A cone and plate viscometer consists of a cone with a very small angle \(\alpha\) that rotates above a flat surface as shown in Fig. P7.16. The torque, \(\mathscr{T}\), required to rotate the cone at an angular velocity \(\omega\) is a function of the radius, \(R\), the cone angle, \(\alpha\), and the fluid viscosity, \(\mu\), in addition to \(\omega\). With the aid of dimensional analysis, determine how the torque will change if both the viscosity and angular velocity are doubled.

Figure P7.16

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