Consider a small, permeable tube of radius R and length L that is closed at one end, as in Fig. P8.2. Suppose that a high external pressure creates a constant inward velocity vw at the wall, but with no flow across the closed end.

(a) Relate u(z), the local mean velocity, to v_w.

(b) For the lubrication approximation to apply, what constraints must be satisfied by v_w and the linear dimensions? 

(c) Assuming that the conditions in part (b) hold, determine v_z(r, z), v_r(r, z), and 

Transcribed Image Text:

ㅏ N R Vw L Figure P8.2 Tube with one end closed and a constant inward velocity at the wall.