Drag factor 295, coefficient

Drag factor, drag coefficient/ Stokes drag... 

According to Eq. 6.11, the DMFC determination of the methanol permeability requires the knowledge of the methanol drag factor, because the electro-osmotic flux could afford for a considerable fraction of the methanol flow, particularly at high methanol concentrations. An important drawback of this method is that the methanol drag coefficient is not well known, so Ren et al. [299] assumed that it was similar to the water drag coefficient ( =2.5). However, some recent NMR [300] and electro-osmosis [301] studies would indicate that this assumption is not valid, leading to considerable uncertainties in the methanol permeability coefficients determined by this method. 

When the solute dimension is no longer orders of magnitude smaller than the pore dimensions, the solute molecules experience an additional transport resistance due to the proximity of the pore wall. The effective diffusion coefficient is reduced further by a hindrance factor/ drag factor Gm i i,rp). If the solute molecules are assumed spherical of radius r, and diffusing through the centerline of the pore of radius, tp, Faxen s expression may be used to estimate Gor for (r,rp) < 0.5 (Lane, 1950 Renkin, 1954) ... 

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... 

We now have all the information necessary to develop some working expressions for particle settling. Look back at equation 3 (the resistance force exerted by the water), and the expressions for the drag coefficient (sidebar discussion on page 261). The important factor for us to realize is that the settling velocity of a particle is that velocity when accelerating and resisting forces are equal ... 

The drag coefficient for an antomohile body is typically estimated from wind-tunnel tests. In the wind tunnel, the drag force acting on a stationaiy model of the vehicle, or the vehicle itself, is measured as a stream of air is blown over it at the simulated vehicle speed. Drag coefficient depends primarily on the shape of the body, but in an actual vehicle is also influenced by other factors not always simulated in a test model. 

In this equation, % is a proportionality factor known as the bead-solvent friction coefficient which purports to account in some kind of average way for the complex molecular interactions as the polymer segments (schematized by the bead) move about in the solvent. Following Stokes law of drag resistance, this friction coefficient is usually given as = 67trisa, with a equal to the bead radius. 

Cd = drag coefficient (shape factor), pa = density of air, uw = wind velocity. 

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,... 

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.,... 

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

The solids contribution to the pressure drop, APls, is a consequence of both the particle-wall and particle-particle interactions. The latter is reflected in the dependence of the friction factor fs on the particle diameter, drag coefficient, density, and relative (slip) velocity by (Hinkel, 1953) ... 

Using these Reynolds number scale factors, the errors in the dimensionless drag coefficient j3L/psua using the simplified scaling models are shown in Figs. 24 and 25 for u0/umf of 10 and 1000, respectively, plotted as a function of Rep, based on parameters for the exact scaled bed. For a particle Reynolds number of 1000 or less, which corresponds to... 

The dimensionless drag coefficient Cd, analogous to the friction factor, is defined by... 

A particle drag coefficient Cd can now be defined as the drag force divided by the product of the dynamic pressure acting on the particle (i.e. the velocity head expressed as an absolute pressure) and the cross-sectional area of the particle. This definition is analogous to that of a friction factor in conventional fluid flow. Hence... 

Air resistance (or drag) is quantified by a dimensionless drag coefficient which is related to the external configuration of the rocket. Other factors that influence drag being the air density, the diameter of the rocket and the square of the rocket velocity. 

The angle of repose is a measure of the incline at which conveyors such as screws or belts can carry the material. The tangent of the angle of repose is the coefficient of sliding friction. This property is a factor in the power needed to transfer the material by pushing or dragging as in pneumatic, screw, flight, and Redler equipment. 

The diameter again is figured from the volumetric rate of the vapor and the linear velocity from Eq. (18.9). Since the upward drag of the vapor is largely absent in a horizontal drum, however, the coefficient K often is raised by a factor of 1.25. Example 18.3 deals with the design of both kinds of drums. 

On one hand, solid materials to be processed with an impinging stream device have various sizes, while, on the other hand, the relative velocity between gas and particles varies from time to time in acceleration and deceleration stages of particle motion. Both factors make the value for Rep vary continuously with considerably large amplitude, which may be across various flow regimes. So, the variation of the drag coefficient, Cd, in various flow regimes has to be taken into account in the solution of the motion equations for the particle in various stages. 

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