I'm not a native english speaker, so I apologize if my explanations are a bit awkward. I do not have a solution to this problem and I'd be grateful if someone could check this/help. I also have absolutely no idea how to even begin. Asked my colleagues, none of them know. I'm pretty desperate.
There's a barrel filled with water. The volume of water inside is V=200L. Its hight is 1m.
We decide to make a hole on the bottom of the barrel. The size of the hole is 1cm2.
How much time will it take for the barrel to become half-empty (when will the height drop to 1/2 of the initial height)?
What I believe is relevant here is:
Applying Bernoulli's principle:
Toricelli (this is derived from Bernoulli's principle in this case from what I understand):
The Attempt at a Solution
I got used to solving problems that include manometers, tubes of different sizes etc., but with a simple problem like this, I'm not sure where to begin.
First I did basic conversions.
My first thought was writing down:
and proceed from there, but I didn't get anything useful, since none of the equations I've written down took the size of the small hole into consideration.
t=v*s would seem fine, but since velocity isn't constant, I need a differential equation, ending up with an integral I cannot solve nor does it seem like a way to solve this (please correct me if I'm wrong).
I tried writing down the Bernoulli equation I've written above and it just leads to v=sqrt(2gh). Again, I'm not getting anything. Tried S1*v1=S2*v2, but since v1 is close to zero, I can't get anything from this equation either.