Avolume of sae 10w-40 oil at 40 °c (viscosity = 79.33 mpa·s) is fully contained between two identical long wide plates each having a surface area 9.0 cm2 and separated by a uniform gap between the plates (in the y-direction) of 500 µm. at time t=0, the top plate is moved forward (in the x-direction) at a velocity of 1.0 cm/s. for these conditions determine:
a) what is the velocity gradient dv_x/dy between the two plates? b) what is the stress on the bottom plate? c) what force is required to keep the top plate moving to the right? d) for a vertical, stationary, axis (perpendicular to both plates), what is the volumetric flow rate between the plates, and e) what is the average fluid velocity between the plates?