How quickly will a can sink in water with a small hole at the bottom?

[i_island0]

Homework Statement

A cylindrical can of height h and base area A is immersed in water to a depth ho and left to sink down. A small hole of area 'a' exists at the bottom of the base of the can. Determine how quickly the can sinks.
http://img80.imageshack.us/my.php?image=fluids1wb7.jpg

Homework Equations

http://img178.imageshack.us/my.php?image=fluidssolmz5.jpg
Thus, vo = sqrt(2gy)
AV = avo
V: velocity of fluid w.r.t. the container

The Attempt at a Solution

Thus,
dy/dt = (a/A)sqrt(2gy)
or, dy/sqrt(y) = (a/A) sqrt(2g) dt
or, on integrating from ho to h, i get

t = sqrt(2/g)[sqrt(h) - sqrt(ho)]A/a

I am not getting the answer, where did i go wrong.

 

[Shooting Star]

In your diagram, y is shown to be the depth of the bottom of the can from the water surface. Have you taken into account that the pressure inside the can will also increase as the water flows in, thus decreasing the rate of water flow inside. Maybe you have, but why don't you just write the justification for your equation?

 

[i_island0]

ah.. thx.. i didn't do that.. i will try to work it out again...

 

[i_island0]

i m not able to do ... can you help me with the solution pls