Hello Mathcad-Community,
I need help on converting the results of a solved differential equation in different coordinates in Mathcad Prime 2.0. Some days ago, I had a problem solving a system of 5 differential equation (some of you might remember). It was about a stream of gas flowing out of a broken tank/pipeline while experiencing wind from one side.
Before I got the equations to start the solving process, I had to convert the coordinates from cartesian to curvilinear coordinates. So actually i changed x,y and z to s (distance from the source in the center of the stream), r (distance from center of the stream) and the angel phi (you can imagine that as a rotation around the center of the stream). The direction of the wind is directed parallel to the y-axis. Maybe this scetch will help: EDIT: you can find the scetch in my file. I tried to implement it in the text, but it didn't work. It's at the top of the file below.
With the 5 differential equations, I was able to calculate the concentration c, Temperature T, Speed u, broadth of the stream b and the angle Theta between the s- and the y-Axis. The stream is axisymmetric, so the value for example c, or T at a certain distance r from the center of the stream is the same for every angle Phi around the axis.
If i take for example the concentration c, I am able to calculate the concentration for every point, dependant on s and r (its the same for all values of Phi, if s and r are known). If I want to know where this point is in cartesian coordinates, I have to use the equations for x, y and z below the charts in my added file. (you can ignore the whole part before the charts, this part works!)
What i want to do now is to re-convert the function into cartesian coordinates, or at least create a new function that does all the work of calculating point for point, so I don't have to do this by hand. I thought about creating a matrix with all the results for (for example) c(s,r) and a new function that takes out point after point of that matrix and converts it into x,y and z coordinates with the 3 functions in my file, but I don't know how that works.
Do you guys have an idea and could maybe help me?
Any help would be appreciated.
Regards
Tim