Drag coefficient spherical particle

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

Drag coefficient versus particle Reynolds number for spherical particles. 

TABLE 4-9 Drag Coefficient for Particles in Example 4-11, Assuming Spherical Shape... 

Assuming spherical particles, the drag coefficient, in the laminar, the Stokes flow regime is... 

The drag force is exerted in a direction parallel to the fluid velocity. Equation (6-227) defines the drag coefficient. For some sohd bodies, such as aerofoils, a hft force component perpendicular to the liquid velocity is also exerted. For free-falling particles, hft forces are generally not important. However, even spherical particles experience lift forces in shear flows near solid surfaces. 

The drag coefficient for rigid spherical particles is a function of particle Reynolds number, Re = d pii/ where [L = fluid viscosity, as shown in Fig. 6-57. At low Reynolds number, Stokes Law gives 24... 

C = Overall Drag Coefficient, Dimensionless Dp = Diameter of Spherical Particle,ft. 

Figure 2.10 Relationship between drag coefficient lfd) and Reynolds number (Re) for a spherical particle settling in a liquid.

In the limit of very high voidage, the drag coefficient can be related to the single particle drag coefficient. For the case of spherical particles,... 

In Eq. (39), Cdo is a function of the particle Reynolds number, Rep — pedp V — Vp /p. For rigid spherical particles, the drag coefficient CD0 can be estimated by the following equations (Rowe and Henwood, 1961) ... 

There are two difficulties which soon become apparent when attempting to assess the very large amount of experimental data which are available on drag coefficients and terminal falling velocities for non-spherical particles. The first is that an infinite number of non-spherical shapes exists, and the second is that each of these shapes is associated with an infinite number of orientations which the particle is free to take up in the fluid, and the orientation may oscillate during the course of settling. 

Fig. 10.15 Drag coefficient for rigid spherical particles in air as a function of Mach number with Reynolds number as parameter, for the case where the absolute temperatures of the particle and fluid are essentially the same.

A. Haider and O. Levenspiel, Drag coefficient and terminal velocity of spherical and nonspherical particles, Powder Technol., 1989, 58, 63-70. 

In this expression yd is a characteristic area of a spherical particle, 2Pfluid is a characteristic kinetic energy for the flow, and Cd is the drag coefficient [27]. 

The origin of the spherical polar coordinate system (r, 9, cp) is held fixed at the center of one particle and the polar axis (9 = 0) is set parallel to E. Let the electrolyte be composed of M ionic mobile species of valence zt and drag coefficient A,-(/ = 1, 2,. . . , M), and let nf be the concentration (number density) of the ith ionic species in the electroneutral solution. We also assume that fixed charges are distributed with a density of pflx. We adopt the model of Debye-Bueche where the polymer segments are regarded as resistance centers distributed in the polyelectrolyte... 

The terminal settling velocity of a spherical particle having a diameter of 0.6 mm is 0.11 m/s. What is the mass density of the particle Assume the settling is type 1 and the temperature of the water is 22°C. What is the drag coefficient ... 

The following relationship is an empirical fit to experimental data for spherical particles, between drag coefficient and Reynolds number for Reynolds number between 0.01 and 1.0 ... 

Haider and Levenspeil [26] presented the following empirical equation relating drag coefficient and Reynolds number for spherical and non-spherical particles, where Reynolds number is based on volume diameter ... 

Petkov et al. described a sensitive method of obtaining q a small spherical particle floats at the Interface and moves under the action of an applied capillary force. From the measured drag coefficient r/ is computed. Results for aqueous solutions of Na DS" and CjgTMA Br agree reasonably with those in the literature. One can consider this method to be the 2D equivalent of the Stokes method for measuring bulk viscosities. 

Using the linear relation between drag coefficient and Reynolds number, a pure laminar flow pattern of the sedimentating particles is implied. For spherical particles, flow is considered as laminar for Reynolds number smaller than 0.1. For Reynolds numbers up to 1, the linear relation with drag coefficient is generally accepted. Several investigators accepted the linear relation as far... 

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