maple - Can you simplify an expression in terms of pre defined variables?

Question

I have some particular dimensionless numbers commonly used in fluid mechanics. I want to express a certain expression in terms of these variables.

If I define my dimensionless numbers and then do

simplify(*expression*)

where the expression is a function of variables that have all been used at least once in the definition of the dimensionless numbers, is it able to give this expression in terms of these dimensionless numbers? Can it be used to save time with this sort of algebra?

Many thanks !

E.g dimensionless numbers :

 Re = (\rho U_0 H_0) / \mu    
 Ca =( \mu U_0 )/ (\sigma)     
 St = (T_0 U_0)/H_0     
Fr = U_0 /(\sqrt(G_0 H_0))   
Oh = (\mu}/\sqrt( \rho \sigma H_0)    
Bo =(\rho G_0 H_0^2) /\sigma

If I do :

simplify(G_0 H_0 / U_0 ^2)

Will it give the answer as 1/Fr^2

Or would I instead need to type something like :

simplify(( G_0/H_0 U_0), )Fr=...)

So e.g will it tell me what combination of dimensionless numbers I can write \mu/(U_0^2 H_0) as, if I write :

Simplify ( mu/U_0^2 H_0   )

Or :

Simplify (( \mu/(T_0 H_0)  ) , Re=...,Fr=...,Ca=...St=..., Bo=..., Oh=...)

Are you going to explain (in response to the query in my Answer) how your expected result `G_0/(H_0*U_0)=1/Fr^2 ` follows from your given equation(s) including `U_0/sqrt(G_0*H_0)=Fr` ? — acer, Dec 31 '20 at 15:17

acer · Answer 1 · 2021-01-08T14:42:23.343

0

Firstly you should correct your formatting, since all your expressions are not pretty-printing properly. (They appear like raw TeX.)

If you want people to show you Maple solutions, then it'd be more helpful to present your equations in plaintext Maple source.

You appear to have the equation,

Fr = U_0 / sqrt(G_0 * H_0)

and you also appear to be expecting that this would allow a manipulation of,

G_0/(H_0 * U_0)

to obtain,

1/Fr^2

How does that follow!? (edit: It doesn't follow.)

There are several Maple commands for substitution and variable elimination that may help here, including:

simplify(expr, {eqs});
eliminate({eqs}, {vars});
solve({eqs}, {vars});
algsubs(eq, expr);

and so on. But first it seems best to confirm that your equations and expectation(s) are as stated.

[edit] Now that the expected target has been edited and corrected, here is one way to get a result.

restart;

eq1 := Uo/sqrt(Go*Ho)=Fr:
new1 := targ1 = Go*Ho/Uo^2:

eval(targ1, new1) =
eval(targ1, solve({new1, eq1},
                  {targ1,Go,Ho,Uo}));

                      Go Ho    1 
                      ----- = ---
                         2      2
                       Uo     Fr

edited Jan 08 '21 at 14:42

answered Dec 30 '20 at 18:23

acer

6,671
15
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yeh okay that was obviously a typo, what I meant was $ G_0 H_0 / U_0 $. – Sara Ismail-Sutton Dec 31 '20 at 18:12
I use stack exchange where the tags are $ for math typing, dont know what they should be here? Why dont you tell me what they should be isntead of going on about 'maple plain source' which i obviously have no idea what means or how do i do, or i would have, obviously. – Sara Ismail-Sutton Dec 31 '20 at 18:13
It doesn't follow that your newer expression $ G_0 H_0 / U_0 $ becomes `1/Fr^2` either, from your given equation that I cited. Also, plaintext means plaintext, as would be entered into Maple as source code that is not marked up in any way. Eg, `Fr = U_0 / sqrt(G_0 * H_0)` – acer Jan 01 '21 at 05:13
$G_0 H_0 / U_0 ^2 $ is what I meant, my apologies. I've edited the question now also. – Sara Ismail-Sutton Jan 01 '21 at 15:49
so now I've been good, do I get a proper answer ? :)) – Sara Ismail-Sutton Jan 02 '21 at 16:13
I edited my answer, in light of your edited formula. – acer Jan 08 '21 at 14:43
ok thank you, and is this supposed to be the output after those commands: Go Ho /Uo^2= 1/Fr^2 – Sara Ismail-Sutton Jan 08 '21 at 19:00
since my maple is doing absolutely nothing after those commands :(( – Sara Ismail-Sutton Jan 08 '21 at 19:06

maple - Can you simplify an expression in terms of pre defined variables?

1 Answers1