Length-to-diameter ratio increase

Applying these factors to the 5= 128 scaleup in Example 5.10 gives a tube that is nominally 125 = 101 ft long and 1.0495 = 4.1 inches in diameter. The length-to-diameter ratio increases to 298. The Reynolds number increases to 85005 = 278,000. The pressure drop would increase by a factor of 0.86 j jjg temperature driving force would remain constant at 7°C so that the jacket temperature would remain 55°C. 

A combination of tapered shaft diameter and increasing pitch is shown in Figure 10a. This allows a length-to-diameter ratio of about 6 1 instead of 3 1. A half pitch screw is used over the tapered diameter. This approach results in an exceUent mass flow pattern provided that the hopper to which it attaches is also designed for mass flow. 

The ratio between length and diameter of the PB cells was about 1 1. For application in cars, more powerful cells have been requested. Recently it was reported [15] that the ratio of length to diameter was increased to 2 1 without changing the mass of sodium or sulfur, i.e., the surface area of the / " —alumina was increased but the capacity of the cells remained unchanged. This results in higher power and energy densities (Table 4). 

Experiments in annular and slug flow were carried out also by Ghajar et al. (2004). The test section was a 25.4 mm stainless steel pipe with a length-to-diameter ratio of 100. The authors showed that heat transfer coefficient increases with increase in liquid superficial velocity not only in annular, but also in slug flow regimes. 

Increase the tube diameter, either to maintain a constant pressure drop or to scale with geometric similarity. Geometric similarity for a tube means keeping the same length-to-diameter ratio L/dt upon scaleup. Scaling with a constant pressure drop will lower the length-to-diameter ratio if the flow is turbulent. 

This section has based scaleups on pressure drops and temperature driving forces. Any consideration of mixing, and particularly the closeness of approach to piston flow, has been ignored. Scaleup factors for the extent of mixing in a tubular reactor are discussed in Chapters 8 and 9. If the flow is turbulent and if the Reynolds number increases upon scaleup (as is normal), and if the length-to-diameter ratio does not decrease upon scaleup, then the reactor will approach piston flow more closely upon scaleup. Substantiation for this statement can be found by applying the axial dispersion model discussed in Section 9.3. All the scaleups discussed in Examples 5.10-5.13 should be reasonable from a mixing viewpoint since the scaled-up reactors will approach piston flow more closely. 

Experimental studies have proved that the influence of vent duct with longitudinal arrangement—located on the roof—decreases markedly with increased vessel length-to-diameter ratio. The increase of the maximum explosion overpressure is at its maximum if vessel ratio UD = 1. 

It has been found that the attachment of a discharge pipe of the same diameter as the orifice immediately beneath it increases the flowrate, particularly of fine solids. Thus, in one case, with a pipe with a length to diameter ratio of 50, the discharge rate of a fine sand could be increased by 50 per cent and that of a coarse sand by 15 per cent. Another method of increasing the discharge rate of fine particles is to fluidise the particles in the neighbourhood of the orifice by the injection of air. Fluidisation is discussed in Chapter 6. 

Experimentally, as indicated in Fig. 12.13, we find that D/Dq depends on the shear stress at the wall xw (a flow variable) and the molecular weight distribution (MWD) (a structural variable) (22). The length-to-diameter ratio of the capillary (a geometric variable) also influences D/Dq. The swelling ratio at constant xw decreases exponentially with increasing L/Dq and becomes constant for L/Dq > 30. The reason for this decrease can be explained qualitatively as follows. Extrudate swelling is related to the ability of polymer melts and solutions to undergo delayed elastic strain recovery, as discussed in... 

Constant pressure—build a reactor that is nominally 12A5/27 = 29 ft long and 1.049A11/27 = 7.6 in in diameter. The length-to-diameter ratio decreases by a factor of S 2l9 to 47. The Reynolds number increases to 8500A16/27 = 151,000. The temperature driving force must increase by a factor of A0,34 = 5.2 to about 36°C so that the jacket temperature would be about 26°C. This design is also... 

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