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[cellml-discussion] Dimensional consistency and units conversions (was [Fwd: Re: ten Tusscher model])


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  • From: dave at bcs.co.nz (David Brooks)
  • Subject: [cellml-discussion] Dimensional consistency and units conversions (was [Fwd: Re: ten Tusscher model])
  • Date: Sat, 21 Apr 2007 09:58:40 +1200
On 21/04/2007 3:14 a.m., David Nickerson wrote:
>> going back to the following equation Andrew supplied:
>>
>> amount_Na [nmol] = 10^-6 [dimensionless] * conc_Na [nmol / L] *
>> vol[microL]
>>
>> How do you make this more 'valid'? (it is already valid dimensionally
>> and numerically).
>>
> but it is not consistent or valid dimensionally.
>
Is there not a confusion between 'dimensionless' and 'unitless' ?? They
mean different things, and the sample equation is invalid because the
bracketed qualities are a mix of unit specification and dimension
specification.

The 10^-6 is dimensionless (being [length^3]/[length^3]) but has units
of L/uL.

In terms of dimensions we have:

amount_Na [amount_of_substance] = 10^-6 [dimensionless] * conc_Na
[amount_of_substance / length^3] * vol [length^3]

With units:

amount_Na [nmol] = 10^-6 [L / uL] * conc_Na [nmol / L] * vol [uL]

Combining both units and dimensions:

amount_Na [amount_of_substance (nmol)]
= 10^-6 [dimensionless (L/uL)] * conc_Na [amount_of_substance
(nmol) / length^3 (L)] * vol [length^3 (ul)]


Regards,

Dave
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