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 radius is half of the geometrical radius. This is odd, no?

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: $D_H = \frac{4 \pi r^2}{2 \pi r} = 2r = D$.

Additional source saying similar things:

General formulation of thermoacoustics for stacks having arbitrarily shaped pore cross sections. Arnott, W. Pat and Bass, Henry E. and Raspet, Richard, The Journal of the Acoustical Society of America, 90, 3228-3237 (1991).


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