Difference between revisions of "Torricelli's Law"
(Eqn + derivation) |
m (Torricelli's law moved to Torricelli's Law over redirect) |
||
| (3 intermediate revisions by 2 users not shown) | |||
| Line 10: | Line 10: | ||
* [[Thermodynamics]] | * [[Thermodynamics]] | ||
* [[Energy]] | * [[Energy]] | ||
| + | |||
| + | [[Category:Theorems]] | ||
| + | [[Category:Physics]] | ||
Latest revision as of 13:58, 22 December 2007
Torricelli's Law, named after Evangelista Torricelli, relates initial velocity, gravity, and height to the flow of a liquid out of an opening:
![\[v_2=\sqrt{2gh+v_1^2}\]](http://latex.artofproblemsolving.com/b/b/0/bb0ce34b3103a0e12af3b6c75f3eb035824668e1.png)
where 
is the speed out of the opening, 
the initial speed, 
gravity, and 
the distance from the top of the hole to the top of the liquid.
Derivation
Torricelli's Law may be derived by considering the mass of water 
at the top of the liquid. This water has potential energy 
relative to the hole and kinetic energy 
, for total energy of 
. At the level of the hole, this water will have converted all potential energy into kinetic energy, so the total energy will now be 
. By the First Law of Thermodynamics, 
, so 
; solving for ,
