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IV.5.1 General Formulation ot of Entrainment Rate
The correlation for entrainment at the entrance section given by Eq.
(25) is developed for the case of the smooth injection of liquid as a film.
In this particular case, the amount of entrainment gradually increases from
zero to the equilibrium value with the distance from the inlet. From this en-
trainment correlation the rate of entrainment can be obtained. Although this
rate applies only to the case with excess liquid on the film, compared to the
equilibrium condition, the generalization of the model can be possible and
will be discussed later.
From Eq. (23) the nond-imensional distance parameter c can be expres-
sed in terms of E/E m as
= 231 IQn[1/(1 - E/E .)] .(37)
By eliminating in Eq. (25) in view of Eq. (37), and using Eq. (34), one ob-
tains
IV. 5 ENTRAINMENT RATE IN ENTRANCE REGION
e2= 1.67 x 10-9 Re1.5 Re0.25 WeQ,n -----------------1
-
offff~(1 -E/E)Em
+ 6.6 x 10-7 Re0.74 Re0.185
..of
We0.9250.26 E
0.74(38) •fff
m
As shown in Fig. 1, because of the existence of the first term on the right
hand side, Eq. (38) gives much higher value of the entrainment rate than Eq.
(36) for large Ref and We in the entrance region where E/E, < 1. The above
rate correlation is a rather complicated function of E/Em, therefore, some
modifications are made to obtain a simplified correlation in entrance region.
By considering the entrainment rate in entrance region, where E/EW < 1, as a
function of E/E m, one can assume the following functional form for the entrainment
rate
uD=f (E/E) +uD(39)
ff
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