The viscosity of a fluid is to be measured by a viscometer constructed of two 80-cm-long concentric cylinders. The outer diameter of the inner cylinder is 15 cm, and the gap between the two cylinders is 1 mm. The inner cylinder is rotated at 300 rpm, and the torque is measured to be 0.8 N·m. Determine the viscosity of the fluid.

The viscosity of the fluid is 0.012 kg m⁻¹ s⁻¹

Explanation:

Given :

Length of concentric cylinders, L = 80 cm = 0.8 m

Outer diameter of inner cylinder, D = 15 cm = 0.15 m

Gap between two cylinders = 1 mm = 0.001 m

Rotation of inner cylinder = 300 rpm

Torque, τ = 0.8 Nm

The relation to determine area is:

A = πDL

A = π x 0.15 x 0.8 = 0.38 m²

The relation to determine velocity is:

Here N is number of rotation per second.

v = 2.36 m/s

The relation to determine force between the two layers:

F = 10.67 N

Using Law of viscosity,

η = 0.012 kg m⁻¹ s⁻¹

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