Search
 
 

FLUID MECHANICS - CASE STUDY

    Introduction


Rotational Cylindrical Viscometer
  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, 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.

     
    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.