Seems to me a simple dimensional analysis shows the fallacy
of Koenemann's argument: The dimensions of f/A are [M][L][T^(-2)] /
[L^2] and of U are [M][L^2][T^(-2)] / [L^3], so the dimensions of
both quantities are the same: [M]/[L][T^2]. Thus both quantities
scale the same way with the dimension of the system, and Koenemann's
conclusion must be incorrect.
Note that if the dimension of the system changes you cannot
assume that both f/A and f are constant, as Koenemann does in the
argument below (see underlined statements).
Rob Twiss
>I did not make the assumption that U is constant. I made the assumption that
>f/A is constant, AND that f/A and U/V are equivalent at all scales. Since I
>have V and U/V, I can get U which then blows up as V -> 0.
>
>In symbolic form, say f/A = U/V.
>
>Replace A by r^2 pi and V by 4/3 r^3 pi and cancel redundant terms.
>
>Result is: f = 3U/r, or U = fr/3.
>
>Make the assumption that f is constant, hence U is proportional to r; thus
>
>if V -> 0, U/V -> infinity.
>
>This cannot be, hence f/A and U/V are not equivalent at varying scale of
>consideration.
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Robert J. Twiss email: [log in to unmask]
Geology Department telephone: (530) 752-1860
University of California at Davis FAX: (530) 752-0951
One Shields Ave.
Davis, CA 95616-8605, USA
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