Reynolds number ranges

The most comprehensive correlation for heat transfer to vertical baffle-type coils is for a disk flat-blade turbine over the Reynolds number range lO to (2)(10 ) ... 

This relationship holds for a Reynolds number range of 2,100 to 10 . For smooth tubes (assumed for heat exchanger tubeside pressure drop calculations), a constant of 23,000 should be used instead of 20,000. 

This correlation is good for a Reynolds number range of between 2,100 and 10 . The Fanning equation for pressure drop is ... 

Those particles with sizes d > d" at a given set of conditions (v, p, Pp, and a ) will settle only in the turbulent flow regime. For particles with sizes d < d, d" will settle only when the flow around the object is in the transitional regime. Recall that the transitional zone occurs in the Reynolds number range of 0.2 to 500. The sedimentation numbers corresponding to this zone are 3.6 < S, < 82,500 and 0.0022 < S2 < 1,515. 

The Peclet numbers decrease when the dispersion coefficients increase. In the Reynolds number range of 10-200, in a packed bed of pellets, Peii = 2 and PeH = 0.5 (119, 120). The dispersions in the transverse... 

An attempt has been made by Johnson and co-workers to relate such theoretical results with experimental data for the absorption of a single carbon dioxide bubble into aqueous solutions of monoethanolamine, determined under forced convection conditions over a Reynolds number range from 30 to 220. The numerical results were found to be much higher than the measured values for noncirculating bubbles. The numerical solutions indicate that the mass-transfer rate should be independent of Peclet number, whereas the experimentally measured rates increase gradually with increasing Peclet number. The discrepancy is attributed to the experimental technique, where-... 

Xu et al. (2000) investigated de-ionized water flow in micro-channels with hy-draulie diameter ranging from 30 to 344 pm at Reynolds numbers ranging from 20 to 4,000. Two test modules were used. The first test module consisted of a cover and an aluminum plate, into which a micro-channel, inlet and outlet sumps were machined. A Plexiglas plate was used to cover the channel. The second module was fabricated from a silicon wafer, and a 5 mm thick Pyrex glass was utilized to... 

Hao et al. (2007) investigated the water flow in a glass tube with diameter of 230 Lim using micro particle velocimetry. The streamwise and mean velocity profile and turbulence intensities were measured at Reynolds number ranging from 1,540 to 2,960. Experimental results indicate that the transition from laminar to turbulent flow occurs at Re = 1,700—1,900 and the turbulence becomes fully developed at Re > 2,500. 

A number of equations have been proposed for use in the calculation of pressure drop in coils of constant curvature [Srinivasan et al (1968)]. The latter are known as helices. For laminar flow, Kubair and Kuloor (1965) gave an equation for the Reynolds number range 170 to the critical value. In terms of the Fanning friction factor, their equation can be written as... 

For turbulent flow, White (1932) gave an equation for the Reynolds number range 15000 to 100000. In terms of the Fanning friction factor, White s equation can be written as... 

For the Reynolds number range 0.2 < Rep< 500, it has been shown that... 

Richardson and Zaki (1954) showed that in the Reynolds number range Rep<0.2, the velocity uc of a suspension of coarse spherical particles in water relative to a fixed horizontal plane is given by the equation... 

Consider two spherical particles 1 and 2 of the same diameter but of different densities settling freely in a fluid of density p in the streamline Reynolds number range Rep< 0.2. The ratio of the terminal settling velocities un/ut2 is given by equation 9.8 rewritten in the form... 

In the paddle method, bulk Reynolds numbers range from Re = 2292 (25 rpm, 900 mL) up to Re = 31025 (200 rpm, 500 mL). In contrast, Reynolds numbers employing the basket apparatus range from Re = 231 to Re = 4541. These Reynolds numbers are derived from dissolution experiments in which oxygen was the solute [(10), Chapter 13.4.8] and illustrate that turbulent flow patterns may occur within the bulk medium, namely for flow close to the liquid surface of the dissolution medium. The numbers are valid provided that the whole liquid surface rotates. According to Levich (9), the onset of turbulent bulk flow under these conditions can then be assumed at Re 1500. 

There were many early experimental investigations of bluff-body stabilization. Most of this work [69] used premixed gaseous fuel-air systems and typically plotted the blowoff velocity as a function of the air-fuel ratio for various stabilized sizes, as shown in Fig. 4.56. Early attempts to correlate the data appeared to indicate that the dimensional dependence of blowoff velocity was different for different bluff-body shapes. Later, it was shown that the Reynolds number range was different for different experiments and that a simple independent dimensional dependence did not exist. Furthermore, the state of turbulence, the temperature of the stabilizer, incoming mixture temperature, etc., also had secondary effects. All these facts suggest that fluid mechanics plays a significant role in the process. 

This is Stokes law which is valid in the particle Reynolds number range 10 < Re < 0.20 where the Reynolds number is defined by... 

Previous correlations of the influence of z on terminal velocities (El, H4, Ml, SI, S6, T3, Ul) are limited to specific systems, fail to recognize the different regimes of fluid particles (see Chapter 2), or are difficult to apply. In the present section we consider both bubbles and drops, but confine our attention to those of intermediate size (see Chapter 7) where Eo < 40 and Re > 1. Only the data of Uno and Kintner (Ul), Strom and Kintner (S6) and Salami et ai (SI) are used since other workers either failed to use a range of column sizes for the same fluid-fluid systems, or it was impossible to obtain accurate values of the original data. This effectively limits the Reynolds number range to Re > 10 for the low M systems studied. 

For the empirical formula (Equation 4), Davies divides the Reynolds number range into two parts. The data for Re are fitted with a fourth-order polynomial in 4Re2 for the higher values. To integrate Equation 3 analytically, one must fit the same data with second-order polynomials. The results are as follows ... 

Turbulent burning velocities of various mixtures, as measured from Bunsen flames, are directly proportional to the laminar burning velocities of the same mixtures. For example, the following equation applies to propane, ethene, and acetylene, over the Reynolds number range 3000 to 40,000 (8) ... 

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