The contraption shown above forms an airtight seal between two soda bottles, allowing water from one to flow into the other. The flow can start in one of two ways:
- Flip the system over at \(t=0\) and let gravity pull the water down.
- Flip the system over at \(t=0\), and give the system a slight twirl, forming a vortex. The center of a vortex is an empty hole through which air can pass.
Which of the two flows will let the water reach the bottom first?