I usually do this in two steps (note: I'm assuming you have the axis of your cylinder aligned with the z-coordinate):

1. Compute the new cylindrical grid:

r = sqrt(x^2 + y^2);

theta= atan(x/y);

z = z;

2. Compute the vectors in new cylindrical coordinates:

U_r =u*cos(theta) + v*sin(theta);

U_theta =-u*sin(theta) + v*cos(theta);

U_z = w;

I found this link helpful:

http://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec05.pdf

It depends on how your cylindrical coordinate system is oriented with respect to Cartesian one

Basic information: http://keisan.casio.com/exec/system/1359534107.

Or make a program array processing, such as Matlab program and apply function 'car2pol'.

If r is the radial distance and θ is the azimuthal angle in cylindrical polar coordinate system. Then Just put x=rcosθ and y=rsinθ in the equation which folows Cartesian coordinate system.

You will get your answer.

I usually do this in two steps (note: I'm assuming you have the axis of your cylinder aligned with the z-coordinate):

1. Compute the new cylindrical grid:

r = sqrt(x^2 + y^2);

theta= atan(x/y);

z = z;

2. Compute the vectors in new cylindrical coordinates:

U_r =u*cos(theta) + v*sin(theta);

U_theta =-u*sin(theta) + v*cos(theta);

U_z = w;

I found this link helpful:

http://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec05.pdf

theta=atan(y/x);

Sorry.

It is clear how someone can convert from cartesian to cylindrical. Assume that we have two points (x1,y1) and (x2,y2) with Ux=(x2-x1)/dt and Uy=(y2-y1)/dt. Of course Ur=Ux*cos(theta) + Uy*sin(theta) and Uf=-Ux*sin(theta) + Uy*cos(theta). But in this case, how's theta calculated from x1,x2,y1,y2? Is it correct to set theta=atan((y2-y1)/(x2-x1)) ?

Let (u, v, w) and (ur, ut, uz) denote the velocity field respectively in cartesian and cylindrical systems. Denote the Jacobian J=[cos (theta) sin(theta) 0; -sin(theta) cos(theta) 0; 0 0 1]

then you can use :

(ur,ut,uz)'=J(u,v,w)'.

Note here I assume uz and w follow the same orientation.

Best