source: George F. Klein, Chemical Engineering, May 3, p.81, 1982, reprinted courtesy àt Chemical Engineering.
source: George F. Klein, Chemical Engineering, May 3, p.81, 1982, reprinted courtesy àt Chemical Engineering.
Klein's method requires that in the diy pressure drop equation, Eq. (6.42), the vapor hole velocity uh is based on the area of holes on the deck of a valve tray (Ado), and not on the slot area. In many valve trays, the orifice diameter is standardized at 1L%2 in. Values of Kc and K0 are listed in Table 6.9. K0 is listed as a function of the tray deck thickness t, not the valve thickness. When the tray deck thickness is not listed in Table 6.9, K0 can be evaluated from
In order to determine whether the valves are fully open, fully closed, or in between, and in order to apply the pressure drop equation between the open and closed balance points, the vapor hole velocities M each balance point must be evaluated. The balance-point hole veloa-ties are evaluated from a balance between the vapor force pushing the valve open and the gravity force tending to close it. This force balancr gives (71,80)
Values of Rvw, Kc, K0, Cuw, and pvm are listed in Table 6.9. The hafc vapor velocities, u^cbp and ti^oBP are based on the area of holes a the tray deck, A^.
&3.3 Pressure drop through the aerated liquid
For sieve trays, most designers (3-5,18,31) have been recommending Fair's pressure drop correlation (18,31). A recent correlation by Bennett et al. (81) was recommended (18,81) for accurate pressure drop prediction. For valve trays, a slight modification of Fair's sieve tray correlation (80) is described.
The pressure drop through the aerated liquid [ht in Eq. (6.41)] is calculated from (3-5,18,30,31,77)
An alternative, more fundamental relationship sometimes used is (12)
where the residual pressure drop hR is often interpreted as the excess pressure required to overcome surface tension when bubbles are formed at the orifice (12).
The relationship in Eq. (6.47a) is more popular and will be adopted here. The tray aeration factor, (3, is obtained from Fig. 6.22a for sieve trays (18,31) and Fig. 6.226 for valve trays (5,80). For sieve and valve trays, hc is calculated from (2-5,18,30)
Figure 6.22 (CWmtteif) Tray aeration factor prediction for pressure drop calculations, (b) A modified version of the correlation in a, suitable for valve trays. {Part b from George F. Klein, Chemical Engineering, May 3, p. 81, 1982, reprinted courtesy of Chemical Engineering)
Figure 6.22 (CWmtteif) Tray aeration factor prediction for pressure drop calculations, (b) A modified version of the correlation in a, suitable for valve trays. {Part b from George F. Klein, Chemical Engineering, May 3, p. 81, 1982, reprinted courtesy of Chemical Engineering)
Liquid height over the weir. how is calculated from a corrected Francis weir formula (2-5,18,31). For segmental weirs how = 0.48Fw (QLf3 (6.49)
The correction term Fw (2-5,9,18,31) corrects the equation for the distortion of the liquid flow pattern as it approaches the weir, and is shown in Fig. 6.23 (18). Some variations of Eq. (6.49) for unique weir designs are
■ For picket-fence weirs and for rectangular notched weirs, and tray liquid level below the top of the teeth, QL in Eq. (6.49) is based on the weir length less the total weir length occupied by the teeth. Fw is based on the total weir length (including the length of the teeth).
■ For weirs with triangular notches, notches not fully covered by liquid (2,67):
■ For weirs with triangular notches, notches fully covered by liquid (2,67).
Hydraulic gradient. The hydraulic gradient, hkg is the head of liquid necessary to overcome the frictional forces in the path of the liquid on the tray. If the gradient is excessive, most of the vapor tends to issue near the outlet weir, where liquid level is low, whereas liquid tends to weep near the liquid inlet to the tray, where the liquid level is high. It has been recommended (18) to avoid hydraulic gradients greater than 40 percent of the dry pressure drop. Hydraulic gradients are negligible for most sieve trays, and the usual practice is to omit this term from the pressure drop calculation (4,18,67). In cases of a long flow path of liquid on the tray, it should be checked using the correlation of Hughmark and O'Connell (66), as recommended by most designers (4,5,18,30,31). The author recommends caution with this equation. On a couple of occasions when he applied it, it appeared to predict very low. The correlation is
Rh is the hydraulic radius of the aerated mass, estimated from
h wetted perimeter 2hf+ 12Df
JJf is the velocity of the aerated mass across the tray (which is also equal to the clear liquid velocity across the tray), given by hf is the froth density, and is estimated from h( = A,/<J>t (6.53'
h; is estimated from Eq. (6.47a) and 4>, is estimated from Fig. 6.22a. As h[ is a weak function of the hydraulic gradient, only a small amount of trial and error is necessary. The friction factor f in Eq. (6.50) is correlated in terms of the Reynolds number,
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