The correct answer is $\frac{{\text{r}}}{2}$.
The boundary layer is a thin layer of fluid in the immediate vicinity of a solid surface where the fluid velocity changes from zero at the surface to the free stream velocity at a distance of the order of the boundary layer thickness.
The boundary layer thickness is defined as the distance from the surface where the fluid velocity reaches 99% of the free stream velocity.
In a pipe of radius $r$, the maximum thickness of the boundary layer occurs at the pipe wall and is given by:
$$\delta = \frac{{\text{r}}}{2}$$
The other options are incorrect because they are either too small or too large. Option A is incorrect because the boundary layer thickness cannot be zero. Option C is incorrect because the boundary layer thickness cannot be equal to the pipe radius. Option D is incorrect because the boundary layer thickness cannot be twice the pipe radius.