Finding torque in rotating cylinder (viscosity )

[bobblehead]

Homework Statement

Homework Equations

τ= η* (dv/dy)

The Attempt at a Solution

so
dA= 2π* r * dr
T = ∫ τ * r * dA
T = ∫((0.01* r* 2*π * 450 /60)/(5*10^-3) ) * r * 2π* r *dr
= (592.1762)*(r^4/4)
T = 0.11 Nm

is this correct?

 

[haruspex]

I think it is more complicated than that. There is a velocity gradient not only horizontally but also down the slope of the rotating cone.