# Degredation of a Circular Flow

Hi I am trying to understand what forces are at work to slow a liquid flowing in a circular pipe

As an example the above torus pipe fully filled with an incompressible low viscosity liquid. This is rotated until the fluid achieves solid body rotation and then the pipe is suddenly stopped but the low viscosity allows the fluid to continue under its own inertia

I understand that a rotational flow pattern will be formed by the solid body rotation and the additional force of the solid container will prevent the formation of a free vortices ? is this correct ?

While I understand that viscosity works to slow the flow , are there other forces due to the circular flow geometry that work against the momentum of the fluid ?

Vorticity - degrades kinetic energy trapped in Circulation to heat ? Can it diffuse the flow momentum any other way ?

Can either

Axial Pressure Variation or -
Body Forces The additional force applied by the solid container degrade the flow (some version of Minor Losses in a pipe) effect how fast the momentum is dissipated ?

Additionally would the answer be different if the pipe wasn't fully filled with an incompressible liquid ?

Is there anything else I need to consider to how quickly the momentum would stop ?

Any readings that someone could recommend ?

I think that wall texture may be significant. At sufficiently high relative velocities, turbulence increases against a smooth wall whereas some wall textures (shark skin) can maintain laminar flow. It may seem counter-intuitive.
Below that critical velocity, it's all laminar flow.

Have you noticed how extreme your toroid image is? I expect the inner wall to have significantly less drag than the outer wall.

Your torroid is quite extreme, with far more surface area on the outside. However, the outside of the torus also has far more volume. Have you considered whether this differential drag on the volume of water may cause large vortices?

Another consideration is the Reynolds number. That is, at sufficiently high relative velocities, turbulence is generated at the smooth wall. The outside wall is going to have a higher relative velocity than the inner wall.

Have you considered wall texture? Shark skin has the counterintuitive property of maintaining laminar flow when a smooth wall would be throwing vortices.