It is desired to predict the effects of imperfections that might occur in fabricating a parallel-plate channel. One possibility is a sinusoidal variation in the halfheight,

as depicted in Fig. P5.2. That is, h might vary from its mean value h₀ by ± εh₀ over a length L. Suppose that a steady flow rate q (volume flow per unit width) is specified.

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

(b) Assuming that the conditions in part (a) hold, determine v_x(x, y).

(c) Will the pressure drop over a length L be less than, equal to, or greater than that for a channel of constant half-height h₀?

Transcribed Image Text:

h(x)= ho 1+ ε sin [1+65 2π.χ. L (P8.1-1)