Deen 7-26

In the game of air hockey, a solid disk is suspended by an air stream emerging from small holes in the playing surface, as shown in Fig. P7-26. The disk has a radius R and density s and the thickness of the air gap is H. The perforations are spaced closely enough that the normal component of the air velocity at the surface is nearly constant at v0. Assume that the dynamic pressure outside the gap is approximately constant.

(a) Assuming that the lubrication approximation can be applied in the gap, determine vr(r, z) in terms of dP/dr and H.

(b) Find P(r) in the gap, again as if H were known.

(c) Determine H as a function of the air velocity, dimensions, and physical properties.