Temp_units

[peter_1610-disa]

As you can see in the attached file, I get incorrect result with units. If I remove the units I get the correct result.

Am I missing something here?

[PhilipOakley]

You have forgotten that temperature is not really in
degrees Celsius, but is in kelvin, which is a number
273 higher, so the the correctness of the integrals
is actually the other way round in 'real' units 😉

I'm guessing the formula you have is an empirical
formula so needs lots of care and attention as to
zero points and scale factors.

I just had one this morning that neatly took the
fourth root of a unitless ratio then multiplied by
mm, We still haven't quite bottomed out some of the
'magic number' constants...

Philip Oakley

[TomGutman]

You should explain what you are doing, what the variables mean, and what you are trying to calculate. If you are trying to get an average temperature, your divisor is wrong. You need to divide by the length of the integration interval (x1/4) and not just x1. Neither of the two values you calculate in your sheet make any sense in terms of the calculations.
__________________
� � � � Tom Gutman

[ptc-1368288]

On 8/5/2009 3:48:46 PM, peter_1610 wrote:
>............................
>Am I missing something here?
_____________________________

Maybe !

In your opinion, what is the "UnitResult" of ln(x [m]) *DT [�C] ?

jmG

[ValeryOchkov]

May be so - see the attach!
Val
http://twt.mpei.ac.ru/ochkov/v_ochkov.htm

[peter_1610-disa]

Thank You all.

It seems to be degC and degF cannot applied to empirical formula.

-Peter

[PhilipOakley]

On 8/6/2009 2:28:27 PM, peter_1610 wrote:
>Thank You all.
>
>It seems to be degC and degF
>cannot applied to empirical
>formula.
>
>-Peter

The application of units to empirical formula needs
a little care, but usually can be done. The other
problem is that degF and degC are actually functions
- so more care again.

Philip Oakley

[peter_1610-disa]

Thanks Philip.

Acutually, I found this document on the web
http://www.chem.mtu.edu/~tbco/cm3450/Temperature_Scales.pdf which says better cancel the units with empirical formulas..
-Peter

[ValeryOchkov]

On 8/6/2009 8:05:59 PM, peter_1610 wrote:
>Thanks Philip.
>
>Acutually, I found this
>document on the web
>http://www.chem.mtu.edu/~tbco/
>cm3450/Temperature_Scales.pdf
>which says better cancel the
>units with empirical
>formulas..
>-Peter
I see one error in the article - not 460.67 but 459.67 (�R-�F)
In SI (K-�C)=273.15 (correct in the article)

Val
http://twt.mpei.ac.ru/ochkov/v_ochkov.htm

[ELSID]

You cancel units within mathcad. I run into this problem all the time. I even came across an empirical formula that multiplied by 12 with no explanation. After reverse engineering the problem, I eliminated the factor of 12 and noted the change in the empirical formula as a unit conversion that was un-necessary since MathCAD does it internally.
As Phil said, be careful and doubly careful with Temperature

No knowledge can be certain if it is not based upon mathematics or upon some other
knowledge which is itself based upon the mathematical sciences. -- Leonardo da Vinci

[ptc-1368288]

When dealing with empirical or deduced formulas, they are necessarily based on a unit system, then you should use them as is (if basically correct) and convert the user data to the formula system. The work sheet starts with user data,
... then continues with converted to engineering formulas,
... then apply to the working formulas.

This is why some standard like ISO have attempted doing, scrapping and recycling tons of books and formulas. A good example of such a cleaning is the orifice plate calculations. All these considerations should be split between the client who should supply the working formulas and the designer applying the formulas... and keep the work traceable. Too much automation is detrimental to public safety.

jmG

[PhilipOakley]

On 8/7/2009 3:22:35 PM, jmG wrote:
>When dealing with empirical or
>deduced formulas, they are
>necessarily based on a unit
>system, then you should use
>them as is (if basically
>correct) and convert the user
>data to the formula system.
>The work sheet starts with
>user data,
>... then continues with
>converted to engineering
>formulas,
>... then apply to the working
>formulas.
>
>This is why some standard like
>ISO have attempted doing,
>scrapping and recycling tons
>of books and formulas. A good
>example of such a cleaning is
>the orifice plate
>calculations. All these
>considerations should be split
>between the client who should
>supply the working formulas
>and the designer applying the
>formulas... and keep the work
>traceable. Too much automation
>is detrimental to public
>safety.
>
>jmG

Peter,

The choice of whether to use, or not use, units is
a long running discussion.

Jean [jmG] favours the approach where the engineer
does the careful conversion first, then uses an established [book] formula to do the numeric
calculation.

My preference is to use MathCAD's built in units
capability to support the error detection - even
careful engineers can make mistakes, but then so
can computers 😉

Philip Oakley

[ValeryOchkov]

On 8/7/2009 1:54:49 PM, ElSid wrote:
>As Phil said, be careful and
>doubly careful with
>Temperature
Typical empirical formula with temperature:

(Addional picture for the capter 6 in the article http://twt.mpei.ac.ru/ochkov/formula/Engindex.html )

Val
http://twt.mpei.ac.ru/ochkov/v_ochkov.htm

[TomGutman]

What empirical formula? I don't think you have a units problem at all. Rather a formula problem. None of your equations make any sense to me. I think they are all wrong. I asked you to explain your variables and your problem. Since you chose not to, there the matter lies.
__________________
� � � � Tom Gutman

[ELSID]

Tom,
Isn't the error in the function? T1 is in degC and the nat log portion is in degC. Dis would mean a deltaC answer and the Collab is using degC

[TomGutman]

When you use Mathcad units values are not "in" any particular units. It makes no difference how you enter the value -- the value is, conceptually, a physical quantity.

The equation for test is probably wrong (incorrect parameters), but it is dimensionally sound. Mathcad represents temperatures using an absolute temperature scale, so arithmetic on temperatures is permissible. Even if not using units properly, a temperature difference can be added to a temperaturs (on a scale) to yield another temperature.
__________________
� � � � Tom Gutman

[Raiko]

On 8/5/2009 3:48:46 PM, peter_1610 wrote:
>As you can see in the attached
>file, I get incorrect result
>with units. If I remove the
>units I get the correct
>result.
>
>Am I missing something here?


Hello Peter,

your equation looks like the radial temperature distribution in a cylindrical body. In such a case you should use Kelvins!
And, although I'm not certain whether it matters, I wouldn't mix physical units with the "dimensionless" x. Better use a range variable which you can multiply with a unit such as:

x:=i*a with a being a step of say 1mm and i the range variable from 0 to N.

Hope this helps

Raiko

[ValeryOchkov]

>like the radial temperature distribution in a
>cylindrical body
See
http://twtmas.mpei.ac.ru/mas/worksheets/therm/Heat_Flow_4.mcd
Val
http://twt.mpei.ac.ru/ochkov/v_ochkov.htm

[ptc-1368288]

Maybe the solution to a DE if you had: abstract + diagram



jmG