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,
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?