Drag coefficients

APPENDIX 4.2. CORRELATIONS FOR DRAG COEFFICIENT A4.2.1. Drag Coefficient for Single Particle 

Morsi and Alexander s (MA) correlation represents the single-particle drag curve accurately. Ma and Ahmadi s correlation predicts values comparable with the MA correlation. Molerus correlation deviates from the MA correlation at higher Reynolds numbers. Patel s correlation is found to give a better fit with the MA correlation than Richardson s correlation. Dalla Ville s correlation overpredicts values of drag coefficient compared to the MA correlation. 

APPENDIX 4.3. INTERPHASE HEAT AND MASS TRANSFER CORREUTIONS 

Re 1 Solid or fluid particle, high Pe and low Re Solid or fluid particle, low Pe and low Re Solid or fluid particle, high Re Solid particles, low Re 

Particles at allPe Granular flows/dense flows 

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The term essentially a drag coefficient for the dust cake particles, should be a function of the median particle size and particle size distribution, the particle shape, and the packing density. Experimental data are the only reflable source for predicting cake resistance to flow. Bag filters are often selected for some desired maximum pressure drop (500—1750 Pa = 3.75-13 mm Hg) and the cleaning interval is then set to limit pressure drop to a chosen maximum value. 

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

The drag coefficient has different functionalities with particle Reynolds number Ri in three different regimes (Fig. 14), which results in the following expressions (1). 

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 Cg can be plotted as a function of the dimensionless product p 5/ R. Thus, equations 40 and 41 are in proper form for direct determination of the speed once the drag is given. 

Suppose that an experiment were set up to determine the values of drag for various combinations of O, p, and ]1. If each variable is to be tested at ten values, then it would require lO" = 10, 000 tests for all combinations of these values. On the other hand, as a result of dimensional analysis the drag can be calculated by means of the drag coefficient, which, being a function of the Reynolds number Ke, can be uniquely determined by the values of Ke. Thus, for data of equal accuracy, it now requires only 10 tests at ten different values of Ke instead of 10,000, a remarkable saving in experiments. 

In addition, dimensional analysis can be used in the design of scale experiments. For example, if a spherical storage tank of diameter dis to be constmcted, the problem is to determine windload at a velocity p. Equations 34 and 36 indicate that, once the drag coefficient Cg is known, the drag can be calculated from Cg immediately. But Cg is uniquely determined by the value of the Reynolds number Ke. Thus, a scale model can be set up to simulate the Reynolds number of the spherical tank. To this end, let a sphere of diameter tC be immersed in a fluid of density p and viscosity ]1 and towed at the speed of p o. Requiting that this model experiment have the same Reynolds number as the spherical storage tank gives... 

Fanning friction factor /i for inner wall and / 2 for outer wall of annulus /l for ideal tube bank sldn friction drag coefficient Dimensionless Dimensionless... 

Chilton-Colburn analogies, Ns = 1-0, (gases), f = drag coefficient. Corresponds to item 5-21-F and refers to same conditions. 8000 < Nr < 300,000. Can apply analogy, jo =//2, to entire plate (including laminar portion) if average values are used. 

Energy dissipation rate per unit mass of fluid (ranges 570 < Ns < 1420) fluid and sphere, m/s. Cq,. = drag coefficient for single particle fixed in fluid at velocity i>,.. See 5-27-G for calculation details and other applica- ... 

Calculated from drag coefficient for single cylinders using maximum velocity — Experimental... 

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... 

FIG. 6-57 Drag coefficients for spheres, disks, and cylinders =area of particle projected on a plane normal to direction of motion C = over-... 

Between about Rop = 350,000 and 1 X 10 , the drag coefficient drops dramatically in a drag crisis owing to the transition to turbulent flow in the boundary layer around the particle, which delays aft separation, resulting in a smaller wake and less drag. Beyond Re = 1 X 10 , the drag coefficient may be estimated from (Clift, Grace, and Weber) ... 

The drag coefficients for disks (flat side perpendicular to the direction of motion) and for cylinders (infinite length with axis perpendicular to the direclion of motion) are given in Fig. 6-57 as a Function of Reynolds number. The effect of length-to-diameter ratio for cylinders in the Newton s law region is reported by Knudsen and Katz Fluid Mechanics and Heat Transfer, McGraw-Hill, New York, 1958). 

Equations (6-236) to (6-239) are based on experiments on cube-oc tahedrons, octahedrons, cubes, and tetrahedrons for which the sphericity f ranges from 0.906 to 0.670, respectively. See also Chft, Grace, and Weber. A graph of drag coefficient vs. Reynolds number with y as a parameter may be found in Brown, et al. (Unit Operations, Whey, New York, 1950) and in Govier and Aziz. 

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