Problem $1\mathrm{.}17$ A $15$ cm diameter vertical cylinder rotates concentrically inside another cylinder of diameter $15\mathrm{.}10$ cm $.$ Both cylinders are $25$ cm high. The space between the cylinders is filled with a liquid whose viscosity is unknown. If a torque of $12\mathrm{.}0$ Nm is required to rotate the inner cylinder at $100$ r$.$p$.$m$.,$ determine the viscosity of the fluid.