Flow outside a cylinder rotating in an infinite bath of fluid $$ u_\varphi = \frac{\Omega_1 R_1^2}{R} $$ Viscous shear stress $$ \sigma_{R\varphi} = \mu \left[ \frac{1}{R}\frac{\partial u_\varphi}{\partial \varphi} + R \frac{\partial}{\partial R} \left( \frac{u_\varphi}{R} \right) \right] = - \frac{2 \mu \Omega_1 R_1^2}{R^2} $$ Mechanical power supplied to fluid $$ (2 \pi R_1) \, \tau_{R\varphi} \, u_\varphi $$