Torricelli

The velocity of a liquid stream exiting from a nozzle, pressured solely by a vertical column of that same liquid, is equal to the free-fall velocity of a solid mass dropped from the sameheight as the top of the liquid column. In both cases, potential energy (in the form of vertical height) converts to kinetic energy (motion):



This was discovered by EvangelistaTorricelli almost 100 years prior to Bernoulli’s more comprehensive formulation. The velocity may be determined by solving for v after setting the potential and kinetic energy formulasequal to each other (since all potential energy at the upper height must translate into kinetic energy at the bottom, assuming no frictional losses).

Note how mass (m) simplydisappears from the equation, neatly canceling on both sides. This means the nozzle velocity depends only on height, not the mass density of the liquid. It also means the velocity of the fallingobject depends only on height, not the mass of the object.
TORRICELLI´S AND BERNOULLI´S EQUATION VERIFICATION

TORRICELLI´S EQUATION
The velocity was determined setting the potencialand kinetic energy formulas to equal (being potencial energy´s formula Ep=mgh and kinetic´s Ek=1/2mv2).

Taking into account that the mass is the same in both cases, it disappears.So the velocity equation is going to depend only in the height and the gravity.

BERNOULLI´S EQUATION
If we try to solve this problem with Brenoulli´s equation, we have to takeinto account 2 points of the tank.



h2 is 0 because we place there the datum plane to calculate the height of the fluid in the tank.
So, to solve the velocity at point2, we have the next equation:

To conclude, we can say that with both theorems the result is the same, and the velocity of the nozzle is only depend on the height and the gravity.