Two circular discs, both with radius a, are parallel with mutual distance d, such that their centers are situated on a line orthogonal to the discs. The volume between the discs is filled with oil with viscosity η. One disc is kept fixed while the other one rotates about an axis through the centers of the discs with a constant angular velocity ω. The motion of the layer of oil between the discs is assumed laminar such that the usual law of friction can be applied.
a. Find the torque N that must be applied to the disc to keep the angular velocity constant.
b. Find the amount of heat Q generated per unit time. c. Find an approximate value of the Reynolds number and check whether it is justified to consider the flow laminar. The following numbers are used:
a = 10 cm, d = 0.1 cm, η = 1.75 · 10-2 Pa · sec, ω = 2π · 5 sec-1.