Ignore turbulence and viscosity.
A cylinder with radius r is filled to depth d. There's a leak in the bottom of the cylinder.
When suspended from a rope, the depth is reduced to d/2 after 10 minutes. From this point, how long should it take to empty completely?
The Attempt at a Solution
My initial thought would be that it would take 10 minutes, but that must be oversimplifying things. As the bucket empties, the pressure will surely decrease, and so, therefore, will the rate of loss of water.
The equation P=ρgd comes to mind, where P is the pressure, ρ the water density, g the acceleration due to gravity and d the depth.
I am unsure how to relate this to time though.
Would I need to find an equation for d, relating it to time, and take the integral, with limits d to d/2, then compare that to the current situation? If so, I have no idea how to actually do this.
Any help appreciated