fractional dimensions

[ahendriks]

How does the UCUM cope with fractional dimensions, like the much used Chezy coefficient (friction coefficient in hydraulic engineering), which has m^½/s as 'unit'?

[gschadow]

The answer is: we don't.

I have seen this, but I don't know enough of it to make sense of this. Obviously one can imagine to put any unit term under any root, but what does this mean? What is the square-root of a meter? Seem rather imaginary to me.

The formula is:

v = C * sqrt(R * i)

where C is this Chezy coefficient, R is radius, dimension L and i is dimensionless (a slope). So here we have a square root of a length. But what does this mean? I think the right way to write this formula would be:

v = sqrt(C² * R * i)

and now your coefficient C² has the dimension L.T^-2, which looks much more reasonable.

I always felt that this fractional dimensionality is arrived at by some nifty engineering trick, as factoring the coefficient before the square root, but really doesn't signify that dimensions can somehow be fractional. [Sounds a bit analogously esoteric as Cantor's continuum hypothesis.]