Drag coefficient Stokes

Equation (7.40) is known as Stokes law, and it applies for particle Reynolds numbers less than 1.0. At = 1.0, Co = 26.5 instead of 24.0 from Eq. (7.38), and since the terminal velocity depends on the square root of the drag coefficient, Stokes law is about 5 percent in error at this point. Equation (7.40) can be modified to predict the velocity of a small sphere in a centrifugal field by substituting rco for g. 

Drag factor, drag coefficient/ Stokes drag... 

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

Fig. 14. Drag coefficient for terminal settling velocity correlation (single particle) where A represents Stokes law B, intermediate law and C, Newton s...

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... 

The drag coefficient based on the theoretical analysis of Stokes is... 

AA-gpjj. Conditionally, the ionic atmosphere is regarded as a sphere with radius r. The valnes of approach the size of colloidal particles, for which Stokes s law applies (i.e., the drag coefficient 9 = where r is the liquid s viscosity) when they... 

Models of the polymer coil are based on the end-to-end distance, which is generally not directly available as a quantitative feature. Coils in dilute solution can be characterized in terms of the radius of gyration, Rg, which is a statistical measure of the distribution of mass about the center of gravity or in terms of the hydrodynamic radius, Rh, that is usually determined through the use of Stokes law and a measurement of a drag coefficient or friction factor, /drag/ for the coil,... 

If the relative velocity is sufficiently low, the fluid streamlines can follow the contour of the body almost completely all the way around (this is called creeping flow). For this case, the microscopic momentum balance equations in spherical coordinates for the two-dimensional flow [vr(r, 0), v0(r, 0)] of a Newtonian fluid were solved by Stokes for the distribution of pressure and the local stress components. These equations can then be integrated over the surface of the sphere to determine the total drag acting on the sphere, two-thirds of which results from viscous drag and one-third from the non-uniform pressure distribution (refered to as form drag). The result can be expressed in dimensionless form as a theoretical expression for the drag coefficient ... 

The corresponding creeping flow drag coefficient can be characterized by a correction factor (X) to the Stokes law drag coefficient ... 

Instantaneous overall drag coefficients determined from the Navier-Stokes equation were within about 10% of values obtained from Eqs. (1 l-30)-(ll-33). This provides an additional justification of the approach discussed above. 

Unfortunately for production facility design, it can be shown that Stokes Law does net govern, and the following more complete formula for drag coefficient must be used ... 

Practically, the initial y-component velocity, equals (greater than 10 ft/s), so Stoke s law does not apply. The drag coefficient Co, takes the form of Eq. (3b). which also represents a deceleration case, as the frictional drag reduces the velocity to Ut in the short interval 0. Substituting Eq. (Sb) for in Eq. (23) results in ... 

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... 

Substituting, respectively, the expressions for the drag coefficient, CD, yields the relationships for the corresponding flow regimes. For example, for the Stokes regime, substituting Eq. (2.6) into Eq. (2.14) results in... 

Example 11.2 Use Eq. (11.17) to derive a general expression for the acceleration length for dilute gas-solid pipe flows. Assume that the Stokes drag coefficient can be used. The friction coefficient of particles at the wall can be estimated by [Konno and Saito, 1969]... 

Assumption Stokes law governs and the drag coefficient CD is not significant. From Perry [7] ... 

The third collision mechanism, differential settling, occurs when larger aggregates settle more rapidly than smaller aggregates and particles (see Fig. lc). The terminal velocity of settling particles and aggregates is typically assumed to follow Stoke s law for Reynold s numbers much less than one, where the drag coefficient is approximated by... 

Here x is a phenomenological parameter measuring the chirality and / is a size scale factor. Since here the Reynolds number is small ( 10 s), the Stokes equation can be used to get r = DS2. where D is the hydrodynamic drag coefficient and 2 is the rotational speed. The drag coefficient for a cylindrical object rotating about its axis with cross-sectional radius r and length L is D = 4ztT)r2L, where tj is the viscosity of the medium [19]. Therefore, D /3 and the rotational speed 2 of the rotor will scale as... 

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