       Re: simultaneous equations

• To: mathgroup at smc.vnet.net
• Subject: [mg2240] Re: simultaneous equations
• From: ianc (Ian Collier)
• Date: Wed, 18 Oct 1995 01:54:17 -0400
• Organization: Wolfram Research, Inc.

```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.
-----------------------------------------------------------
tel:(217)-398-0700     fax:(217)-398-0747      ianc at wri.com