Inertia effects in rheometrical flow systems Part 3: Some energy considerations with respect to the flow field in the balance rheometer

Following up a previous paper by one of the presents authors on the flow field in the balance rheometer, inertia effects being included, in this paper some energy considerations with respect to this flow field are presented. It is shown that in a frame rotating with the same angular velocity as the hemispheres the power supplied by these hemispheres equals the rate of energy dissipation in the sample, i.e. in this coordinate system there is no “stress power paradox”. Further it is shown that the “elastic” couple for a Newtonian liquid, appearing in the calculations, stems from the extra kinetic energy caused by the deviation of the actual flow field from the flow field that appears when inertia effects are ignored.