The viscosity of some fluids changes when a strong electric field is applied on them. This...

The viscosity of some fluids changes when a strong electric field is applied on them. This phenomenon is known as the electrorheological (ER) effect, and fluids that exhibit such behavior are known as ER fluids. The Bingham plastic model for shear stress, which is expressed as τ = τy + μ(duldy) is widely used to describe ER fluid behavior because of its simplicity. One of the most promising applications of ER-clutch A typical multidisk ER clutch consists of several equally spaced steel disks of:inner radius R1 and outer radius R2, N of them attached to the input shaft. The gap h between the parallel disks is filled with a viscous fluid, (a) Find a relationship for the torque generated by the clutch when the output shaft is stationary and (b) calculate the torque for an ER clutch with N = 11 for R1 = 50 mm, R2 = 200 mm, and  rpm if the fluid is 10 with μ = 0.1 Pa • s, τy = 2.5 kPa, and h = 1.2 mm.