The Rotation Viscometer

The rotation viscometer consists of two concentric cylinders; the outer rotates at a constant speed and the inner is hung suspended by a torsion wire. Between the two cylinders is placed the liquid of unknown viscosity. Consider the cylinder system as depicted in figure 10.

Figure 10. The Rotation Viscometer

Let the angular velocity of rotation of a cylinder of liquid radius (r) be (w). Then the linear velocity at this point will be, 

Now (w) represents the angular motion that the layer would have if there was no viscous slip while , the second term is responsible for the viscous stress introduced. Thus, applying Newton’s Law                    .

                 Then,

Thus rearranging and integrating from (r = b) to (r = a) and (= 0) to (=)

In this development the drag on the base has been ignored. However, its effect can be eliminated by taking measurements with the cylinder immersed in the liquid at different depths. If the torque on the base is f(B)and the two depths of immersion are (l₁) and (l₂),

 Thus,                                   

The torque is usually measured from the twist on the suspension.