RE: Dimensionality Checking (Ada 20XX)

["Steven Deller" <deller@smsail.com>]

Thomas,
Actually, you are missing a divisor in your computation of vapor load.
It actually is
  Vapor Load = V_l = V_cfs * sqrt( rho_v/(rho_l-rho_v)) 
and this results in length^3/time whole units:
  V_cfs = length^3/time
  rho_* = mass/length^3
  so,  length^3/time * sqrt( mass/length^3 / (mass/length^3 -
mass/length^3))
  = length^3/time

The following site has a full chem eng distillation analysis:
  http://chemeng.uah.edu/courses/che446sp99/spray1.html

Every computation I saw had full units (or unitless ratios).  There did
not seem to be a need for non-integral units.

The line computing V_l states it is Vapor Load, ft/s but is is clearly
cu ft/s (which makes more sense if one is computing a vapor load on a
column).

INMHO, fractional units simply make no sense for any stated value.  They
*might* occur in a partial computation, e.g. sqrt(length1) *
sqrt(length2), though that would more properly be written as
sqrt(length1*length2).  I cannot think of any computation where
fractional units *do* occur, even in partial results.  

It would be nice to have one clear example from the real world where
fractional units occur before building a solution for something that
will never be used.

Regards,
Steve

> -----Original Message-----
...
> 
> 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. _______________________________________________

>