# Torricelli/bernoulli physics homework

• Lairreiy
In summary, the conversation discusses a homework problem involving a tank filled with liquid and a hole at the bottom. The top of the tank is open and the hole is labeled as "a". The goal is to find equations for the velocity of the liquid and the time it takes to drain the tank. The conversation also includes hints and explanations for solving the problem, such as using Torricelli's Law and considering the relationship between V and dh/dt.
Lairreiy

## Homework Statement

The homework my professor gave me is...

We have a tank filled with a liquid, it has a hole at the bottom of the tank. The tank does not taper. the hole is at the bottom and not on the side. No extra pressure is applied to the liquid to help it drain and the top of the tank is open too. The top is labeled with an A for the area at the top of the tank. The height is on the side. The hole at the bottom of the tank is labeled a.
He is wanting us to find the equations, the reason the letters have no values. I attached a picture of the tank/drawing and labeling.

## Homework Equations

I will list the questions here.

1. What is the velocity of "a"?
2. What is the time to drain the tank with initial velocity of "a"?
3. What is the actual time to drain entire tank?

## The Attempt at a Solution

1. V2=√2χgχh
3. V=Q/A

I was curious to know if I was on the right track. It has been really tough trying to remember. Honestly I am not sure if i ever covered this before. Please help me.

#### Attachments

• hwhp.jpg
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Hi Lairreiy! Welcome to PF!

(please don't use χ for "times": either use nothing, or use * )
Lairreiy said:
1. V2=√2χgχh

Shouldn't there be a density in there somewhere?

Hint: what is the relation between V and dh/dt ?

Ok Tiny Tim sorry for the X's. I was not sure what most would prefer. My instructor uses them for some odd reason and I was trying to be as specific as possible. Honestly to answer your question about the relations ship about V and dh/dt, I have no idea. I just really need to get some references in a book to find these problems by monday and I knew this would be the best way. It is so hard at an older age to remember things. I really need some help on this one. Do you know the equations? Or Am I on the right path? Thank you very much for hints! :)

Hi Lairreiy!

(just got up :zzz:)
Lairreiy said:

Hint: if the main area is A and the area of the hole is a,

imagine that there's a pipe of area a attached to the hole …

if the pipe fills to a length x, how much does the height h go down?

tiny-tim said:
Hi Lairreiy! Welcome to PF!

(please don't use χ for "times": either use nothing, or use * )

Shouldn't there be a density in there somewhere?

Hint: what is the relation between V and dh/dt ?

Tim: Torricelli's Law states that the outflow velocity is a function of g and the height of the liquid above the hole. The density is not a factor.

http://en.wikipedia.org/wiki/Torricelli's_law

SteamKing said:
Tim: Torricelli's Law states that the outflow velocity is a function of g and the height of the liquid above the hole. The density is not a factor.

oops! i don't know what i was thinking

thanks

## 1. What is Torricelli's theorem?

Torricelli's theorem, also known as Torricelli's law or Torricelli's principle, states that the speed of liquid flowing from an opening in a container is equal to the speed an object would have if it fell from a height equal to the liquid's surface level.

## 2. How is Bernoulli's principle related to Torricelli's theorem?

Bernoulli's principle is a generalization of Torricelli's theorem, stating that the total energy of a fluid, which includes both its kinetic and potential energy, remains constant along a streamline. This principle is derived from the conservation of energy and helps explain the relationship between fluid speed and pressure.

## 3. Can Torricelli's theorem be applied to gases?

Torricelli's theorem is based on the assumption of an incompressible fluid, so it cannot be directly applied to gases. However, it can be used as an approximation for gases at low speeds and high pressures.

## 4. How is Torricelli's theorem used in practical applications?

Torricelli's theorem is used in various real-life scenarios, including the flow of liquids in pipes and nozzles, the operation of water fountains and sprinklers, and the design of carburetors in vehicles.

## 5. What are some limitations of Torricelli's theorem?

Some limitations of Torricelli's theorem include the assumption of an incompressible fluid, the neglect of factors such as viscosity and turbulence, and the need for ideal conditions for accurate results. In practical applications, it is often used as a starting point for more complex calculations.

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