shoot of over twice the head. The effect for straight weirs is probably less, and Edminster (Ref. 7) has suggested neglecting the portion of the weir that is closer to the wall than the value of Acr. This would appear to be a reasonable assumption.
For large downspouts running full, it is recommended that Eq. (16-11) be used, employing for D four times the hydraulic radius, which is equal to the cross-sectional area of the downspout divided by the perimeter.
When the liquid head over the weir is low, the discharge from one side to the other will vary if the top edge is not level. This variation can be reduced by using a V-notched top which reduces the effective weir length at low rates of flow. In general, it is desirable to keep the head over the weir low because this reduces the variation of liquid depth on the plate for different operating rates. Values of her of 1.0 in. are common, but they seldom exceed 3 in.
In some cases, under- and overweirs are used at the outlet to handle
two liquid layers on a plate. Such an arrangement can also be used to hold back foam from the down pipe. The clearance between the underweir and the plate must be adequate to handle the liquid load.
The bottoms of downflow pipes must have enough clearance to allow the liquid to flow easily, but they should not allow vapor to by-pass up through them. This vapor by-passing is usually prevented by a positive seal which holds liquid above the bottom of the down pipe (see Fig. 16-1). In large columns, this seal is often made an inlet weir which serves to distribute the liquid as well as seal the down pipe.
For the reversal loss at the bottom of the down pipe, it is recommended that a loss equal to one kinetic head be used with a coefficient of 0.6.
= 0.57|, where hD = loss in head at bottom of down pipe, in.
Vd = maximum velocity at bottom of down pipe, f.p.s.
Liquid Gradient. One of the important factors that must be considered in the design of a bubble plate is the liquid gradient across the plate. It is obvious that the liquid level will normally be higher at the liquid inlet than at the outlet. In small towers, this difference in level offers no serious difficulties, but in towers of moderate and large diameters it can become so great that the vapor distribution is poor and the overflow may by-pass the plate by dumping through the caps.
The gradient is due to the resistance to liquid flow across the plate and results from (1) friction with the caps and the plate, (2) eddy losses in the liquid due to repeated acceleration and deceleration, and (3) resistance due to the effects of vapor flow.
Experimental data on this gradient have been published by several investigators (Refs. 10, 11, 12, 13, 18, 19,29). Gonzales and Roberts (Ref. 12) studied a plate with 4%-in.-diameter caps which were in. tall using air and water. Their column was rectangular in shape with 12 rows of caps in the direction of liquid flow. Based on liquid flow around staggered pipes, they developed the following equation for the gradient as a function of the number of rows of caps:
where h liquid depth on plate A,B *= constants
Their data were taken at liquid levels less than the top of the caps and agreed well with the equation for both aerated and unaerated conditions. A and B were functions of both the water and air rates.
Bijawat (Ref. 2) reviewed the data obtained by Gonzales and Roberts and, on the basis of orifice-type flow of the liquid between the caps, suggested h* = A' - B'n (16-15)
This equation correlated the data about as well as Eq. (16-14). Seuren (Ref. 29), Ghormley (Ref. 11), and Kesler (Ref. 19) obtained data on a rectangular plate with 10 rows of 4-in. caps in the direction of liquid flow. Good, Hutchinson, and Rousseau (Ref. 13) investigated the liquid gradient on a rectangular plate having 12 rows of 3-in. caps for a number of operating conditions.
Klein (Ref. 20a) has investigated the factors that cause the loss in head of the liquid flowing across the plate. His data indicate that with no vapor flow there is essentially no hydraulic gradient even at liquid rates considerably greater than those normally employed. It was concluded that the loss in head was due to high frictional losses for the flow of the vapor-liquid mixture. The drag per unit area was determined by measuring the force on a plate suspended in the aerated liquid, and values ten times as large as for unaerated liquid flowing at the same linear velocity were found. Abnormally high frictional losses have also been reported for the flow of mixtures of vapor and liquids in pipes.
Klein confirmed the observation of Ghormley and Kesler that the hydrostatic head of the liquid in the aerated section was frequently less than that at either the inlet or outlet to the plate. Klein, Kesler, and Bloecher (Ref. 2a) measured the potential head of the liquid by determining the hydrostatic head as a function of depth and then integrating up from the bottom of the plate. The potential head is equal to the number of inches above the tray at which all the water present would give the same total potential energy as the aerated liquid. For a nonaerated liquid the potential head, according to this definition, is equal to one-half the liquid depth. It was shown that the potential head decreases progressively across the plate. It is this head, and not the hydrostatic head, which is the driving force for liquid flow. The flow across a bubble plate can be considered in terms of five zones. (1) There is the inlet unaerated section in which the potential head is twice the hydrostatic head. (2) There is the transition section from the first zone to the aerated region. This transition occurs a short distance upstream from the first row of caps to about the second row of caps. In this region (a) the apparent depth of liquid rises sharply owing to the aeration, (b) the hydrostatic pressure drops abruptly, and (c) the potential head remains almost constant. For the potential head to remain constant the hydraulic head must decrease because some of the liquid is at a higher level. Near the plate the pressure in the liquid in Zone 1 is higher than in the transition section and liquid flows towards the caps, but at higher levels the reverse is true and the liquid flows back (against the normal flow). (3) The third zone is the main aerated section in which the hydrostatic head remains essentially constant and there is a progressive decrease in the potential head. (4) The fourth zone is the outlet transition zone which extends from the last two rows of caps to the calming section before the outlet weir. The phenomena are similar to those for the inlet transition zone, i.e., the apparent depth of the liquid drops sharply, (b) the hydrostatic head increases abruptly, and (c) the potential head remains almost constant. In this case there is a flow of liquid back toward the caps near the plate and toward the outlet section at the higher levels. (5) The final region is the unaerated calming section before the outlet weir. These effects are illustrated in Fig. 16-6. At low air rates there is a decrease in hydrostatic head in the aerated zone, but a clear liquid layer on the plate extends from the inlet to the outlet. At higher vapor rates the liquid becomes "completely aerated," and no apparent clear liquid layer remains. This condition is shown in diagram A of Fig. 16-6. Data on the hydrostatic and potential head for a completely aerated condition are shown in diagram B. The sharp drop and rise in the hydrostatic head at the two ends of the plate are clearly shown, but there is essentially no change in the aerated section. The value of twice the potential head is plotted so that it will be numerically equal to the hydrostatic head in the two nonaerated sections. The potential head decreases regularly across the plate.
Referring again to diagram 5, Fig. 16-6, the hydrostatic head given is the value at the bottom of the plate. If values are determined in planes parallel to, but above, the plate, it is found that the hydrostatic head decreases more rapidly with height in the nonaerated sections than in the bubbling zone owing to the lower density of the vapor-liquid mixture. Eventually, at a height less than h0, the hydrostatic head in the outlet transition zone (Zone 4) becomes equal to that in Zone 5, and at higher heights above the plate the aerated section has the higher head. Thus, the hydrostatic head is a complicated function of the position and the distance above the plate.
Klein found that for a given liquid rate the hydraulic gradient increased with increasing vapor rate until the liquid-vapor mixture in the aerated section had an apparent density approximately one-third that of the liquid but further increases in vapor rate did not appreciably change the loss in head. He termed the condition for the mixture density equal to one-third the liquid density "complete aeration."
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