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Separator Design 295

placed by an equivalent diameter for the noncircular flow area. The equivalent
diameter is equal to four times the hydraulic radius, which is defined as the cross-
sectional area of the stream (flow area) divided by the wetted perimeter. The defi-
nition of hydraulic radius is only valid for turbulent flow, as discussed by Bird et
al. [68]. For a liquid-liquid interface located at the center of the decanter, the flow
area is equal to 1A the cross-sectional area of the separator, and the wetted perime-
1
ter is equal to the separator diameter plus A its circumference.
Table 6.15 Summary of Equations for Sizing Liquid-Liquid Separators

Subscripts: L = light phase - H = heavy phase
D = dispersed phase - C = continuous phase

Transport Relations
v 'fpL'UH'V- 30
L
e = — I —— I (6.15.1)

V D = V L' or V D =V H' — from Table 6.13 — V D, light or heavy phase (6.15.2)

VLorvD = VH — from Table 6.13 — VD, light or heavy phase (6.15.3)
VD =
PL' or PC =PH' — from Table 6.13 — p, light or heavy phase (6.15.4)
PC =
c
PD = PL' or p D = p H' — from Table 6.13 — p D, light or heavy phase (6.15.5)

LL C = |i L ' or u c = UN' — from Table 6.13 — Uc, light or heavy phase (6.15.6)
2
g(d') (p D '- Pc ')
v d = ————————— (6.15.7)
18 nc
t D = D/2v d (6.15.8)

L s = v D t D (6.15.9)

H D = 0.1D (6.15.10)

(1/2) H D A,
t R '= —————— (6.15.11)
V D

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