When is Torricelli’s Law an Approximation?

In summary, the conversation discusses the phenomenon of Torricelli's Law and its relation to Bernoulli's equation when the source area is much greater than the exit area. It is mentioned that when the source and exit areas are closer in size, the phenomenon is no longer referred to as Torricelli's Law. Instead, it may be referred to as Bernoulli's principle. However, there may not be a specific name for the general case. Further clarification is given on the difference between P and Po values in relation to Torricelli's theorem.
  • #1
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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,
1669866344741.png

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!
 
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  • #2
Callumnc1 said:
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?
 
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  • #3
haruspex said:
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!
 
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Related to When is Torricelli’s Law an Approximation?

1. What is Torricelli's Law?

Torricelli's Law is a scientific principle that describes the flow of liquid through an opening in a container. It states that the speed of the liquid as it exits the opening is directly proportional to the square root of the height of the liquid in the container.

2. When is Torricelli's Law an approximation?

Torricelli's Law is considered an approximation when the opening through which the liquid is flowing is significantly smaller than the height of the liquid in the container. In this case, the law may not accurately predict the speed of the liquid.

3. What factors can affect the accuracy of Torricelli's Law?

The accuracy of Torricelli's Law can be affected by factors such as the shape and size of the container, the viscosity of the liquid, and the presence of any obstacles or obstructions near the opening.

4. Can Torricelli's Law be used for any type of liquid?

Torricelli's Law can be used for most liquids, as long as they are incompressible and have a constant density. However, it may not be accurate for highly viscous liquids or those with varying densities.

5. How is Torricelli's Law relevant in real-world applications?

Torricelli's Law has many practical applications, such as predicting the flow rate of water through pipes, designing fountains and sprinkler systems, and understanding the behavior of fluids in hydraulic systems. It is also used in weather forecasting to study the movement of air masses and the formation of tornadoes.

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