# What is the difference between hydraulic radius and geometrical radius in a cylindrical pore?

What is the difference between hydraulic radius and geometrical radius in a cylindrical pore? I was going through the 'stacks' present in an thermoacoustic refrigerators there I came across the hydraulic radius and geometrical one. What is the difference?

The hydraulic diameter (in general) is defined to be $4A/P$ ($A$ being cross-sectional area; $P$ being the wetted perimeter).
The hydraulic radius (mostly in thermoacoustics) is defined to be $A/P$ (check out Swift's book).
Subbing in, you get $\frac{\pi r^2}{2 \pi r} = \frac{r}{2} = r_h$.
Well that's odd. But if you use the hydraulic diameter, you get the geometrical diameter back: $D_H = \frac{4 \pi r^2}{2 \pi r} = 2r = D$.