Yes, your answer is correct.

The water pressure on the ground of a container is only determined by the height of the water head above the ground.This is indicated by the hydrostatic paradox, which has already been discovered by Blaise Pascal during that experiment in 1648.

The barrel broke apart, because the long tube was filled with water. In case of that tube only the height of the water head is relevant and not the width of the tube. Because of the extremely high water head, the water pressure became too high.
The water barrel could not withstand that pressure.

Think about how this insight can help you solve the brain-teaser.
Have you got an idea?
If not, take a look at another hint.