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:
[tex]v=\frac{\pi DN }{60}[/tex]
Here N is number of rotation per second.
[tex]v=\frac{\pi\times0.15\times300 }{60}[/tex]
v = 2.36 m/s
The relation to determine force between the two layers:
[tex]F=\frac{\tau}{r}[/tex]
[tex]F=\frac{0.8}{0.075}[/tex]
F = 10.67 N
Using Law of viscosity,
[tex]\eta=\frac{F/A}{\Delta v/\Delta y }[/tex]
[tex]\eta=\frac{10.67/0.38}{2.36/0.001}[/tex]
η = 0.012 kg m⁻¹ s⁻¹
