Francis weir formulae columns

Smith recommends obtaining the settling height (tray spacing minus clear liquid depth) by applying the familial Francis Weir formula. For our purposes of rapidly checking column diameter, a faster approach is needed. 

The liquid rates throughout the column will not be the same dynamically. They will depend on the fluid mechanics of the tray. Often a simple Francis weir formula relationship is used to relate the liquid holdup on the tray (M,) to the liquid flow rate leaving the tray (L ). 

The Francis weir formula is used in distillation column design to find the height of the liquid crest over the weir that controls liquid flow from the plate in the column... 

The equivalent height of vapor-free liquid over the weir may be calculated for circular columns by use of a modified version of the Francis weir formula which was proposed by Bolles.1 For a straight segmental weir... 

We assume constant density, equimolal overflow, theoretical trays, total condenser, partial reboiler, and five-minute holdups in the column base and the overhead receiver. Tray holdups and the liquid hydraulic constants are calculated from the Francis weir formula using a one-inch weir height. 

With segmental downcomers the column wall constricts the liquid flow, and the weir crest will be higher than that predicted by the Francis formula for flow over an open weir. The constant in equation 11.85 has been increased to allow for this effect. 

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