In Newtonians fluids, the shear stress is proportional to the velocity gradient.

First of all, the shape of the velocity we are expecting is an hyperbolic form. If we consider that the same momentum is applied in the cylinder, it means that the constraints is decreasing with the radius augmentation (We can symbolize, in a first approach as: Momentum = constraints * radius ). Then, the velocity gradient will also evolve with the radius, it will decrease, with the constraints. That is why the velocity profile expected is not linear, but hyperbolic (in the shape).

It could be interesting to compare the results given by the code with the theoretical ones.

Theory

The theory gives the following expression for the tangential speed :

In our case, this relation is simplified as :

We have R=1 and K=0.5. With w0=0 and wi=1 rpm = 0.1047 rad/s, and it leads to A=0.0349 SI