Conical Tank Water Drainage: Finding Time to Empty with Differential Equations

[chae]

Homework Statement

Water drains out of an inverted conical tank at a rate proportional to the depth (y) of water in the tank. Write a diff EQ as a function of time.

This tank's water level has dropped from 16 feet deep to 9 feet deep in one hour. How long will it take before the tank is empty.

Homework Equations

V=1/3pir²y

dV/dt=pi(r₀/y₀)²y²dy/dt

The Attempt at a Solution

The solution to the first question is: dy/dt=-k(y₀/r₀)²(1/piy)

I don't really know how to go about finding the time it will take to empty the tank.

Please help!

 

[BruceW]

hey, welcome to physicsforums! your solution to the first question is correct. (I'm guessing you're using 'k' as a constant. this is good.) So now, you need to make use of this differential equation to get 'y' as a function of time. You have hopefully done this kind of integral before. It just needs a bit of rearranging to get a nice answer.