Quote by mr. vodka
Angular momentum for a spinning object is mass times velocity times radius. As momentum is preserved and as the radius decreases (because of the water going out), the velocity must increase.

That's corect, but that was an answer to a different question.
Consider the numerical exapmle.
R = 30 cm, r = 3 cm.
Immediately after opening the hole in the bath, we have:
v(R) = 1 cm/sec, v(r) = 10 cm/sec
A minute later, BOTH of the speeds, the speed far from the funnel and the speed close to funnel becomes much larger,
for example
v(R) = 12 cm/sec, v(r) = 120 cm/sec
The question is:
Why a minute later the speed at the distance 30 cm from funnel increased from 1 cm/sec to 12 cm/sec? Why a minute later the speed at the distance 3 cm from funnel increased from 10 cm/sec to 120 cm/sec?