Reynolds number for

The Reynolds number for flow in a tube is defined by dvpirj, where d is the diameter of the tube, V is the average velocity of the fluid along the tube, p is the density of the fluid, and rj is its dynamic viscosity. At flow velocities corresponding with values of the Reynolds number of greater than 2000, turbulence is encountered. 

The dimensionless quantities in brackets are, respectively, the reciprocal of the Froude number, the Euler number, and the reciprocal of the Reynolds number for the system. 

Fig. 4. Mathcad simulations (Cp = 5000 mg/L) as a function of Reynolds number for a NaCl solution (a) concentration polarization (CP), and (b) (-...

Fig. 1. Diag coefficient vs particle Reynolds number for spherical particles where (-) corresponds to the theoretical value of = 24/Re (eq. 4).

Rothfus, Monrad, Sikchi, and Heideger [Ind. Eng. Chem., 47, 913 (1955)] report that the friction factor/g for the outer wall bears the same relation to the Reynolds number for the outer portion of the anniilar stream 2(r9 — A, )Vp/r9 l as the fricBon factor for circular tubes does to the Reynolds number for circular tubes, where / is the radius of the outer tube and is the position of maximum velocity in... 

Friction Factor and Reynolds Number For a Newtonian fluid in a smooth pipe, dimensional analysis relates the frictional pressure drop per unit length AP/L to the pipe diameter D, density p, and average velocity V through two dimensionless groups, the Fanning friction factor/and the Reynolds number Re. 

The critical Reynolds number for transition from laminar to turbulent flow in noncirciilar channels varies with channel shape. In rectangular ducts, 1,900 < Re < 2,800 (Hanks and Ruo, Ind. Eng. Chem. Fundam., 5, 558-561 [1966]). In triangular ducts, 1,600 < Re < 1,800 (Cope and Hanks, Ind. Eng. Chem. Fundam., II, 106-117 [1972] Bandopadhayay and Hinwood, j. Fluid Mech., 59, 775-783 [1973]). 

For condensing vapor in vertical downflow, in which the hquid flows as a thin annular film, the frictional contribution to the pressure drop may be estimated based on the gas flow alone, using the friction factor plotted in Fig. 6-31, where Re is the Reynolds number for the gas flowing alone (Bergelin, et al., Proc. Heat Transfer Fluid Mech. Inst., ASME, June 22-24, 1949, pp. 19-28). 

Figure 6-40 shows power number vs. impeller Reynolds number for a typical configuration. The similarity to the friction factor vs. Reynolds number behavior for pipe flow is significant. In laminar flow, the power number is inversely proportional to Reynolds number, reflecting the dominance of viscous forces over inertial forces. In turbulent flow, where inertial forces dominate, the power number is nearly constant. 

Continuous Flat Surface Boundaiy layers on continuous surfaces drawn through a stagnant fluid are shown in Fig. 6-48. Figure 6-48 7 shows the continuous flat surface (Saldadis, AIChE J., 7, 26—28, 221-225, 467-472 [1961]). The critical Reynolds number for transition to turbulent flow may be greater than the 500,000 value for the finite flat-plate case discussed previously (Tsou, Sparrow, and Kurtz, J. FluidMech., 26,145—161 [1966]). For a laminar boundary layer, the thickness is given by... 

Continuous Cylindrical Surface The continuous surface shown in Fig. 6-48b is apphcable, for example, for a wire drawn through a stagnant fluid (Sakiadis, AIChE ]., 7, 26-28, 221-225, 467-472 [1961]). The critical-length Reynolds number for transition is Re = 200,000. The laminar boundary laver thickness, total drag, and entrainment flow rate may be obtained from Fig. 6-49 the drag and entrainment rate are obtained from the momentum area 0 and displacement area A evaluated at x = L. 

The film coefficient h is for the inner wall Dj is the inside diameter of the mixing vessel. The term L N p/ is the Reynolds number for mixing in which L is the diameter and Nr the speed of the agitator. Recommended values of the constants a, b, andm are given in Table 18-2. 

FIG. 20-38 Newton number as a Function of Reynolds number for a horizontal stirred bead mill, with fluid alone and with various filling fractious of 1-mm glass beads [Weit and Schwedes, Chemical Engineering and Technology, 10(6), 398 04 (1987)]. (N = power input, W d = stirrer disk diameter, m n = stirring speed, 1/s i = liquid viscosity, Pa-s Qj = feed rate, mVs.)... 

Hicks et al. [8] developed a correlation involving the Pumping number and impeller Reynolds number for several ratios of impeller diameter to tank diameter (D /D ) for pitched-blade turbines. From this coiTclation, Qp can be determined, and thus the bulk fluid velocity from the cross-sectional area of the tank. The procedure for determining the parameters is iterative because the impeller diameter and rotational speed N appear in both dimensionless parameters (i.e., Npe and Nq). 

Figure 7-15. Power number and Pumping number as functions of Reynolds number for a pitched-blade turbine and high-efficiency impeller. (Source Bakker, A., and Gates L. , Properly Choose Mechanical Agitators for Viscous Liquids," Chem. Eng. Prog., pp. 25-34, 1995.)...

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

Reynolds number for the fluid being released. For sharp edged orifices with Reynolds numbers approaching 30,000, it approaches 0.61. For these conditions, the exit velocity of the fluid is independent of the size of the hole. For a rounded opening, Cj approaches 1. For a short section if pipe (length/diameter > 3), Cj = 0.81. For cases where is unknown or uncertain use C. = I i[Pg.338]

The similarity of velocity and of turbulence intensity is documented in Fig. 12.29. The figure shows a vertical dimensionless velocity profile and a turbulence intensity profile measured by isothermal model experiments at two different Reynolds numbers. It is obvious that the shown dimensionless profiles of both the velocity distribution and the turbulence intensity distribution are similar, which implies that the Reynolds number of 4700 is above the threshold Reynolds number for those two parameters at the given location. 

FIGURE 12.40 Normalized velocity versus Reynolds number for a vortex exhaust. The location of the measuring point is indicated in the figure. 

This also applies to circular pipes or ducts and oval and rectangular ducts not flowing full. The equivalent diameter is used in determining the Reynolds number for these cases, but does not apply to very narrow or slotted or annular flow cross-sections. 

Figure 2-33. Reynolds number for compressible flow, steel pipe. By permission, Crane Co., Technical Paper 410, Engineering Div., 1957. Also see 1976 edition.

Figure 5-11 [28] presents an analysis of pumping number versus Reynolds Number for various vessel dimensional relationships, for turbine mixers. 

Viscosity, centipoise = Distance baffles off wall. Figure, 5-34 = Correction factor for Reynolds number for riscosity effects... 

Reynolds number for gas S = length of corrugation side Uge = effective velocity of gas Ug = superficial velocity of gas Ui = superficial velocity of liquid Ap = pressure drop per unit packed height e = packing void fraction 0 = angle of flow channel (from horizontal) fi = viscosity p = density... 

Pierce proposes and illustrates good agreement between the test data and the correlation for a smooth continuous curve for the Colburn factor over the entire range of Reynolds numbers for the laminar, transition, and turbulent flow regimes inside smooth tubes ... 

The Reynolds number for gases can be calculated directly in terms of flowrate and gas gravity as, , ... 

Calculate Reynolds number for the fluid (1) inside drill pipe, (2) inside drill collars, (3) in drill collar annulus, and (4) in drill pipe annulus. 

Fig. 6.6. Power number versus Reynolds number for various impellers (flat blades, turbine, vaned disk and marine propeller).

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