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From: dmitry@elros.cbb-automation.de (Dmitry A. Kazakov)
Newsgroups: comp.lang.ada
Subject: Re: Dimensionality Checking (Ada 20XX)
Date: Mon, 17 Dec 2001 14:30:57 GMT
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Date: 2001-12-17T14:30:57+00:00
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On 17 Dec 2001 13:16:11 +0100, Thomas.Koenig@online.de (Thomas Koenig)
wrote:

>Dmitry A. Kazakov <dmitry@elros.cbb-automation.de> wrote:
>
>>The equation X <unitX>*X <unitX> = Y <unitY> has a solution when Y is
>>not negative and <unitY> has even powers of all base units. Thus we
>>could define sqrt.
>
>In order to be sufficiently general, dimensions would have to be
>factional numbers for intermediate results, at least.  There are
>too many cases where square or cubed or other roots turn up in
>normal calculations.
>
>For example, one important factor in distillation column design,
>the vapor load, is defined as F = w * rho^(1/2), where w is the
>speed in (Length/Time) and rho is the density (Mass/Length^3),
>so its unit actually is  kg^0.5/m^0.5/s in SI units.  And
>yes, people do publish values and correlations for this factor.

Well, I am not a physicist to judge whether it has *physical* sense.
Maybe a dimensioned factor get lost somewhere or the dependency is
empirical. Intuition wispers that it should somehow ram relativity
theory. But mathematically it is no problem to continue units with
natural powers to ones with rational ones.

Regards,
Dmitry Kazakov