Reynolds number and drag coefficient

This result can also be applied directly to coarse particle swarms. For fine particle systems, the suspending fluid properties are assumed to be modified by the fines in suspension, which necessitates modifying the fluid properties in the definitions of the Reynolds and Archimedes numbers accordingly. Furthermore, because the particle drag is a direct function of the local relative velocity between the fluid and the solid (the interstitial relative velocity, Fr), it is this velocity that must be used in the drag equations (e.g., the modified Dallavalle equation). Since Vr = Vs/(1 — Reynolds number and drag coefficient for the suspension (e.g., the particle swarm ) are (after Barnea and Mizrahi, 1973) ... 

At low Reynolds numbers, the drag coefficient varies inversely with and the equations for C, Fj, and u, are... 

At a high Reynolds number, the drag coefficient shows an increase with Mach number reaching a maximum value for light supersonic flow. This increase is due to the formation of shock waves on the particle and the attendant wave drag (essentially form drag). Mach number effects become significant for a Mach number of 0.6, which is the critical Mach number, that is, when sonic flow first occurs on the sphere. 

At a low Reynolds number, the drag coefficient uniformly decreases with increasing Mach number and does not display a maximum value near unity. This is due to the prevalence of rarefied flow. 

Equation 3-1 contains a drag coefficient C ), which is a function of the Reynolds number. This drag coefficient is highly dependent on the fluid regimes of laminar and turbulent. For the laminar regime, Stokes (1851) solved the fluid dynamics equations for flow past a sphere, determining the drag force in the sphere as... 

Fd was evaluated from the drag coefficient at bubble Reynolds number and the projected area of the bubble. As the Reynolds number varied from 2 to 700, the drag coefficient CD was evaluated by the Schiller and Naumann (S4) equation ... 

The vaporization rates and drag coefficients for 2,2,4-trimethylpentane (iso-octane) sprays in turbulent air streams were determined experimentally by Ingebo (40), who reported that the effect of relative velocity on the evaporation rate was represented by the 0.6 power of the Reynolds number and that the drag coefficient varied inversely with the relative velocity of the drops in the spray. By assuming that the evaporation rate was independent of velocity and the drag coefficient for droplets obeyed Stokes s law, the present author derived a mathematical theory for the ballistics of droplets injected into an air stream for which the velocity varied linearly with distance (57) and... 

Fig. 6.6 Comparison between equations relating drag coefficient to Reynolds number and experimental data...

Within the precipitation field, a particle experiences the following forces acting upon it a momentum force, /v = ma an electrical force, = QpE and a drag force, Ed = ReACo (Re is the Reynolds number and Co the Cunningham coefficient). 

Swanson [145] reviewed the investigations of the Magnus force, and presented experimental drag and lift coefficients for an infinite, rotating cylinder at different Reynolds numbers and velocity ratios. For velocity ratios less than 0.55, and Reynolds numbers between 12.8 x 10 and 50.1 x 10 the cylinder would experience negative lift. 

The curves for the drag coefficient and the terminal velocity converge for small and large bubbles. This is likely to be because there is always some surface active contaminants present, even in distilled water, that will prevent the internal circulation of the smallest bubbles. For the large bubbles the surface tension forces are not important. Several different drag formulations are given based on the Reynolds number and the density ratio of the gas and liquid [54, 163, 78]. 

The drag coefficient is a variable depending on the flow conditions represented by the particle Reynolds number and is given in Table 9.6 or Figure 9.25. 

From dimensional analysis, the drag coefficient of a smooth solid in an incompressible fluid depends upon a Reynolds number and the necessary shape... 

In steady pipe flow it was found experimentally that / depends on only the Reynolds number and the relative roughness. It has been found similarly that the drag coefficient for smooth spheres in steady motion depends on only the Reynolds number. Here we must redefine the Reynolds number, which previously included the pipe diameter. The common practice is to define a particle Reynolds number, in which the particle diameter takes the place of the pipe diameter ... 

For a sphere, Ap = nDl /4, where Dp is the sphere diameter. A correlation of the Reynolds number and the drag coefficient can be observed, moreover, in the laminar region, for low Reynolds numbers (Re < 1) ... 

The tube can be designed such that the quadratic relationship between area and height is nearly linear. When the rotameter is calibrated for the operating conditions, the variation of the physical properties related to the Reynolds number, and hence the drag coefficient, may be lumped together to give the following relationship ... 

From the numerical results, correlations, which give the variation of the drag coefficient as function of Reynolds number, and viscosity ratio were proposed. For Re < 50 and viscosity ratio K< 1.4, the Abdel-Alim and Hamielec [19] results were htted in an empirical equation ... 

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