Archive for November 26, 2017

The Problem of the Water Tank

Posted in Cute Problems on November 26, 2017 by telescoper

Here’s a nice problem I remember hearing in the pub on Friday and figured out this afternoon.

A water tank or sink is open to the air at the top where it can be filled using a tap connected to an infinite reservoir. Water can be drained from the container through an opening at the bottom  by removing a stopper. The effects of viscosity on the outflow from the tank can be neglected.

The time taken for the tank to fill when the tap is fully open and the stopper in place is the  same as the time taken for it to empty from full  when the tap is closed and the stopper is removed.

If the tank is initially empty, the stopper removed and the tap turned full on, how full is the tank when a steady state is reached?