Answer to Question #130091 in Mechanics | Relativity for Ariyo Emmanuel

Question

The viscosity of a fluid is to be measured by a
viscometer constructed of two 40-cm-long
concentric cylinders (adjacent Fig.). The outer
diameter of the inner cylinder is 12 cm, and
the gap between the two cylinders is 0.15 cm.
The inner cylinder is rotated at 300 rpm, and
the torque is measured to be 1.8 N m.
Determine the viscosity of the fluid?

Answer 1

What is given:

Gap between two concentric cylinders = $1 mm$

The frequency of inner cylinder = $300 rpm$

Length of the concentric cylinders, $L=75 cm$

Torque acting $1.8 N m.$

Outer diameter of the inner cylinder=$15 cm$

$\mu=\frac{Te}{4\pi^2R^3\dot{n}L} =\frac{(1.8N.m)(0.0015m)}{4\pi^2(0.06m)^3(300/601/s)(0.4m)}$

=$0.158N.s/m^2$