The conservtion form in cartesian coordinates is

dU/dt + dF/dx + dG/dy + dH/dz = 0

U = [rho rho*u rho*v ...]

F = [rho*u rho*u*u + P - tau_xx rho*u*v - tau_xy ...]

G = [rho*v rho*u*v - tau_yx rho*v*v + P - tau_yy ... ]

How can I express these in cylindrical coordinates?

Shuo

You can derive it yourself. Take an elementary volume in cylindrical coordinates and apply the conservation principle to it.

Is there a reference I can compare my derivations to?

If you look at appendices of Batchelor's Fluid Dynamics, there are equations in all coordinate frames. But they are not given in conservation form. Also try the book of Aris, Vectors, Tensors and the equations of fluid dynamics.