To illustrate the shape of a typical ideal cascade, we shall work out the variation of interstage flow with stage number for an ideal cascade to separate natural uranium (zp = 0.0072) into enriched uranium with yp = 0.90 and depleted uranium tails with дсц/ = 0.003 by gaseous diffusion, with a = 1.00429.

To produce 1 mol of product, the amount of feed, from (12.54), is

and the amount of tails, from (12.55), is

The heads separation factor is given by (12.90), with

/3 = V1.00429 = 1.00214 (12.110)

The total number of stages n is twice the minimum, given by (12.74), less 1, or 3738. The number of stages in the stripping section n$ is given by (12.94), with

The heads flow rate in the enriching section, from (12.106), is

(1 -1.00214′-3738X050)

0. 00214

+ (ййщ) d -002143738 -‘ — 1 X0.10) (410 < і < 3738)

The heads flow rate in the stripping section, from (12.107), is

Mj = ^^[(1.00214X1.00214/ — 1X0.003) + (1 — 1.00214’/’X0.997)] (0 </ < 410)

(12.113)

Figure 12.17 is a plot of these equations represented as a tapered column whose height is proportional to stage number above tails and whose width is proportional to heads flow rate.

The large interstage flow rate at the feed point (М410//>= 58,229) and its rapid decrease as the product and tails ends of the plant are approached are characteristic of an ideal cascade.