I'm wanting to plot some stream functions of which I have the functions for. I know what my stream function is in terms of u & v, but now I want to express the solution in terms of x & y, of which I have. Since I know that the stream function is a constant, any choice for u or v has a solution.
Currently psi = -2*C*sinh(u)*cos(v) = constant, and C is an arbitrary constant.
To plot out the points on a continuous line, I let v for instance = 0, phi/4...2*phi. I can then get the values for u, which are unique, and can then through a programming function, get the converted values of these two vectors for x(u,v) and y(u,v), therby giving me a line. I can add other lines by changing the value of psi = constant.
However, when I want to get the stream lines for say, letting u=0,0.5,3 , there are multiple solutions to the value of v. As I am symbolically solving the equations, I'm wanting to know if there is a way to 'bound' the symbolic solution to v between say 0 & phi, which would allow a vector output, of which I can then use to plot.
I have attached (the second version) of the spreadsheet. The first one crashed when I tried solve, v, 0, 2phi.
I would also like to know if I can make the stream functions solve, some variable output be equal to a vector iteself.
Thank you for any help in advance =).
Solved! Go to Solution.
I have gone back and put the items in as functions. I am attaching a new sheet that will detail the problem abit more closely. It is when I solve for the velocity potential that mathcad provides two answers for.
I redefined the velocity potential so that the solving for u wouldn't fail, so I renamed it. The velocity potential 'should' be orthogonal to the stream function. I'm trying to plot it to confirm my results.
Any help would be much appreciated.
Its not that difficult to simply select the first of the two solutions for q(), but to be able to plot a function at least one single argument in the plotrange must yield a real result.
You are plotting acosh(B/sin(v)), so you must chose B and the v-range in a way that at least for one of the v-values B/sin(v) is greater than 1. This means the plot fails for B=0 and it also fails for B>0 and pi<v<2pi.