Polar Coordinates Homework: Converting to Cartesian and Strain Rate Tensor

[JSBeckton]

Homework Statement

The velocity field for a line source in polar coordinates (r,theta) is given by:

V=m/(2(pi)r) (in the "e" little r vector direction)

convert to cartesian and calculate the strain rate tensor.

Homework Equations

R=Sqrt(x2+y2);
Theta=ArcTan(Y/X);

Cartesian form:
X= R*cos(Theta)
Y= R*sin(Theta)

The Attempt at a Solution

I just need to convert this, i understand how to get the strain rate tensor. I know how to compute between polar and cartesian but need theta. Or am I suppposed to assume theta=0?

if theta=0 then y=0 andf x=r*sin(theta) but what do i use for r? If i solve for r i th efirst equation I get r=m/(2pi)

x=rcos(0)
x=m/(2pi)

This doesn't seem right becasue I need a velocity field in terms of V(u,v) where u and v are in terms of x and y.

Any help is greatly appreciated, Thanks

 

[sutupidmath]

I do not know what exactly you are asking, but if you are just asknig how to get from cartesian coordinates to polar ones than

theta=arctan(y/x) while R=sqrt(x^2+y^2)

 

[JSBeckton]

I understand that as stated in my post under "Relevant Equations", thanks anyways