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. ----------------------------------------------------------- tel:(217)-398-0700 fax:(217)-398-0747 ianc at wri.com Wolfram Research Home Page: http://www.wri.com/ -----------------------------------------------------------