and, including the square root of the density terms, Eq. (16-5) becomes h9 m 0.12 * + 0.72 (h*V, ,PQ°'75 (16-6)
It is believed that Eq. (16-3) with a value of K by Eq. (16-4) gives better results for specific cases, but that Eq. (16-6) is helpful for general cases.
With the usual plate design the slots become completely open for vapor flow at values of he less than h* due to the fact that the average density of the vapor-liquid mixture around the cap is only % to that of the liquid. For studies of single caps this lowered-density effect is of less importance. At vapor rates higher than those corresponding to complete opening of the slots, the relation between h8 and V8 should be modified. In some cases the bottoms of the caps are raised above the plate to allow excess vapor to escape. With this arrangement, high capacities can be obtained without excessive pressure drops, although the vapor-liquid contact for such operation is probably of low effectiveness. In other cases, the bottoms of the caps are sealed to the plates, and any excess vapor is forced through the slots. For this condition the following equation is suggested for h8 greater than h*:
where V* is vapor velocity in Eq. (16-3) for h8 equal to h* and h* is the value of h8 for slots completely open. For conventional plate arrangements it is suggested that hf be taken equal to }ih*.
Pressure Drop Due to Liquid Head above Slots. The pressure drop due to the liquid head above the top of the slot is customarily taken as equal to the actual liquid depth above the slots. This liquid depth is frequently taken as weir height, hw, plus the weir crest, hCT) minus the height of the top of the slot, h3p, thus hL = hw + her — hsp (16-8)
In some cases a correction is added for the additional liquid head at the cap in question owing to the liquid gradient. This method of evaluating hL is simple, but the data of Seuren (Ref. 29), Ghormley (Ref. 11), and Kesler (Ref. 19) show that the actual liquid head in the aerated section of a plate can be considerably less than that at the weir. This effect is the result of liquid flow from a nonaerated section to an aerated section and back to a nonaerated section. This condition will be discussed in the section on Hydraulic Gradient. The use of Eq. (16-8) with a correction for the hydraulic gradient will give high values for the liquid head.
The over-all pressure drop for a plate, hp, is calculated by hv - hc + K + hL (16-9)
Liquid Flow. Weirs and Down Pipes. The liquid depth on a plate is controlled by exit overflow weirs. The action of the liquid flowing over the weir is complicated by the action of the caps and by the restrictions due to the wall. The last row of caps may blow a con-
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Successive i plates rotated by this amount
Successive i plates rotated by this amount
F Split flow Chord weirs
siderable quantity of liquid over the weir as spray and in surges. The walls may be so close to the downstream side of the weir that they interfere with the liquid flow.
A variety of different weir and down-pipe arrangements are employed (see Fig. 16-4).
In small columns, the overflow from plate to plate is usually carried in pipes, the upper end of the pipe projecting above the plate surface to form an overflow weir and maintain a liquid seal on the plate. The lower end extends into a well on the plate below, thereby sealing the pipe so that the vapor may not pass upward through it. In larger columns, straight overflow weirs placed on a chord across the tower are often used.
Locke (Ref. 22) from a study of circular down pipes with the tops acting as weirs concluded that at least three types of liquid flow were possible in circular down pipes with liquid seals at the bottom. At low rates of liquid flow, the top of the pipe acted as a weir, and the liquid flowed down in a film. As the liquid head was increased, the pipe became full and sucked vapor bubbles down with it; at still higher liquid rates, the pipe ran full but did not entrap vapor. The first type flow occurred for liquid head less than one-sixth to one-fifth of the pipe diameter, and this type of flow could be represented by the familiar Francis weir formula:
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