Reynolds number friction factor

The results also show that the normalized slip length and the average friction factor-Reynolds number product exhibit Reynolds dependence. Furthermore, the predictions reveal that the impact of the vapor cavity depth on the overall frictional resistance is minimal provided the depth of the vapor cavity is greater than 25% of its width. 

Figure 3.10 shows a friction factor - Reynolds number chart for Bingham plastics at various values of the Hedstrom number. The turbulent flow line is that for Newtonian behaviour and is followed by some Bingham plastics with low values of the yield stress [Thomas (1962)]. 

Wheeler, J. A. and Whissler, E.H., The friction factor-Reynolds Number Relation for the Steady Flow of Pseudoplastic Fluids through Rectangular Ducts. Part 1. Theory, Am. Inst. Chem. Eng. J., 11, 207 (1965)... 

Fio. 4. Friction factor-Reynolds number diagram for Bingham plastics. 

Weltmann (W4) presented this relationship on a friction factor-Reynolds number diagram similar to Fig. 4 for Bingham-plastic fluids. Excellent agreement between predicted and measured results was found by Salt for two carboxymethylcellulose solutions Weltmann shows no data to support her somewhat more useful rearrangement but cites three literature references for this purpose. Review of these shows that none dealt explicitly with this method of approach, as claimed. 

Fig. 5. Friction factor-Reynolds number diagram for non-Newtonians-low range. Taken from reference (Mil) with permission.

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. 

FIG. 6-9 Fanning Friction Factors. Reynolds number Re = I) pyu where D = pipe diameter, V = velocity, p = fluid density, and p = fluid viscosity. (Based on Moody, Trans. ASME, 66, 671 [1944].)... 

TABLE 6.6 Laminar Flow Volumetric Flow Rate, Friction Factor, Reynolds Number, and Hedstrom Number... 

Internally finned tubes are ducts with internal longitudinal fins. These tubes are widely used in compact heat exchangers. The friction factor-Reynolds number product and the Nusselt number for such internally finned tubes, designated as (/ Re), and Nu/,c> respectively, are computed from the following definitions ... 

G. F. Round, An Explicit Approximation for the Friction Factor-Reynolds Number Relation for Rough and Smooth Pipes, Can. J. Chem. Eng., (58) 122-123,1980. 

In the latter case the experimental data can often be correlated and simplified by the use of dimensionless ratios (e.g., the friction factor, Reynolds number, relative roughness plot). 

For turbulent flow of newtonian fluids in pipes, the experimental pressure-gradient data are represented by a friction factor-Reynolds number plot (Fig. 6.10). It seems logical to do the same for nonnewtonian fluids, but in so doing we must redefine the Reynolds number. 

Friction Factor/Reynolds Number Correlation for Flow Around Spheres. The magnitude of the dynamic force exerted across the tlnid-solid interface provides the basis for macroscopic momentum transfer correlations. The component of this dynamic force in the primary flow direction. 

The main value of data describing turbulent energy requirements is in the computation of pressure drop-flow rate characteristics for installed plant but there are also examples of performance evaluation using energy data -. As with laminar flow characteristics, although different, those for turbulent flow are relatively simple and easily described in terms of the friction factor-Reynolds number relationship used to describe empty tube. 

Figure 3.6 Friction factor - Reynolds number behaviour for...

Edwards and Smith [10] suggested that the well-established Newtonian friction factor-Reynolds number relation can be used for non-Newtonian flow as... 

Drag coefficient. From the previous discussions it is evident that the geometry of the immersed solid is a main factor in determining the amount of total drag force exerted on the body. Correlations of the geometry and flow characteristics for solid objects suspended or held in a free stream (immersed objects) are similar in concept and form to the friction factor-Reynolds number correlation given for flow inside conduits. In flow... 

The friction-factor-Reynolds-number correlation can be expressed for smooth pipe as (Bird et al., 1960, p. 186)... 

As with Newtonian fluids, it is a pretty safe bet that flow is laminar for Re <2100, but drag-reducing additives often seem to delay the laminar-turbulent transition to higher Re s. The friction factor-Reynolds number relation remains a function of pipe roughness. 

One of the objectives of this program was to prove or modify the basic equation of single-phase flow. A brief analysis of the theoretical friction factors, Reynolds number, pressure drop, and insulation may help in understanding the test data. Formulas and their derivation will not be included in this report but will be found in the final program report. 

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