Pressure friction-factor methods

The friction factor method can also be used to determine the pressure drop for homogeneous slurries. It is applied in the same way as for Newtonian fluids but the friction factor depends on a new definition for the Reynolds number. 

The hydrauhc diameter method does not work well for laminar flow because the shape affects the flow resistance in a way that cannot be expressed as a function only of the ratio of cross-sectional area to wetted perimeter. For some shapes, the Navier-Stokes equations have been integrated to yield relations between flow rate and pressure drop. These relations may be expressed in terms of equivalent diameters Dg defined to make the relations reduce to the second form of the Hagen-Poiseulle equation, Eq. (6-36) that is, Dg (l2SQ[LL/ KAPy. Equivalent diameters are not the same as hydraulie diameters. Equivalent diameters yield the correct relation between flow rate and pressure drop when substituted into Eq. (6-36), but not Eq. (6-35) because V Q/(tiDe/4). Equivalent diameter Dg is not to be used in the friction factor and Reynolds number ... 

As an example of method 3, in bubbly flow with a low quality it would be appropriate to calculate the friction factor based on the properties of the liquid. The frictional component of the pressure gradient for the actual two-phase flow is given by... 

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. 

For orientation purposes, the pressure drop in steel pipes may be found by the rapid method of Table 6.3, which is applicable to highly turbulent flow for which the friction factor is given by von... 

A simpler method due to Kem (1950, pp. 147-152) nominally considers only the drop across the tube banks, but actually takes account of the added pressure drop through baffle windows by employing a higher than normal friction factor to evaluate pressure drop across the tube banks. Example 8.8 employs this procedure. According to Taborek (HEDH, 1983, 3.3.2), the Kern predictions usually are high, and therefore considered safe, by a factor as high as 2, except in laminar flow where the results are uncertain. In the case worked out by Ganapathy (1982, pp. 292-302), however, the Bell and Kem results are essentially the same. 

Fluid properties are evaluated at the average bulk temperature. Heat transfer and fluid friction inside the tubes are evaluated with the hydraulic diameter method discussed in Chap. 6. Pressure drop is calculated with the chart friction factor / and the following relation ... 

Most manufacturers of static mixers have published (either in sales literature or in the technical literature) design methods for pressure drop. The pressure drop design methods, from Myers et al. (1997) for the Kenics HEM and Kenics HEV mixers are presented. The Darcy friction factor for the standard HEV mixer, Ntr = 2, L/D = 1, (with X/D = 3 downstream pipe) is presented in Figure 10.31. The friction factor is not given below Nrc = 1,000 because the HEV mixer should not be used for Nrc < 3,000. 

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