Problem #1 A thin 30 cm x 30 cm flat plate is pulled at 6 m/s horizontally through a 3.6 mm thick oil layer sandwiched between two plates, one stationary and the other moving at a constant velocity of 0.6 m/s, as shown in the figure below. The dynamic viscosity of the oil is 0.027 Pa's. Assuming the velocity in each oil layer to vary linearly, (a) plot the velocity profile and find the location where the oil velocity is zero and (b) determine the force that needs to be applied on the plate to maintain this motion. Fixed wall 1 mm h₂ = 2.6 mm V=6 m/s V.w=0.6m/s F

A torque is applied to rotate a cylindrical shaft (diameter D 1 , length L) at a constant angularspeed ω, inside a co-axial, stationary cylinder of the same length and diameter D 2. The gapbetween the bottom surface of the shaft and that of the stationary cylinder is h.(a) Develop a general expression of the torque in terms of the geometric dimensions andthe viscosity μ of an oil filling the gaps between the shaft and the stationary cylinder.Assume linear velocity profiles in all the gaps.(b) Determine the numerical value of the torque in the case of an oil of viscosity of 0.1Pa.s. [D 1=5cm, D 2=5.2cm, L=10cm, ω=50rpm, h=1mm]