Obtain the continuity equation in cylindrical coordinates by expanding the vector form in cylindrical coordinates. To do this, make use of the following relationships connecting the coordinates and the velocity components in cartesian and cylindrical coordinates:
x = Rcos(theta)
y = Rsin(theta)
z = z
u = u_(R)cos(theta) - u_(theta)sin(theta)
v = u_(R)sin(theta) + u_(theta)cos(theta)
w = u_(z)