4,000 10,000 4-0,000
Re- Modified Reynolds number
correlated were for essentially standard caps and plate arrangements, and the relation should be used with caution for plate layouts that differ significantly.
It will be noted for Fig. 16-7 that /' is essentially inversely proportional to the value of Re'. Combining this relationship with the fact
that for large plates 2L0 is small in comparison with b gives
This relation would indicate that the hydraulic gradient is directly proportional to the liquid flow rate per foot of plate width and to the length of the bubbling section. The outlet hydrostatic head is probably the most important factor determining the hydraulic gradient, and high outlet weirs should be an effective method of reducing the loss in head.
Equation (16-21) indicates that the gradient is approximately proportional to the liquid viscosity. The liquid viscosities studied ranged from that of water at room temperature to glycerine. Gardner (Ref. 10) studied the hydraulic gradient on a plate with tunnel caps using water at different temperatures and concluded that the liquid viscosity was not a factor. The plate design was unusual in that the liquid flow was across rather than along the tunnel caps. However, until additional data are available it is recommended that pL be taken equal to 0.00067 pounds per f.p.s. for all liquids of lower viscosity and equal to the actual viscosity for those having higher values.
Liquid Head. As shown in Fig. 16-6 the hydrostatic head in the bubbling section can be less than at the outlet weir. However, the liquid head above the top of the slots may be greater or less than the difference in the height of the outlet liquid and the top of the slots owing to the increased depth of the vapor-liquid mixture. The value of the liquid head calculated by Eq. (16-8) should be satisfactory for most cases, but the actual value may differ somewhat due to the aeration effects.
Plate Stability. The term "plate stability" has been used to describe the vapor and liquid distribution on a plate.. A stable plate has been defined as one in which all the caps are handling vapor, although the quantity of vapor per cap may vary widely from one side of the plate to the other. The plate is stable in the sense that liquid is flowing across the plate and not by-passing by "dumping" through the cap risers, but the distribution of vapor may be quite poor.
The term "stable plate" does not differentiate between the various types of plate action and in this text the following terms will be used.
Uniform vapor distribution—will indicate the condition when each cap on the plate handles the same amount of vapor per unit time.
Active cap—will indicate that vapor is passing through the cap.
Inactive cap—will indicate that vapor is not passing through the cap. Completely active plate—will indicate that all caps are active. Partly active plate—will indicate that only part of the caps are active. Plate dumping—will indicate that liquid is flowing to the plate below through some of the cap risers.
The distribution of the vapor among the various caps is a function of the pressure drops involved. The lateral pressure difference in the vapor space above a plate is usually small and, when this condition is true, hp = hc + h8 + hL = constant
Because hL varies across the plate, he + h8 must vary. Substituting the values from Eqs. (16-2) and (16-3) in the above equation gives
1.17| fc) + 0.12 — + K (h0Va L^— ) +hL = hp (16-22) \PL/ PL \ \PL — PV/
and, for a given plate, this can be condensed to hV2 + faV* + hL = hp- 0.12-2- (16-23)
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