When is Torricelli’s Law an Approximation?

[member 731016]

Homework Statement

An enclosed tank containing a liquid of density row has a hole in its side at a distance y1
from the tank’s bottom (Fig. 14.20). The hole is open to the atmosphere, and its
diameter is much smaller than the diameter of the tank. The air above the liquid is
maintained at a pressure P. Determine the speed of the liquid as it leaves the hole
when the liquid’s level is a distance h above the hole.

Relevant Equations

Bernoulli’s equation

Hi!

For this problem,

When Area 2 > Area 1, but not by much, is this phenomenon no longer called Torricelli's Law because the water is not approximately stationary at the top surface? What is this called now?

Many thanks!

 

[haruspex]

When Area 2 > Area 1, but not by much, is this phenomenon no longer called Torricelli's Law because the water is not approximately stationary at the top surface? What is this called now?

Torricelli's Law is the approximation of Bernoulli's equation when the source area is much greater than the exit area. So if you are not making that approximation it is called ... what do you think?

 

[member 731016]

Torricelli's Law is the approximation of Bernoulli's equation when the source area is much greater than the exit area. So if you are not making that approximation it is called ... what do you think?

Bernoulli's equation? I guess there is no name for the general case.

Many thanks!

 

[Steve4Physics]

Bernoulli's equation? I guess there is no name for the general case.

Many thanks!

'Bernoulli's principle' might be a better term, in your original context.
(e.g. https://en.wikipedia.org/wiki/Bernoulli's_principle)

 

[Lnewqban]

As P and Po do not have the same value, this is not a case in full compliance with the Torricelli's theorem.

Please, see:
https://en.m.wikipedia.org/wiki/Torricelli's_law#Torricelli's_original_derivation

 

[member 731016]

'Bernoulli's principle' might be a better term, in your original context.
(e.g. https://en.wikipedia.org/wiki/Bernoulli's_principle)

Thank you @Steve4Physics !

 

[member 731016]

As P and Po do not have the same value, this is not a case in full compliance with the Torricelli's theorem.

Please, see:
https://en.m.wikipedia.org/wiki/Torricelli's_law#Torricelli's_original_derivation

Thank you @Lnewqban !