Height over the weir

The Smith et al. correlation (20, Fig. 6.11). This is another early entrainment flooding prediction method that has sometimes been recommended (11). Compared to Fair s correlation, the Smith et al. correlation is claimed (20) to be less conservative. It was derived from a small base of field data for sieve, valve, and bubble-cap trays. Similar to Fair s correlation, Smith s correlation uses CSB versus a flow parameter plot, but here the dependence of CSB on the flow parameter is weaker, and there is no surface tension correction factor. CSB and flood 316 both based on the net area AN, and are evaluated from Fig. 6.11 and Eq. (6,9), respectively. The height over the weir, how, is obtained from Eq, (6.49). 

The clear liquid height is equal to the sum of the weir height, the height over the weir, and hah1 the hydraulic gradient, giving... 

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

Multichordal downcomers can increase weir length (Fig. 6). Fig. 6 shows a combined multichordal and stepped downcomer. The increased weir length decreases the liquid crest height over the weir. This decreases total tray pressure drop. The stepping is a variation of a sloped downcomer. The step increases the downcomer inlet area with a minimum decrease in tray active area. 

Picket fence weirs are used in low-liquid-rate applications (Fig. 8). Picket fence weirs can serve two purposes at low liquid rates. First, they reduce the effective length of the weir for liquid flow increases the liquid height over the weir. This makes tray operation less sensitive to out-of-level installation. Second, pickets can prevent liquid loss (blowing) into the downcomer by spraying. This occurs at low liquid rates when the vapor is the continuous phase on the tray deck. Picket fence weirs should be considered if the liquid load is less than 1 gpm per inch of weir (0.0267 ft /sec/ft, 0.00248 m /sec/m). At liquid rates lower than 0.25 gpm per inch of weir (0.00668 ft / sec/ft, 0.000620 m /sec/m) even picket fence weirs and splash baffles have a mixed record in improving tray efficiency. Operation at liquid rates this low strongly favors the selection of structured packing. 

Calculation of the Height Over the Weir how at the Maximum Liquid Rate... 

The height over the weir is calculated from a form of the Francis equation, which for a straight segmental weir is... 

Minimum Weir Loading A very low weir loading is manifested when the liquid height over outlet weir, is less than the limit of 0.25-0.5 in. (Chase, 1967 Davis and Gordon, 1961 Kister, 1992). A sufficient liquid height over the weir above the limit provides a stable liquid distribution. We can apply the Francis correlation in equation (12.27) to determine the minimum weir loading ... 

The notch or weir, in which the fluid flows over the weir so that its kinetic energy is measured by determining the head of the fluid flowing above the weir. This instrument is used in open-channel flow and extensively in tray towers 3 where the height of the weir is adjusted to provide the necessary liquid depth for a given flow. 

Water flows in an open channel across a weir which occupies the full width of the channel. The length of the weir is 0.5 m and the height of water over the weir is 100 mm. What is the volumetric flowrate of water ... 

An organic liquid flows across a distillation tray and over a weir at the rate of 15 kg/s. The weir is 2 m long tmcl the liquid density is 650 kg/m3. What is the height of liquid flowing over the weir ... 

Use is made of the Francis formula (equation 6.43). where, as in the previous example, n — 0. In the context of this example the height of liquid flowing over the weir is usually designated hmv and the volumetric liquid flow by Q. Rearrangement of equation 6.43 gives ... 

The clear liquid depth is equal to the height of the weir hw plus the depth of the crest of liquid over the weir how this is discussed in the next section. 

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 ... 

M perfectly mixed, isothermal CSTR has an outlet weir. The flow rate over the weir proportional to the height of hquid over the weir, h, to the 1.5 power. The weir height is. The cross-sectional area of the tank is A. Assume constant density. 

Finally we can now calculate the vapor flow rate through the tray from the pressure drop through the tray (P i - P ) and the liquid height on the tray, which we can get from the weir height fi and the height of liquid over the weir... 

As illustrated, liquid accumulates on the low side of this tray. Vapor, taking the path of least resistance, preferentially bubbles up through the high side of the tray deck. To prevent liquid from leaking through the low side of the tray, the dry tray pressure drop must equal or exceed the sum of the weight of the aerated liquid retained on the tray by the weir plus the crest height of liquid over the weir plus the 2-in out-of-levelness of the tray deck. 

To derive a flow equation for the weir, consider an elementary area dA = B dh in the plane of the crest, and assume the velocity through this area to be equal to (2gh)V2. B is the width of the crest, and H is the height of liquid flowing over the crest or height of the weir. The apparent flow through this area is... 

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... 

A sieve-tray tower has an ID of 5 ft, and the combined cross-sectional area of the holes on one tray is 10 percent of the total cross-sectional area of the tower. The height of the weir is 1.5 in. The head of liquid over the top of the weir is 1 in. Liquid gradient is negligible. The diameter of the perforations is in., and the superficial vapor velocity (based on the cross-sectional area of the empty tower) is 3.4 ft/s. The pressure drop due to passage of gas through the holes may be assumed to be equivalent to 1.4 kinetic heads (based on gas velocity through holes). (Tray thickness = hole diameter and active area = 90 percent of total area-see Fig. 16-12). If the liquid density is 50 lb/ft3 and the gas density is 0.10 lb/ft3, estimate the pressure drop per tray as pounds force per square inch. 

To derive the equation that is used to calculate the flow in rectangular weirs, refer to Figure 3.2. As shown, the weir height is P. The vertical distance from the tip of the crest to the surface well upstream of the weir at point 1 is designated as H. H is called the head over the weir. 

A suppressed weir measures a flow in an open channel at a rate of 0.3 m /s. The length and head over the weir are 0.2 m and 2.0 m, respectively. Calculate the height of the weir. 

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