Re: simultaneous equations
- Subject: [mg2240] Re: simultaneous equations
- From: ianc (Ian Collier)
- Date: Wed, 18 Oct 1995 05:54:17 GMT
- Approved: usenet@wri.com
- Distribution: local
- Newsgroups: wri.mathgroup
- Organization: Wolfram Research, Inc.
- Sender: daemon at wri.com ( )
In article <DGIy5I.I8x at wri.com>, heath andersen <ha20 at uow.edu.au> wrote:
> i am having trouble solving this set of simultaneous equations. it is
> probably my maths that is letting me down here, or lack of Mma use, or both,
> but, i can not work it out and have not had much luck asking round.
>
> In case u wanted to know i am trying to work out the volumetric flow rates
> for a dust extraction system, using an electrical analogy, where 'p' is the
> pressure(Pa), 'r' the resistance to flow and 'q' is the volumetric flow
> rate. the numbers ar the node opoints of the system, for example, 'p78', is
> the pressure at node 78, and 'p7880' is the node where 'p78' and 'p80' come
> together abd so on...
>
> also, [q7880]^2 = [q78 + q80]^2
>
> Here is exactly what i typed in and what Mma gave me back.
>
> ----------------------------------------------------------------------------
> --------
> p78 = p80 = p81 = 101300
> 101300
>
> p788081 = 100100.6
> 100100.6
>
> r78 = r80 = 220
> 220
>
> r81 = 219.5
> 219.5
>
> r7880 = 54.86
> 54.86
>
> Solve[{ p78 - p7880 == q78^2 * r78,
> p80 - p7880 == q80^2 * r80,
> p7880 - p788081 == r7880[q78 +q80]^2,
> p81 - p788081 == q81^2 * r81},
> {q78, q80, p7880, q81}]
> Solve::tdep:
> The equations appear to involve
> transcendental functions of the
> variables in an essentially
> non-algebraic way.
> 2
> Solve[{101300 - p7880 == 220 q78 ,
>
> 2
> 101300 - p7880 == 220 q80 ,
>
> 2
> -100101. + p7880 == 54.86[q78 + q80] ,
>
> 2
> 1199.4 == 219.5 q81 },
>
> {q78, q80, p7880, q81}]
Square brackets are used to enlose the arguments to funtions so
r7880[q78 +q80]
is interpreted as a function called r7880 evaluated at
q78 +q80
which is further complicated by r7880 being set to 54.86.
I suspect that you want to group these symbols in which case you
need to use the regular parentheses ( "(" & ")" ).
The following works without error:
Solve[{ p78 - p7880 == q78^2 * r78,
p80 - p7880 == q80^2 * r80,
p7880 - p788081 == r7880(q78 +q80)^2,
p81 - p788081 == q81^2 * r81},
{q78, q80, p7880, q81}]
I hope this helps.
--Ian
-----------------------------------------------------------
Ian Collier
Technical Sales Support
Wolfram Research, Inc.
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tel:(217)-398-0700 fax:(217)-398-0747 ianc at wri.com
Wolfram Research Home Page: http://www.wri.com/
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