Special Cases

Standard ideal cascade, p = q = 1. For the standard ideal cascade, p — q= 1. From Eqs. (12.242) and (12.243),

/3 = 7 = a}n

and the coefficient of z in Eq. (12.254) is identically zero. Hence which is equivalent to Eq. (12.142a).

Close-separation case. In many multistage isotope separation processes a — 1 < 1, so that /3—1^1 and 7 — 1 < 1. The gaseous diffusion process for separating uranium isotopes and the water distillation process for enriching deuterium are examples.

Define

То the second order in 5 and e this reduces to

Z6e _ ZQ3 — lXy ~ 1) 2 2

which is independent of z. Hence, the concept of separative capacity may be used to evaluate the total flow rate in a close-separation, ideal cascade for all values of p and q.

Low-enrichment case, z<£l. In the largest and most important stages of a deuterium enrichment or uranium isotope separation plant z < 0.03. For this low-enrichment case z[((3 + 1X7 ~ l)ln(3 — (7 + 1)03—l)ln7] in Eq. (12.254)is small compared with7ОЗ— 1)In 7 — (7 — 1) In 6 and may be neglected for values of (3 and 7 under 2.

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