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= 135 inches of liquid
.
0.732
59.5
Superficial velocity based on bubbling area = Ua = 75.0(2.26/22.6) = 7.5 ft/s
From Eq. (653), Ks = U a ρV
ρ L − ρV 1/ 2 = 7.5 0.0408
59.5 − 0.0408 1/ 2 = 0.196 ft/s From Eq. (652), φe = exp(4.257Ks0.91) = exp[4.257(0.196)0.91] = 0.381 Exercise 7.48 (continued)
Analysis: (b) (continued)
From Eq. (654), Cl = 0.362 + 0.317 exp(−3.5hw ) = 0.362 + 0.317 exp[−3.5(2.0)] = 0.362
Weir length = Lw = 42.5 in.
Volumetric liquid rate = qL = 2,578(18.1)/[60(8.33)(59.5/62.4)] = 97.9 gpm
From Eq. (651), hl = φe hw + Cl qL
Lw φe 2/3 97.9
= 0.381 2 + 0.362
( 42.5 ) 0.381 2/3 = 1.22 in. liq From Eq. (655), with maximum bubble size = DH = 3/16 inch = 0.00476 m and liquid density =
59.5 lb/ft3 or 954 kg/m3, and σ = 58 dyne/cm = 0.058 kg/s2,
hσ = 6σ / gρ L DBmax = 6(0.058) / (9.8)(954)(0.00476) = 0.0078 m = 0.31 in. liquid
From Eq. (2), ht = hd + hl + hσ = 1.35 + 1.22 + 0.31 = 2.88 inches liquid = 0.098 psi/tray.
(c) Applying the criterion of Eq. (668) to the top tray, hd + hσ = 3.39 + 0.13 = 3.52 in., which is
greater than hl = 0.74 in. Therefore, weeping will not occur.
Applying the criterion of Eq. (668) to the bottom tray, hd + hσ = 1.35 + 0.31 = 1.66 in., which is
greater than hl = 1.22 in. Therefore, weeping will not occur.
(d) From Fig. 6.28 for the top tray, with FLV = 0.0192 and % flood = 73%, fractional
entrainment = ψ = 0.11, which is fairly high.
From Fig. 6.28 for the bottom tray, with FLV = 0.0473 and % flood = 39%, fractional
entrainment = ψ = 0.0065, which is very low.
The fractional entrainment is defined as, ψ = e/(L + e). Rearranging, entrainment rate = e =
ψL/(1  ψ).
At the top tray, e = 0.11(727)/(1  0.11) = 90 lbmol/h
At the bottom tray, e = 0.0065(2,578)/(1  0.0065) = 16.9 lbmol/h
(e) From Eqs. (670) and (672), the froth height in the downcomer = hdf =(ht + hl + hda) / 0.5
Estimate the head loss for flow under the downcomer from Eq. (671). Area for flow under the
downcomer apron = Ada = Lwha = 42.5(2  0.5) = 63.8 in2 = 0.433 ft2 59.4
For the top tray, qL = 59.4 gpm. hda = 0.03
100(0.433)
hdf = (4.26 + 0.74 + 0.056) / 0.5 = 10.1 in. liquid 2 = 0.056 in. liquid 98.3
For the bottom tray, qL = 98.3 gpm. hda = 0.03
100(0.433)
hdf = (2.88 + 1.22 + 0.155) / 0.5 = 8.5 in. liquid 2 = 0155 in. liquid
. Exercise 7.49
Subject: Tray hydraulics for methanolwater separation. Given: Data from Exercise 7.41, except that feed rate is increased by 30%.
Find: (a) Percent of flooding.
(b) Tray pressure drop in psi.
(c) Entrainment rate.
(d) Downcomer froth height.
Is operation acceptable or should packing be used in one or both sections?
Analysis: Use the material balance from Exercise 7.41. Make calculations at the top and
bottom trays. But take into account the 30% increase in all flow rates.
(a) At the top of the column, the reflux rate is 1.3(0.947)(768) = 945 lbmol/h. The overhead
vapor rate = 1.3[0.947(768) + 768] = 1,944 lbmol/h. Use the entrainment flooding correlation of
Fig. 6.24,...
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 Spring '11
 Levicky
 The Land

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