100 Points
Describe the independent and dependent variables in Torricelli’s law.

Torricelli had interests in various aspects of physics and mathematics and torricelli’s theorem was one of his biggest achievements. The law explains the relation between fluid leaving a hole and the liquid’s height in that container.

The relationship can be summarized in the following manner. If you have a container filled with fluid with small holes at the bottom of the container, the fluid leaves through the hole with velocity same as it would experience if dropped from the same height to the hole level. If the liquid is dropped from a height h, it would have a velocity v and this v is the same velocity at which the liquid leaves the hole when the height of fluid h is same as liquid dropped in the container.

We also assume that it is an ideal fluid which means that the liquid is in compressible, non-viscous and laminar flow. These factors cannot be neglected since same rules cannot be applied to non-fluids as their viscosity and flow may not be same across the liquid itself.

Torricelli’s Law 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.

g

h

+

p

a

t

m

ρ

=

v

2

2

+

p

a

t

m

ρ

v² = 2gh

V = √2gh

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.

Explanation:

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