Reynolds number friction factor correlation

It was shown that a normalized version of the two-phase friction factor, CfTpl CfQ, is uniquely related to X. The normalizing friction factor, CfQ, is calculated from single-phase friction factor correlations using a Reynolds number calculated as if both phases flow as liquid,... 

The wall friction zw may be evaluated in terms of a friction-factor correlation based on a local Reynolds number. 

Their mass-transfer and friction factor correlations were derived for a range of Reynolds numbers between 20 and 60. 

Several friction factor correlations for fully developed turbulent flow in smooth, circular ducts are listed in Table 5.8. According to Bhatti and Shah [45], these formulas were derived from highly accurate experimental data for a certain Reynolds number range. 

The pressure drop is calculated from the normal friction factor correlation which is a function of Reynold s number. The viscosity value for the Reynold s number is based on the API Technical Data Book.( ) Specific heat for temperature calculations... 

Pressure Drop. The prediction of pressure drop in fixed beds of adsorbent particles is important. When the pressure loss is too high, cosdy compression may be increased, adsorbent may be fluidized and subject to attrition, or the excessive force may cmsh the particles. As discussed previously, RPSA rehes on pressure drop for separation. Because of the cychc nature of adsorption processes, pressure drop must be calculated for each of the steps of the cycle. The most commonly used pressure drop equations for fixed beds of adsorbent are those of Ergun (143), Leva (144), and Brownell and co-workers (145). Each of these correlations uses a particle Reynolds number (Re = G///) and friction factor (f) to calculate the pressure drop (AP) per... 

The dimensionless relations are usually indicated in either of two forms, each yielding identical resiilts. The preferred form is that suggested by Colburn ran.s. Am. In.st. Chem. Eng., 29, 174—210 (1933)]. It relates, primarily, three dimensionless groups the Stanton number h/cQ, the Prandtl number c Jk, and the Reynolds number DG/[L. For more accurate correlation of data (at Reynolds number <10,000), two additional dimensionless groups are used ratio of length to diameter L/D and ratio of viscosity at wall (or surface) temperature to viscosity at bulk temperature. Colburn showed that the product of the Stanton number and the two-thirds power of the Prandtl number (and, in addition, power functions of L/D and for Reynolds number <10,000) is approximately equal to half of the Fanning friction fac tor//2. This produc t is called the Colburn j factor. Since the Colburn type of equation relates heat transfer and fluid friction, it has greater utility than other expressions for the heat-transfer coefficient. 

The correlation studies of heat and mass transfer in pellet beds have been investigated by many, usually in terms of the. /-factors (113-115). According to Chilton and Colburn the two. /-factors are equal in value to one half of the Fannings friction factor / used in the calculation of pressure drop. The. /-factors depend on the Reynolds number raised to a factor varying from —0.36 to —0.68, so that the Nusselt number depends on the Reynolds number raised to a factor varying from 0.64 to 0.32. In the range of the Reynolds number from 10 to 170 in the pellet bed, jd should vary from 0.5 to 0.1, which yields a Nusselt number from 4.4 to 16.1. The heat and mass transfer to wire meshes has received much less attention (110,116). The correlation available shows that the /-factor varies as (Re)-0-41, so that the Nusselt number varies as (Re)0-69. In the range of the Reynolds number from 20 to 420, the j-factor varies from 0.2 to 0.05, so that the Nusselt number varies from 3.6 to 18.6. The Sherwood number for CO is equal to 1.05 Nu, but the Sherwood number for benzene is 1.31 Nu. 

Figure 3.40. Metzner and Reed correlation of friction factor and Reynolds number...

Fig. 2.20 (a) Dependence of the friction factor on Reynolds number for tube of diameter 705 pm. Reprinted from Maynes and Webb (2002) with permission, (b) Turbulent flow friction correlations. Reprinted from Sobhan and Garimella (2001) with permission... 

Several correlating equations for the friction factor have been proposed for both the laminar and turbulent flow regimes, and plots of fM (or functions thereof) versus Reynolds number are frequently presented in standard fluid flow or chemical engineering handbooks (e.g., 96, 97). Perhaps the most useful of the correlations is that represented by the Ergun equation (98)... 

All models for turbulent flows are semiempirical in nature, so it is necessary to rely upon empirical observations (e.g., data) for a quantitative description of friction loss in such flows. For Newtonian fluids in long tubes, we have shown from dimensional analysis that the friction factor should be a unique function of the Reynolds number and the relative roughness of the tube wall. This result has been used to correlate a wide range of measurements for a range of tube sizes, with a variety of fluids, and for a wide range of flow rates in terms of a generalized plot of/ versus /VRe- with e/D as a parameter. This correlation, shown in Fig. 6-4, is called a Moody diagram. 

The Fanning friction factor may be determined either from a chart for both rough and smooth tubes or from a variety of correlations (Knudsen and Katz, 1958, pp. 173,176). The following correlation applies for turbulent flow in smooth tubes and for Reynolds numbers between 3,000 and 3,000,000 ... 

A correlation relating the friction factor with the Reynolds number (Re). 

Equation (e) is merely a definition of the mass flow rate. Equation (/) is a standard correlation for the friction factor for turbulent flow. (Note that the correlation between /and the Reynold s number (Re) is also available as a graph, but use of data from a graph requires trial-and-error calculations and rules out an analytical solution.)... 

Turbulent flow of Newtonian fluids is described in terms of the Fanning friction factor, which is correlated against the Reynolds number with the relative roughness of the pipe wall as a parameter. The same approach is adopted for non-Newtonian flow but the generalized Reynolds number is used. 

Obviously, correlations of one of these friction factors with an analogous Reynolds number, or with two-phase pressure-drop, throws little light on the other variables concerned, and these quantities will appear as parameters in any proposed relationship. However, Govier and Omer point out that plots of such a form do give a systematic spread of data above the single phase lines and allow easy comparison of trends. 

The utility of this generalized Reynolds number has been shown (Mil) by the correlation of all available literature data on flow of non-Newtonian fluids on the conventional friction factor-Reynolds number diagram which is reproduced in Figs. 5, 6, and 7. The curves shown are not drawn through the data points but rather represent the conventional... 

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. 

These dimensionless groups also appear in empirical correlations of the turbulent flow region. Although even in the approximate Eq. (9) of Table 6.7, group He appears to affect the friction factor, empirical correlations such as Figure 6.5(b) and the data analysis of Example 6.10 indicate that the friction factor is determined by the Reynolds number alone, in every case by an equation of the form, / = 16/Rc, but with Re defined differently for each model. Table 6.7 collects several relations for laminar flows of fluids. 

Laminar and Turbulent Flow Below a critical Reynolds number of about 2,100, the flow is laminar over the range 2,100 < Re < 5,000 there is a transition to turbulent flow. Reliable correlations for the friction factor in transitional flow are not available. For laminar flow, the Hagen-Poiseuille equation... 

Li et al. [36] performed an extensive study on AP in a Sulzer SMX static mixer with both Newtonian and non-Newtonian fluids. They showed that AP increased by a factor of 23 in a SMX static mixer in the laminar flow regime. Figure 7-24 shows their correlation between the Fanning friction factor and the Reynolds number for experimental points under various operating conditions. 

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