Is the vortex in a kitchen sink an example of a singularity? Say you have your kitchen sink full of water and you pull the plug. Then a nice little vortex will form where the water disappears into the drain.
My question is:

Is this an example of a mathematical singularity occurring in real
  life? And if it is, what is the function of which it is a singularity
  of?

Edit
A singular point of a $C^1$-map $f: M \to N$ where $M$ is a smooth $m$-manifold and $N$ a smooth $n$ manifold is any point $x_0$ where $f'(x_0) = 0$.
 A: It all depends on how you define a singularity.
Wikipedia says:

In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability.

A vortex in the kitchen sink can be described as an irrotational vortex.
A simple example of an irrational vortex is given by the velocity field
$$v(x,y)=\frac{\alpha}{x^2+y^2}\cdot(-y,x).$$
$v(x,y)$ is the velocity of the fluid at a given point $(x,y)$ (we forgot about the 3rd dimension for simplicity).
At the center of the vortex $(x,y)=(0,0)$, the magnitude of the velocity is divergent $|v(0,0)|\rightarrow\infty$. The direction of the velocity is given by the angle
$$\theta(x,y)=\arctan (-y/x),$$
which is not defined in the center of the vortex $x=y=0$.
Therefore, a vortex in a kitchen sink is a singular point in the velocity field of the water, since the velocity diverges and is not differentiable at the center of the vortex.
Actually, it is a topological singularity, since there is no continuous transformation of the velocity field which removes the singular point of an irrotational vortex.
PS: One has to assume that the water is a continuous medium, i.e., one has to forget the fact that water or any other fluid is an ensemble of many microscopical molecules. In fact, at a microscopical level, there cannot be any singularity in a kitchen sink.
