       simultaneous equations

• Subject: [mg2232] simultaneous equations
• From: ha20 at uow.edu.au (heath andersen)
• Date: Wed, 18 Oct 1995 05:52:52 GMT
• Approved: usenet@wri.com
• Distribution: local
• Newsgroups: wri.mathgroup
• Organization: Wolfram Research, Inc.
• Sender: daemon at wri.com ( )

```
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}]
----------------------------------------------------------------------------
----------
thanks

h.andersen
university of wollongong
nsw australia

```

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