A 5.0 kg block falls vertically in a very long, stationary tube of square cross section that is filled with oil of viscosity 0.3 Pa s. The oil exerts a viscous force on the block as it falls. The block has cross section = 25 mm by = 25 mm in the horizontal plane and is = 80 mm long. The square tube has inner dimensions = 28 mm by = 28 mm and is open to oil reservoirs on both ends (not pictured). The block remains centered in the tube in the horizontal plane as it falls under the action of gravity. After some time, the block reaches a constant terminal velocity that is to be determined. Assume a linear velocity profile in the oil gaps between the block and the tube. Account for frictional forces resulting from fluid motion in the gaps, but neglect drag due to the pressure acting on the top and bottom surfaces of the block.

(a) Draw a free body diagram of the block and Calculate the constant terminal velocity of the block