Two fluid layers with different viscosities ( u1= 0.1 pa ∙ s and u2 = 0.2 pa ∙ s) are sandwiched between two plates of area a = 1 m2. each layer is h = 1 mm thick. find the force f necessary to make the upper plate move at a speed u = 1 m/s. also, find the fluid velocity at the interface between the two fluids.

Explanation:

The given data is as follows.

            = 0.1 Pa.s,             = 0.2 Pa.s

            = = 1 mm =   (as 1 m = 1000 mm)

As the velocity gradients are linear so, the shear stress will be the same throughout.

                  = velocity at the interface

or,                

Now, putting the given values into the above formula as follows.

                          =        

                          = 0.667 m/s

Hence, force required will be F =          

or,                  F =

                         =

                         = 66.67 N

Thus, we can conclude that the fluid velocity is 0.667 m/s and force necessary to make the upper plate move at a speed U = 1 m/s is 66.67 N.

the answer is option a.