A circular disc of radius 0.20 m rotates at angular speed 20 rad/s above a fixed plate. A Newtonian liquid film of thickness 1 mm and viscosity 0.50 Pa·s lies between them. If the viscous torque is Nπ N·m, find N.
Physics · Properties of solid and fluid · viscosity and terminal velocity
JEE Mains NEET JEE Advanced

Question

A circular disc of radius 0.20 m rotates at angular speed 20 rad/s above a fixed plate. A Newtonian liquid film of thickness 1 mm and viscosity 0.50 Pa·s lies between them. If the viscous torque is Nπ N·m, find N.

Physics · Properties of solid and fluid · viscosity and terminal velocity

G1 Physics · Accepted Answer

The viscous torque on the rotating disc is Γ = πηωR⁴/(2d). Substitute: η = 0.50 Pa·s, ω = 20 rad/s, R = 0.20 m, d = 1 mm = 10⁻³ m. Now, R⁴ = (0.20)⁴ = 0.0016. Therefore, Γ = π×0.50×20×0.0016/ [2×10⁻³]. The numerator excluding π is 0.016. Hence, Γ = 0.016π/0.002 = 8π N·m. Therefore, N = 8.