Torricelli/bernoulli physics homework

[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
2. I have not found anyway to calculate yet.
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.

 

[tiny-tim]

Hi Lairreiy! Welcome to PF!

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

1. V2=√2χgχh

Shouldn't there be a density in there somewhere?

2. I have not found anyway to calculate yet.

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

 

[Lairreiy]

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! :)

 

[tiny-tim]

Hi Lairreiy!

(just got up :zzz:)

… to answer your question about the relations ship about V and dh/dt, I have no idea.

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?

 

[SteamKing]

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

 

[tiny-tim]

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 ​