Normal drag coefficient

Figure 23.6 Electoosmotic drag coefficient for Nafion as a function of its solvent (water and/or methanol) volume fraction data from Refs. [12, 87, 88, 117-123] and unpublished data from the author s laboratory. The normalized drag coefficients for water and methanol are plotted together because they are virtually identical. (Reproduced with kind permission from Chemical Reviews.)...

Figure 2. Response surface polynomial for (normalized) fatigue damage versus the (normalized) drag coefficient for pressure armour (longitudinal direction). (SN-curve corresponds to H2S being present).

Figure 9.37 Dp (A), Dr iO), and s (0) of 92.5 nm radius spheres in 4 MDa xanthan, all reported [left axis] as nominal normalized drag coefficients /o//, and shear viscosity ( ) rj/rjo [right axis, note inverted scale], after data of Koenderink, etal 12).

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

Cross-sectional aiea allocated to light phase, sq ft Area of particle projected on plane normal to direction of flow or motion, sq ft Cross-sectional area at top of V essel occupied by continuous hydrocarbon phase, sq ft Actual flow at conditions, cu ft/sec Constant given in table Volume fiaction solids Overall drag coefficient, dimensionless Diameter of vessel, ft See Dp, min Cyclone diameter, ft Cyclone gas exit duct diameter, ft Hy draulic diameter, ft = 4 (flow area for phase in qiiestion/wetted perimeter) also, D in decanter design represents diameter for heavy phase, ft... 

Drag coefficient Cd c - Fd Cd 1PV2A Fd =drag force A = area normal to flow (Drag stress)/ ( momentum flux) External flows... 

Here, p is the density of the fluid, V is the relative velocity between the fluid and the solid body, and A is the cross sectional area of the body normal to the velocity vector V, e.g., nd1/4 for a sphere. Note that the definition of the drag coefficient from Eq. (11-1) is analogous to that of the friction factor for flow in a conduit, i.e.,... 

For flow past a circular cylinder with L/d > normal to the cylinder axis, the flow is similar to over for a sphere. An equation that adequately represents the cylinder drag coefficient over the entire range of NRc (up to... 

Apr = the area of the particle projected on a plane normal to the direction of flow (projected area perpendicular to flow) ula. = the terminal velocity CD = an empirical drag coefficient. 

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].)... 

CD is known at the drag coefficient. Drag coefficients are normally expressed in the form Cd = (F j A) ji puff), where A is the projected or cross-sectional area of the particle in the direction of flow. Hence the particular form shown in Equation (9). Re is the particle Reynolds number, Re = (pit, dip). and is the reciprocal of the second dimensionless group found above. 

Whitaker [234] (chap 8) explains the convention normally used to distinguish between these two types of parameters. The friction factors for dispersed bodies immersed in a flowing fluid is traditionally referred to as dimensionless drag coefficients, whereas the drag force for flow inside closed conducts is generally expressed in terms of a dimensionless friction factor. 

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