# How can I convert an annular sector to a rectangular region?

I have an annular region $v=\{(r,\theta): r_1<r<r_2, a<\theta<b\}$. How can I transform this region to a rectangular region $u=\{(x,y): -1<x<1, m<y<n\}$? Thanks..

• what kind of transformation are you looking for? what is the context in which you encountered this question? May 15 '18 at 16:27
• i am working on fluid flow problem in the annular region. But i have some problems about fluid structures. So i want to compare rectangles with annular. Actually, may be i need a conformal mapping between these regions. May 17 '18 at 12:40

$$x = 2\frac{r - r_1}{r_2 - r_1} - 1 ~~~\mbox{and}~~~ y = \theta$$