Between 2 horizontal flat plates (distance between the plates = d = 0.06 m) is a viscous oil (density = 800 kg/m3 and dynamic viscosity = 0.02 kg/m.s). The top plate is suddenly moved with a velocity vp=0.8 m/s to the right, while the bottom plate is kept in rest. Initially the oil is also in rest.

a.) Calculate the velocity of the oil at a distance of 0.01 m from the top-plate at 4 seconds after the top-plate started to move. Calculate for this time the force per unit area that has to be act on the top plate to force this movement. Till what time t * are the equations you used valid?

b.) Make a clear sketch of the development of the velocity profile of the viscous oil between the plates with time.