A cylinder with mass M=.225kg slides down a long vertical tube. The tube is lubricated with a thin layer of glycerin at T=30C in the gap between the cylinder and the tube. The tube is diameter is D=30.1mm, the cylinder is H=20.5mm tall and the gap width is estimated at h=.00125mm. At a certain instant in time, the cylinder is traveling downward with V=12.5mm/sec. If the pressure above and below the cylinder can be assumed to be equal and constant, estimate the acceleration of the cylinder at this instant. Also, estimate the ultimate speed the cylinder would reach after sliding down the tube a long way. Finally, if the initial height (where V=12.5mm/sec) of the cylinder(bottom) is 20 cm above the bottom of the tube, and the air pressure in the enclosed region is 102kPa at that instant, develop an expression for estimating the instantaneous acceleration for any time, t. The top of the cylinder is exposed to standard atmospheric air.