what is torricelli law? derive it.
Answers
Answer:
Torricelli law states that the speed of flow of fluid from an orifice is equal to the speed that it would attain if falling freely for a distance equal to the height of the free surface of the liquid above the orifice. Consider any vessel which has an orifice (slit)filled with some fluid.
Torricelli's equation, or Torricelli's formula, is an equation created by Evangelista Torricelli to find the final velocity of an object moving with a constant acceleration along an axis (for example, the x axis) without having a known time interval.
A simple experiment to test Torricelli's law can also be performed by a soda bottle by puncturing the bottom with a small hole. As the height in the reservoir decreases, the exit velocity decreases.
Derivation :-
Assuming that the fluid is in compressible, Bernoulli’s principle states that:
v²/2 + gh p/ρ = constant
Where,
v is speed of liquid,
g denotes gravitational acceleration,
h shows liquid’s height over reference point,
ρ is density.
P is equal to atmospheric pressure at the top of the container.
v is considered as 0 because the liquid surface drops in height slowly compared to the speed at which liquid leaves the tank.
h is 0 and p is atmospheric pressure at opening h = 0.
gh+patmρ=v22+patmρ
v² = 2gh
V = √2gh