fluid mechanics

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 ) .

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  ) .