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