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I'm totally new to Sage. I was hoping I could use it for simple and complex application problems I run into at work. For example the relationship between flow rate, Q, and pressure drop, dP, for flow of a powerlaw fluid (m, n) in a cylindrical tube (L, R) is:

Q = (piR^3/((1/n)+3))(Tau/m)^(1/n)

So I want to rearrange this expression for dP in terms of Q, m, n, L, R so I can then compute a table of results, plot dP versus Q etc. Now of course I can do the rearrangement by hand with pen and paper (or in my head on better days) but I was hoping that using the Sage notebook I could work through the rearrangement and thus have an digital record of the transformation so that others can follow along. However in all the hours of reading and watching tutorials, I have yet to see this simple process in action.

So far in my sage book I have:

Q, L, R, m, n, dP = var("Q, L, R, m, n, dP")

Tau = dP/(2*L/R)

Q = (piR3/((1/n)+3))(Tau/m)(1/n)

(Note that the preview doesn't show the power symbol **, hope it appears in the posted question)

Is there a method, say, Q.rearrange(dP) that yields dP = f(Q, L, R, m, n)? If not, how do I write the intermediate steps in sage speak to give this expression?

Sorry if this is such a basic question.

I'm totally new to Sage. I was hoping I could use it for simple and complex application problems I run into at work. For example the relationship between flow rate, Q, and pressure drop, dP, for flow of a powerlaw fluid (m, n) in a cylindrical tube (L, R) is:

Q = (piR^3/((1/n)+3))(Tau/m)^(1/n)
(pi*R^3/((1/n)+3))*(Tau/m)^(1/n)

Q, L, R, m, n, dP = var("Q, L, R, m, n, dP")
 
dP")
Tau = dP/(2*L/R)
 
dP/(2*L/R)
Q = (piR3/((1/n)+3))(Tau/m)(1/n)(pi*R**3/((1/n)+3))*(Tau/m)\*\*(1/n)

I'm totally new to Sage. I was hoping I could use it for simple and complex application problems I run into at work. For example the relationship between flow rate, Q, and pressure drop, dP, for flow of a powerlaw fluid (m, n) in a cylindrical tube (L, R) is:

Q = (pi*R^3/((1/n)+3))*(Tau/m)^(1/n)

So I want to rearrange this expression for dP in terms of Q, m, n, L, R so I can then compute a table of results, plot dP versus Q etc. Now of course I can do the rearrangement by hand with pen and paper (or in my head on better days) but I was hoping that using the Sage notebook I could work through the rearrangement and thus have an digital record of the transformation so that others can follow along. However in all the hours of reading and watching tutorials, I have yet to see this simple process in action.

So far in my sage book I have:

Q, L, R, m, n, dP = var("Q, L, R, m, n, dP")
Tau = dP/(2*L/R)
Q = (pi*R**3/((1/n)+3))*(Tau/m)\*\*(1/n)
(pi*R**3/((1/n)+3))*(Tau/m)**(1/n)

(Note that the preview doesn't show the power symbol **, hope it appears in the posted question)

Is there a method, say, Q.rearrange(dP) that yields dP = f(Q, L, R, m, n)? If not, how do I write the intermediate steps in sage speak to give this expression?

Sorry if this is such a basic question.