Equation for the Rotational Viscometer

This method works well for viscosities from 1 to 103 Pa-s. For somewhat higher viscosities, the torque on the spindle becomes excessive. For these viscosities, a crucible rotation speed is selected so that the spindle lag is near the maximum measurable value. The rotation is then stopped, and the spring loading of the spindle is then allowed to drive the spindle back to its rest point (zero torque). The elapsed time between two selected angles from the rest point is measured during the return. The viscosity is then measured from the following equation [4]  

While all of the viscosity measurements can be calibrated using well-characterized viscosity standards, the viscosity using these instruments may in fact be calculated from first principles. As an example, a derivation in full is provided for the Margules viscometer  

In order to determine the shear strain incurred by the element, we must determine the change in angle between AD and 

In order to determine the shear strain, the contributions to these angles from rigid body rotation must be subtracted. That angle simply corresponds to that swept in moving A to A, that is gg/r. Hence the shear strain is  

The torque at any given point is the radial distance r multiplied by the tangential force (shear stress multiplied by the cylindrical area)  

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