A disk of radius r 0 rotates at angular velocity ꞷ inside an oil bath of viscosity µ, as shown in Fig. Assuming a linear velocity profile and neglecting shear on the outer disk edges, derive an expression for the viscous torque on the disk.
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Sol. τ = µ(dv/dy) = µ(rw/h) (on both sides)
dT = (2) (r τ dA) = (2) {(r)[µ(rꞷ/h)] (2 π rdr)} = (4µꞷ π /h) (r 3 dr)
T = 
(r 3 dr) = 
= 
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