# Time it takes for a water tank to empty

1. Oct 27, 2012

### Flipmeister

1. The problem statement, all variables and given/known data
A cylindrical tank of diameter 2R contains water to a depth d. A small hole of diameter 2r is opened in the bottom of the tank. r<<R, so the tank drains slowly. Find an expression for the time it takes to drain the tank completely.

2. Relevant equations
$$p_1+\frac{1}{2}ρv_1^2+ρgh_1=p_2+\frac{1}{2}ρv_2^2+ρgh_2\\ Q=vA=\frac{\delta V}{\delta t}$$

3. The attempt at a solution
I believe, since $p_1$ and $p_2$ are the same, that Bernoulli's equation becomes $2\rho gd=v_2^2$. I am assuming I need to use the equation of volume rate of flow for time, but then I would need the velocity $v_2$. But how do I solve for time from that? How am I to find Q?

Last edited: Oct 27, 2012
2. Oct 27, 2012

### TSny

Hello. Hmm, you have a factor of 2 in the third term on the left of Bernoulli's equation. Check to make sure that's right.

It would help if you told us where you're picking points 1 and 2.

What is the justification for cancelling the terms that involve h1 and h2?

3. Oct 27, 2012

### Flipmeister

Whoooops I should have reread my post. Typos everywhere. I've edited now; thanks for pointing them out.

4. Oct 27, 2012

### TSny

OK, so I presume point 2 is at the little hole at the bottom and that you made the approximation $v_1≈0$. Still looks like a little error (or typo) in your expression for $v_2^2$. Can you find it?

5. Oct 27, 2012