Reynolds number worked example

Data reported in the literature are often obtained from tubes with similar diameters operated at different velocities, i.e. the Reynolds numbers (and hence the turbulence level) were different for each tube. Work by Pujo and Bott [1991] sought to examine the effect of velocity at fixed Reynolds number. An example of their work is shown on Fig. 12.11. For a given Reynolds number of 12,200 it may be seen that velocity does still affect the extent of the biofilm. Biofilm thickness passes through a peak value with increasing velocity till at a velocity of 2 m/s the biofilm thickness is severely limited and may be attributed to the shear effects. 

If we accept this as the definition of the laminar-flow Reynolds number, then for any constitutive equation which can be integrated twice to give the nonnewtonian equiyalent of the Poiseuille equation, Eq. 15.9 cian be used to define a working Reynolds number. For example, for power-law fluids (Eq. 15.7) this leads (Prob. 15.7) to... 

Example 5.10 A liquid-phase, pilot-plant reactor uses a 12-ft tube with a 1.049-in i.d. The working fluid has a density of 860 kg/m, the residence time in the reactor is 10.2 s, and the Reynolds number is 8500. The pressure drop in the pilot plant has not been accurately measured, but is known to be less than 1 psi. The entering feed is preheated and premixed. The inlet temperature is 60°C and the outlet temperature is 64°C. Tempered water at 55°C is used for cooling. Management loves the product and wants you to design a plant that is a factor of 128 scaleup over the pilot plant. Propose scaleup alternatives and explore their thermal consequences. 

The second approach assigns thermal resistance to a gaseous boundary layer at the heat transfer surface. The enhancement of heat transfer found in fluidized beds is then attributed to the scouring action of solid particles on the gas film, decreasing the effective film thickness. The early works of Leva et al. (1949), Dow and Jacob (1951), and Levenspiel and Walton (1954) utilized this approach. Models following this approach generally attempt to correlate a heat transfer Nusselt number in terms of the fluid Prandtl number and a modified Reynolds number with either the particle diameter or the tube diameter as the characteristic length scale. Examples are ... 

This second method does not lend itself to the development of quantitative correlations which are based solely on true physical properties of the fluids and which, therefore, can be measured in the laboratory. The prediction of heat transfer coefficients for a new suspension, for example, might require pilot-plant-scale turbulent-flow viscosity measurements, which could just as easily be extended to include experimental measurement of the desired heat transfer coefficient directly. These remarks may best be summarized by saying that both types of measurements would have been desirable in some of the research work, in order to compare the results. For a significant number of suspensions (four) this has been done by Miller (M13), who found no difference between laboratory viscosities measured with a rotational viscometer and those obtained from turbulent-flow pressure-drop measurements, assuming, for suspensions, the validity of the conventional friction-factor—Reynolds-number plot.11 It is accordingly concluded here that use of either type of measurement is satisfactory use of a viscometer such as that described by Orr (05) is recommended on the basis that fundamental fluid properties are more readily determined under laminar-flow conditions, and a means is provided whereby heat transfer characteristics of a new suspension may be predicted without pilot-plant-scale studies. 

The last of these methods has been applied particularly to chemical reaction vessels. It is covered in detail in Chapter 17. In most cases, however, the RTDs have not been correlated with impeller characteristics or other mixing parameters. Largely this also is true of most mixing investigations, but Figure 10.3 is an uncommon example of correlation of blend time in terms of Reynolds number for the popular pitched blade turbine impeller. As expected, the blend time levels off beyond a certain mixing intensity, in this case beyond Reynolds numbers of 30,000 or so. The acid-base indicator technique was used. Other details of the test work and the scatter of the data are not revealed in the published information. Another practical solution of the problem is typified by Table 10.1 which relates blend time to power input to... 

The Reynolds number is useful for characterizing flow of a Newtonian fluid through a tube. The variables in dimensional analysis can be arranged to suggest a valid ratio when none exists. Therefore, established dimensionless variables should be used where applicable. A number of these dimensionless variables have been proven to work in scaleup applications. Examples include the Reynolds, Nusselt, Grashof, and Sherwood numbers, all of which are completely described in Perry s Chemical Engineers Handbook. 

However, the available flux densities often result from several contributions as for example the sum of radiation from a hot wall and exchange with a hot gas. Having in mind that the equation (5) related to this last process represents a minimum (qco can be much higher in the case of high particle Reynolds numbers), the values of q, + qco can approach the limit flux density deflned in this work. In these conditions, we can expect that low char fractions will be formed. 

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