Reynolds number internal

Dorgan, a. J. Loth, E. 2007 Efficient calculation of the history force at finite Reynolds numbers. International Journal of Multiphase Flow 33, 833-848. 

K = value of at a Reynolds number of 1 K = value of Kat high Reynolds numbers = internal pipe diameter in inches. 

Klein, M. (2005). Direct numerical simulation of a spatially developing water sheet at moderate Reynolds number. International Journal of Heat and Fluid Flow, 26, 722-731. 

Flow Past Deformable Bodies. The flow of fluids past deformable surfaces is often important, eg, contact of Hquids with gas bubbles or with drops of another Hquid. Proper description of the flow must allow for both the deformation of these bodies from their shapes in the absence of flow and for the internal circulations that may be set up within the drops or bubbles in response to the external flow. DeformabiUty is related to the interfacial tension and density difference between the phases internal circulation is related to the drop viscosity. A proper description of the flow involves not only the Reynolds number, dFp/p., but also other dimensionless groups, eg, the viscosity ratio, 1 /p En tvos number (En ), Api5 /o and the Morton number (Mo),giJ.iAp/plG (6). 

Reynolds Number. The Reynolds number, Ke, is named after Osborne Reynolds, who studied the flow of fluids, and in particular the transition from laminar to turbulent flow conditions. This transition was found to depend on flow velocity, viscosity, density, tube diameter, and tube length. Using a nondimensional group, defined as p NDJp, the transition from laminar to turbulent flow for any internal flow takes place at a value of approximately 2100. Hence, the dimensionless Reynolds number is commonly used to describe whether a flow is laminar or turbulent. Thus... 

The Reynolds number is sufficient as a parameter for describing the internal flow characteristics, such as discharge coefficient, air core ratio, and spray angle at the atomizer exit. 

The relationship between adsorption capacity and surface area under conditions of optimum pore sizes is concentration dependent. It is very important that any evaluation of adsorption capacity be performed under actual concentration conditions. The dimensions and shape of particles affect both the pressure drop through the adsorbent bed and the rate of diffusion into the particles. Pressure drop is lowest when the adsorbent particles are spherical and uniform in size. External mass transfer increases inversely with d (where, d is particle diameter), and the internal adsorption rate varies inversely with d Pressure drop varies with the Reynolds number, and is roughly proportional to the gas velocity through the bed, and inversely proportional to the particle diameter. Assuming all other parameters being constant, adsorbent beds comprised of small particles tend to provide higher adsorption efficiencies, but at the sacrifice of higher pressure drop. This means that sharper and smaller mass-transfer zones will be achieved. 

Scope, 52 Basis, 52 Compressible Flow Vapors and Gases, 54 Factors of Safety for Design Basis, 56 Pipe, Fittings, and Valves, 56 Pipe, 56 Usual Industry Pipe Sizes and Classes Practice, 59 Total Line Pressure Drop, 64 Background Information, 64 Reynolds Number, R,. (Sometimes used Nr ), 67 Friction Factor, f, 68 Pipe—Relative Roughness, 68 Pressure Drop in Fittings, Valves, Connections Incompressible Fluid, 71 Common Denominator for Use of K Factors in a System of Varying Sizes of Internal Dimensions, 72 Validity of K Values,... 

The enhancement ratio (fiie/hi) for tube inserts can be correlated as a function of Reynolds number based on the internal diameter of the tube Re = pVdi/fi10. Different tube inserts can be compared on the basis of plots of enhancement ratio (hTe/hT) versus Reynolds number. 

Here, 7VRe is the Reynolds number, which is dimensionless, as are Af and the constants A and Kt. However, the term ID is the internal diameter of... 

Reynolds number flows /vRe N -°Vp /vRe — pV2 pV/D AQp izDp PV2 Tw/8 Pipe flow rw =wall stress (inertial momentum flux)/ (viscous momentum flux) Pipe/internal flows (Equivalent forms for external flows)... 

Here, IDin is the internal diameter (in inches) of the pipe that contains the fitting. This method is valid over a much wider range of Reynolds numbers than the other methods. However, the effect of pipe size (e.g., 1 /IDin) in Eq. (7-37) does not accurately refect observations, as discussed below. 

Figure 33. Dimensionless spoutdiametersasafunctionof dimensionless height for small columns. Case A test case Case B all dimensionless parameters matched, bed diameter halved Case C particle Reynolds number mismatched Case D Froude number mismatched Case E density ratio, Reynolds number mismatched Case F bed Reynolds number mismatched Case G internal friction angle, loose packed voidage mismatched. (From He et al., 1995.)...

For pipe fittings, valves, and other flow obstructions the traditional method has been to use an equivalent pipe length Lequiv in Equation 4-30. The problem with this method is that the specified length is coupled to the friction factor. An improved approach is to use the 2-K method,s-6 which uses the actual flow path length in Equation 4-30 — equivalent lengths are not used — and provides a more detailed approach for pipe fittings, inlets, and outlets. The 2-K method defines the excess head loss in terms of two constants, the Reynolds number and the pipe internal diameter ... 

Re is the Reynolds number (dimensionless), and /Djnches is the internal diameter of the flow path (inches). 

Measurements with different fluids, in pipes of various diameters, have shown that for Newtonian fluids the transition from laminar to turbulent flow takes place at a critical value of the quantity pudjp in which u is the volumetric average velocity of the fluid, dt is the internal diameter of the pipe, and p and p. are the fluid s density and viscosity respectively. This quantity is known as the Reynolds number Re after Osborne Reynolds who made his celebrated flow visualization experiments in 1883 ... 

The Reynolds number characterizing laminar-turbulent transition for bulk flow in a pipe is about Re 2300 provided that the fluid moves unidirectionally, the pipe walls are even and behave in a hydraulically smooth manner, and the internal diameter remains constant. However, intestinal walls do not fulfill these hydraulic criteria due to the presence of curvatures, villi, and folds of mucous membrane, which are up to 8 mm in the duodenum, for instance (Fig. 18). Furthermore, the internal diameter of the small intestine is estimated to... 

H3, Tl), it is unimportant that the Reynolds number of the internal motion was rather large for many flow visualization studies which set out to verify the Hadamard-Rybczynski predictions, so long as the Reynolds number based on the continuous fluid properties was small and the fluid particle spherical. The observed streamlines show excellent qualitative agreement with theory, although quantitative comparison is difficult in view of refractive mdex differences and the possibility of surface contamination. When a trace of surface-active contaminant is present, the motion tends to be damped out first at the rear of... 

When a fluid sphere exhibits little internal circulation, either because of high K = Pp/p or because of surface contaminants, the external flow is indistinguishable from that around a solid sphere at the same Re. For example, for water drops in air, a plot of versus Re follows closely the curve for rigid spheres up to a Reynolds number of 200, corresponding to a particle diameter of approximately 0.85 mm (B5). In fact, many of the experimental points used in Section II to determine the standard drag curve refer to spherical drops in gas streams, where high values of k ensure negligible internal circulation. 

The internal resistance is always decreased substantially when a bubble or drop oscillates, but the external resistance may be unaffected if the Reynolds number is high enough. A rough criterion can be obtained from Eq. (11-63) for vibration of a particle in an axial stream. Oscillation has negligible effect on the external resistance if... 

Sy et al (S8, S9) and Morrison and Stewart (M12) analyzed the initial motion of fluid spheres with creeping flow in both phases. For bubbles (y = 0, k = 0), the condition that internal and external Reynolds numbers remain small is sufficient to ensure a spherical shape. However, for other k and y, the Weber number must also be small to prevent significant distortion (S9). For k = 0, the equation governing the particle velocity may be transformed to an ordinary differential equation (Kl), to give a result corresponding to Eq. (11-16), i.e.,... 

Axial dispersion Low Z/D and low Reynolds number flow conditions Vessel with baffles or internals obstructing flows High ZID and high Reynolds flow in open pipes... 

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