Need help solving for a formula

Archiver

I am trying to solve for a variable within this formula.

The formula solves for the amount of dissolved CO2 within pressurized liquids
(pop & beer).
I have the temperature and pressure, and I need to solve for V (Volumes of CO2)



P = -16.6999 - 0.0101059 T + 0.00116512 T^2 + 0.173354 T V + 4.24267 V -
0.0684226 V^2


T = temp in degrees F (typically from 32 to 50F)
P = PSI of CO2 (Typically from 0 to 30 PSI)
V = volumes of CO2 (Typically from 0 to 4 units)

Can this be done on a BS2? Would a lookup table be better? I don't need
extreme accuracy or resolution either (0.1 volume unit resolution). Is there an
easier way?

Thanks
Allan

Archiver

Hi Alan,

It looks like you might be able to disregard the term in V^2, which
looks like it will be much less than the V and the T*V terms.

That would help some, because you can then solve for V, and V would
be directly proportional to P. It is still a tough problem for the
Stamp due to the temperature dependence. A lookup table could do it,
but you would probably end up with a need for double interpolation.
I would be inclined to try for a formula, but it would probably be a
few hours of work to get it scaled right.

-- Tracy Allen


>I am trying to solve for a variable within this formula.
>
>The formula solves for the amount of dissolved CO2 within
>pressurized liquids (pop & beer).
>I have the temperature and pressure, and I need to solve for V
>(Volumes of CO2)
>
>
>
>P = -16.6999 - 0.0101059 T + 0.00116512 T^2 + 0.173354 T V + 4.24267
>V - 0.0684226 V^2
>
>
>T = temp in degrees F (typically from 32 to 50F)
>P = PSI of CO2 (Typically from 0 to 30 PSI)
>V = volumes of CO2 (Typically from 0 to 4 units)
>
>Can this be done on a BS2? Would a lookup table be better? I don't
>need extreme accuracy or resolution either (0.1 volume unit
>resolution). Is there an easier way?
>
>Thanks
>Allan

Archiver

alan,
stamp math is definetly not my strong suit, but this
is how id approach it (unless i grossly overlooked
something???). i "think" you can boil your problem
down to several managable chunks. reference
http://www.emesystems.com/BS2math3.htm for math
related stuff (a higher precesion squareroot):

basically it is just a quadratic equation, so we
actually only need to solve the coefficients and then
the quad formula. after doing some algabrae, i get:
-.068V^2+V(.1734T+4.24)+(P+16.7+.01T-.0011T^2) = 0
A B C
Quad Eqn. = (B +- ((B^2-4AC)^0.5)/2A

coefficients in terms of all knowns then approximatley
equal:
A=-.068
B=.1734 (T) + 4.24
C = P+16.7+.01T-.0011T^2

with A=-.068, that simplifies expression:
Quad Eqn. = (B +- ((B^2+.272*C)^0.5)/-.136
so now, given P and T, solve B & C and put into proper
stamp math, something "like":

Volume = B + SQR((B*B) + ((34/125)*C)) / (-17/125)
use 34/125 = .272 and 17/125=.136 for integer math

of course you only need 1 solution since the other
will be negative. accuracy??? the link above for the
SQR should improve it. seems workable to me, unless i
missed something?
ross



--- Tracy Allen <tracy@e...> wrote:
> Hi Alan,
>
> It looks like you might be able to disregard the
> term in V^2, which
> looks like it will be much less than the V and the
> T*V terms.
>
> That would help some, because you can then solve for
> V, and V would
> be directly proportional to P. It is still a tough
> problem for the
> Stamp due to the temperature dependence. A lookup
> table could do it,
> but you would probably end up with a need for double
> interpolation.
> I would be inclined to try for a formula, but it
> would probably be a
> few hours of work to get it scaled right.
>
> -- Tracy Allen
>
>
> >I am trying to solve for a variable within this
> formula.
> >
> >The formula solves for the amount of dissolved CO2
> within
> >pressurized liquids (pop & beer).
> >I have the temperature and pressure, and I need to
> solve for V
> >(Volumes of CO2)
> >
> >
> >
> >P = -16.6999 - 0.0101059 T + 0.00116512 T^2 +
> 0.173354 T V + 4.24267
> >V - 0.0684226 V^2
> >
> >
> >T = temp in degrees F (typically from 32 to 50F)
> >P = PSI of CO2 (Typically from 0 to 30 PSI)
> >V = volumes of CO2 (Typically from 0 to 4 units)
> >
> >Can this be done on a BS2? Would a lookup table be
> better? I don't
> >need extreme accuracy or resolution either (0.1
> volume unit
> >resolution). Is there an easier way?
> >
> >Thanks
> >Allan
>
> To UNSUBSCRIBE, just send mail to:
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> Text in the Subject and Body of the message will be
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>
>
> Your use of Yahoo! Groups is subject to
> http://docs.yahoo.com/info/terms/
>
>


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Archiver

Thanks Ross and Tracy. I'll need a few days to work my way through all the good
information you guys have posted. I'll probably be back with more questions
though, as it has been a few years since I was in college. [noparse]:([/noparse]

Allan Dobler

Klutch wrote:
>
> alan,
> stamp math is definetly not my strong suit, but this
> is how id approach it (unless i grossly overlooked
> something???). i "think" you can boil your problem
> down to several managable chunks. reference
> http://www.emesystems.com/BS2math3.htm for math
> related stuff (a higher precesion squareroot):

Archiver

I'm in this thread a little late, but I wanted to point out that while
you can probably work out an integer way to do this, another alternative
would be to add a PAK-I, II, or IX to your project. See
http://www.al-williams.com/pak1.htm

I'm behind this month as you can tell since the Stamp project of the
month is late. Pretty sure it will be done today and it should be worth
the wait.

Al Williams
AWC
* Easy RS-232 Prototyping
http://www.al-williams.com/awce/rs1.htm

> >
> >
> > >I am trying to solve for a variable within this
> > formula.
> > >
> > >The formula solves for the amount of dissolved CO2
> > within
> > >pressurized liquids (pop & beer).
> > >I have the temperature and pressure, and I need to
> > solve for V
> > >(Volumes of CO2)
> > >
> > >
> > >
> > >P = -16.6999 - 0.0101059 T + 0.00116512 T^2 +
> > 0.173354 T V + 4.24267
> > >V - 0.0684226 V^2
> > >
> > >
> > >T = temp in degrees F (typically from 32 to 50F)
> > >P = PSI of CO2 (Typically from 0 to 30 PSI)
> > >V = volumes of CO2 (Typically from 0 to 4 units)
> > >
> > >Can this be done on a BS2? Would a lookup table be
> > better? I don't
> > >need extreme accuracy or resolution either (0.1
> > volume unit
> > >resolution). Is there an easier way?
> > >
> > >Thanks
> > >Allan
> >
> > To UNSUBSCRIBE, just send mail to:
> > basicstamps-unsubscribe@yahoogroups.com
> > from the same email address that you subscribed.
> > Text in the Subject and Body of the message will be ignored.
> >
> >
> > Your use of Yahoo! Groups is subject to
> > http://docs.yahoo.com/info/terms/
> >
> >
>
>
> __________________________________________________
> Do you Yahoo!?
> Y! Web Hosting - Let the expert host your web site
http://webhosting.yahoo.com/

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