Students are given a simple device called a rotational
cylindrical viscometer, as shown in the figure, and asked to determine
the viscosity of an unknown liquid.
The outer cylinder is fixed while the inner cylinder is rotating at a constant angular speed
of ω by applying a torque T.

Questions

Derive an equation for the viscosity in terms
of angular velocity, ω, torque, T,
submerged inner cylinder height, L, inner cylinder radius, R_{i},
and outer cylinder radius, R_{o}.
Calculate the viscosity value when ω = 55 rev/min, T = 0.9 N-m, L = 0.3 m, R_{i} = 0.12 m and R_{o} = 0.13 m.

Approach

Assume the
velocity profile between the container and the rotating cylinder is linear.

Neglect the end effects and bottom surface of the cylinder.

Assume the liquid is a Newtonian fluid.

Assume the force (F) is perpendicular to its moment arm (r), hence
the torque is given by
T = Fr.

Practice Homework and Test problems now available in the 'Eng Fluids' mobile app
Includes over 250 problems with complete detailed solutions.
Available now at the
Google Play Store and
Apple App Store.