I remember from school, one time a teacher explain us the following: two containers of the same volume, but one is thin and tall, and the second is short and wide. then if we fill them with water from the same input, the container that is thin and tall will get filled faster. he gave us some mathematical proofs on it, but it was 30 years ago. does anyone knows if this is true and how can be proved?
It is not true. Imagine each container displaces one liter and that we are feeding these containers with a constant-speed pump running at one liter per minute. It will then take one minute to fill either of those two containers; their shape has nothing to do with it.