Francis weir formulae

Open-loop behavior of multicomponent distillation may be studied by solving modifications of the multicomponent equations of Distefano [Am. Inst. Chem. Eng. J., 14, 190 (1968)] as presented in the subsection Batch Distillation. One frequent modification is to include an equation, such as the Francis weir formula, to relate liquid holdup on a tray to liquid flow rate leaving the tray. Applications to azeotropic-distillation towers are particularly interesting because, as discussed by and ihustrated in the Following example from Prokopalds and Seider... 

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 height of the liquid crest over the weir can be estimated using the Francis weir formula (see Volume 1, Chapter 5). For a segmental downcomer this can be written as ... 

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 ). 

Liquid hydraulics are calculated from the Francis weir formula. 

C DIMENSIONS ARE IN METERS, FLOW IS IN KG MOLE/MIN C HOLDUP IS IN KG-MOLE C FRANCIS WEIR FORMULA USED REAL M,L,M1,M2... 

Froth-Emulsion Froth-emulsion transition occurs [Hofliuis and Zuiderweg, I. Cherrt. E. Symp. Ser. 56, p. 2, 2/1 (1979)] when the aerated mass begins to obey the Francis weir formula. Using this criterion, the latest version of this transition correlation is... 

Francis weir formula. In 1848 to 1852 at Lowell, Massachusetts, James B. Francis made precise investigations of the flow of water over weirs of large size. His observations showed the flow varied as H147, but he adopted H3/2 for greater convenience. He then selected a constant average value of Cd = 0.622 in Eq. (10.72), so that for a suppressed weir with negligible velocity of approach... 

Pi "1 are the bounds on. The authors considered a detailed dynamic model (similar to those presented in Chapter 4) but included pressure drop model and Francis weir formula to calculate liquid flow rate from the tray. Refer to the original work for further details on modelling. 

Liquid height over the weir. h0U1 is calculated from a corrected Francis weir formula (2-5,18,31). For segmental weirs... 

Sieve trays, troth regime. Most dear liquid height and froth density correlations (35,68,81-86) are based on the Francis weir formula. A correlation by Colwell (68), based on a model of froth flow over the weir, was demonstrated to agree with experimental data better than other published correlations. Colwell s correlation is recommended by the author and by Lockett (12), and was successfully used as a building block in weeping correlations (56,63,69) and in froth regime entrainment correlation (40). Colwell s correlation is... 

The head of liquid over the weir, based on a straight segmental downcomer, can be estimated by the following modification of the Francis weir formula ... 

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 weir crest is obtained from the Francis weir formula as /low = 0.4(gpm/Lwi), in which is the effective weir length in inches. 

Where Hq is in inches, L is in cubic feet per second, and W is in feet, then Kis = 4.47. Where He is in millimeters, L is in cubic meters per second, and Wis in meters, then Kis = 554. Where He is in inches, L is in gallons per minute, and W is in inches then Kis = 0-4-This is a version of the Francis weir formula without modification for weir height. 

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... 

Neglect the momentum balance for each tray and assume that the molar flow rate of the liquid leaving each tray is related to the liquid holdup of the tray through the Francis weir formula ... 

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. 

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