Drag coefficient for disk

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). 

With this definition all the steady-state drag data on single, smooth spheres moving in infinite , quiescent, newtonian fluids at moderate velocities can be represented by aj single curve on Fig. 6.22. This figure shows also drag coefficients for disks and cylinders, to be discussed later. It is limited to steady velocities of less than about one half the local speed of sound velocities higher than this are discussed elsewhere [18]. 

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

Figure 11-2 Drag coefficient for spheres, cylinders, and disks. (From Perry, 1984.) o Eq. (11-5), spheres. Eq. (11-7), cylinders.

FIG. 6-57 Drag coefficients for spheres, disks, and cylinders A = area of particle projected on a plane normal to direction of motion C = overall drag coefficient, dimensionless Dp - diameter of particle Fd = drag or resistance to motion of body in fluid Re = Reynolds number, dimensionless u = relative velocity between particle and main body of fluid (I = fluid viscosity and p = fluid density. (From Lapple and Shepherd, Ind. Eng. Chem., 32, 60S [1940].)... 

Evans EA, Sackmann E. Translational and rotational drag coefficients for a disk moving in a liquid membrane associated with a rigid substrate. J. Fluid Mech. 1988 194 553-561. 

The literature in the field of fluid mechanics [8] provides us with an expression as the definition of the fiictional drag coefficient For spheres, disks, cylinders, and similar bodies, the diameter is... 

In axial flow past disks, which are the limit cases of axisymmetric bodies of small length, the drag coefficients are given in [94] for the entire range of Reynolds numbers calculated with respect to the radius. These formulas approximate numerical results and experimental data ... 

DRAG COEFFICIENTS OF TYPICAL SHAPES. In Fig. 7.3, curves of versus JVrc p are shown for spheres, long cylinders, and disks. The axis of the cylinder and the face of the disk are perpendicular to the direction of flow these curves apply only when this orientation is maintained. If, for example, a disk or cylinder is moving by gravity or centrifugal force through a quiescent fluid, it will twist and turn as it moves freely through the fluid. 

The curve of Cj, versus for an infinitely long cylinder normal to the flow is much like that for a sphere, but at low Reynolds numbers, does not vary inversely with because of the two-dimensional character of the flow around the cylinder. For short cylinders, such as catalyst pellets, the drag coefficient falls between the values for spheres and long cylinders and varies inversely with the Reynolds number at very low Reynolds numbers. Disks do not show the drop in drag coefficient at a critical Reynolds number, because once the separation occurs at the edge of the disk, the separated stream does not return to the back of the disk and the wake does not shrink when the boundary layer becomes turbulent. Bodies that show this type of behavior are called bluff bodies. For a disk the drag coefficient Cj, is approximately unity at Reynolds numbers above 2000. 

The foregoing pertains entirely to spheres. We can use Eq. 6.53 for other shapes, if we agree on what area A represents. Generally, in drag measurements it refers to the frontal area perpendicular to the flow that is the definition on which the coefficients in Fig. 6,22 are based. Moreover, we must decide on which dimensions to base the Reynolds number in our correlation of Cj versus in Fig. 6.22 the Reynolds number for cylinders takes the cylinder diameter as /), and that for disks takes the disk diameter. 

Values for the drag coefficient have been determined for bodies of regular shape such as spheres, cylinders, and flat disks [97,98]. The drag coefficients are usually shown on a log-log plot, as a function of the Reynolds number. 

For each particular shape of object and orientation of the object with the direction of flow, a different relation of Cp versus exists. Correlations of drag coefficient versus Reynolds number are shown in Fig. 3.1-2 for spheres, long cylinders, and disks. The face of the disk and the axis of the cylinder are perpendicular to the direction of flow. These curves have been determined experimentally. However, in the laminar region for low Reynolds numbers less than about 1.0, the experimental drag force for a sphere is the same as the theoretical Stokes law equation as follows. 

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