Maple- simplifing an expression in terms of pre-defined variables?

In summary, the speaker is asking if it is possible to express an expression in terms of dimensionless numbers commonly used in fluid mechanics by using the command "simplify". They provide examples of dimensionless numbers and ask if the command can give the answer in terms of these numbers. They also mention asking for help on mapleprimes.com.
  • #1
binbagsss
1,254
11
I have some dimensionless numbers commonly used in fluid mechanics and I want to express a certain expression in terms of these dimensionless numbes

If I, after defining my dimensionless numbers, enter the command :

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?
E.g dimensionless numbers :

## Re = \frac{\rho U_0 H_0}{ \mu } ##

## Ca =\frac{ \mu U_0 }{ \sigma} ##

## St = \frac{T_0 U_0}{H_0} ##

##Fr = \frac{U_0 }{\sqrt{G_0 H_0}}##

##Oh = \frac{\mu}{\sqrt{ \rho \sigma H_0}} ##

##Bo =\frac{\rho G_0 H_0^2 }{\sigma} ##

If I do :

simplify(## \frac{G_0}{H_0 U_0}##)

Will it give the answer as ##\frac{1}{Fr^2}##

Or would I instead need to type something like :

simplify(( ##\frac{G_0}{H_0 U_0}##), )Fr=...)

So e.g will it tell me what combination of dimensionless numbers I can write ##\frac {\mu}{U_0^2 H_0 } ## as, if I write :

Simplify (##\frac {\mu}{U_0^2 H_0 } ## )

Or :

Simplify ((##\frac {\mu}{T_0 H_0 } ##) , Re=...,Fr=...,Ca=...St=..., Bo=..., Oh=...)

Many thanks !
 
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  • #2
I advise you to ask your question in mapleprimes.com

They are very helpful there with this software.
 

1. What is Maple and how does it simplify expressions?

Maple is a computer algebra system that is used for mathematical computations, such as simplifying expressions. It uses a combination of symbolic and numerical techniques to manipulate and solve mathematical equations.

2. Can Maple simplify expressions that contain pre-defined variables?

Yes, Maple has the capability to simplify expressions that contain pre-defined variables. These variables can be assigned specific values or left as symbolic variables for further manipulation.

3. Are there any limitations to Maple's simplification capabilities?

While Maple is a powerful tool for simplifying expressions, it does have limitations. It may not be able to simplify certain complex expressions or may provide a solution that is not in the desired form.

4. How do I define variables in Maple?

To define a variable in Maple, you can use the assignment operator ":=" to assign a value to the variable. For example, "x := 5" will assign the value 5 to the variable x. You can also define a variable as a symbolic variable by using the command "var x" or "x := x".

5. Can Maple simplify expressions involving trigonometric functions and other special functions?

Yes, Maple has built-in functions for trigonometric, logarithmic, exponential, and other special functions. It can handle these functions in simplification and provide exact or approximate solutions.

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