The correct answer is $\boxed{\text{A}}$.
The hydraulic diameter is a dimensionless quantity used to compare the hydraulic resistance of different-shaped conduits. It is defined as the diameter of a hypothetical circular pipe that would have the same hydraulic resistance as the actual conduit.
For a circular pipe, the hydraulic diameter is equal to the diameter of the pipe. For a square pipe, the hydraulic diameter is equal to the side length of the square divided by $\sqrt{4/\pi}$, which is approximately equal to 1.095.
The other options are incorrect because they do not represent the hydraulic diameter of a square pipe.