-pressure surface but in case of vertical Variation it’s Vary .If the weight of the fluid can be neglected, the pressure in a fluid is the same throughout its volume. But often the fluid’s weight is not negligible and under such condition pressure increases with increasing depth below the surface .
dp/dy = ρg . ( This is the general expression  of variation of pressure with depth  ) .