# Sinking bucket - differential equations

1. Oct 2, 2013

### markswabinski

1. The problem statement, all variables and given/known data

Let's have a bucket flowing in water. Now we make a hole underwater. How fast will the bucket sink completely under water?

It is a question from course called Ordinary Differential Equation, so I'm supposed to establish an ODE to solve this problem. I understand how to solve such equation, but I'm really bad at creating models.

The details about water, where the hole is or how the bucket looks like are not specified - can either be general or taken to be insignificant.

3. The attempt at a solution

I've tried by specifying the t0 state: we know that it floats, so buoyancy equals gravity: m0 = rho_w * h * Ab (where m0 is the mass of bucket, rho_w is the density of water, h is how much the bucket has sunk when floating and Ab is the area of base of backet assuming rectangular bucket for simplicity).

Now the hole appears. I have no idea how to employ the rate of flowing water (since differentials are to be used) into the equations to come up with an model to solve.

Any help or the nudge towards right direction (articles / solved examples) highly appreciated.

Last edited: Oct 2, 2013
2. Oct 2, 2013

### tiny-tim

hi markswabinski! welcome to pf!

i assume the bucket starts empty

suppose the rate of filling the bucket is v(t)

what do you think v is likely to be proportional to?

write that as a differential equation (don't bother with any constants such as ρ or A, just include them all in one big constant C ) …

show us what you get