Question

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.

Answer 1

Answer:

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:

$v=\frac{\pi DN }{60}$

Here N is number of rotation per second.

$v=\frac{\pi\times0.15\times300 }{60}$

v = 2.36 m/s

The relation to determine force between the two layers:

$F=\frac{\tau}{r}$

$F=\frac{0.8}{0.075}$

F = 10.67 N

Using Law of viscosity,

$\eta=\frac{F/A}{\Delta v/\Delta y }$

$\eta=\frac{10.67/0.38}{2.36/0.001}$

η = 0.012 kg m⁻¹ s⁻¹