Question

1. The viscosity of SAE 10 motor oil at room temperature is about 0.25Pa-s. Consider a 5cm- thick oil layer between two 5m2 surfaces.

   1. a) Calculate the force on the bottom layer if the top later is moving at a constant speed of

      3.5m/s.

   2. b) If the force were to remain constant, how long will it take until the two layers are moving at the same speed?

   3. c) Of course the problem is not that simple, explain what happen with the force and speed as

      time passes.

Answer 1

By using the Newton's law of viscocity we get:

where tau is the shear stress, v is the velocity and y is the height between the lower and upper surfaces separated by oil layer.

For our case of study, considering oil a Newtonian fluid we get:

The velocity profile could be considered as linear with respect to y, therefore (all units are SI format):

Then, the shear stress is given by:

The force on the bottom layer is given by:

As we consider the bottom layer to be not moving because the force is being applied on the top layer and because the fluid is Newtonian, then the speed of the bottom layers is zero all of the fime, even though there is a shear stress on the top layer, on the bottom layer there is a stress that goes on the contrary direction of the top layer's, therefore, forces on the top and bottom layers are opposite, which makes the speed zero at the bottom. It results in the cancelling of the top force with the bottom force, that is why there is zero speed on the bottom layer.