Radial positions

In the Couette flow inside a cone-and-plate viscometer the circumferential velocity at any given radial position is approximately a linear function of the vertical coordinate. Therefore the shear rate corresponding to this component is almost constant. The heat generation term in Equation (5.25) is hence nearly constant. Furthermore, in uniform Couette regime the convection term is also zero and all of the heat transfer is due to conduction. For very large conductivity coefficients the heat conduction will be very fast and the temperature profile will... 

Velocity Profiles In laminar flow, the solution of the Navier-Stokes equation, corresponding to the Hagen-PoiseuiUe equation, gives the velocity i as a Innction of radial position / in a circular pipe of radius R in terms of the average velocity V = Q/A. The parabolic profile, with centerline velocity t ce the average velocity, is shown in Fig. 6-10. 

Laminar Flow With highly viscous fluids the linear velocity along a streamline varies with the radial position. Laminar flow is charac teristic of some polymeric systems. Figure 23-21 shows how the conversion is poorer in laminar flow than with uniform flow over the... 

Concurrent with the liquid-shiny interface moving radially outward, the cake layer builds up with the cake-slurry interface moving radiaUy inward, with radial position given by ... 

Laminar or power law velocity distribution in which the linear velocity varies with radial position in a cylindrical vessel. Plug flow exists along any streamline and the mean concentration is found by integration over the cross section. 

Effectiveness As a reac tant diffuses into a pore, it undergoes a falling concentration gradient and a falling rate of reaction. The concentration depends on the radial position in the pores of a spherical pellet according to... 

Laminar Flow A mathematically simple deviation from uniform flow across a cross section is that of power law fluids whose linear velocity in a tube depends on the radial position = r/R, according to the equation... 

In the multistage compressor, the vanes are rectangular and located in a radial position ahead of the first impeller, with a linkage connecting the vanes to a power positioner. From that point, the control is affected in the same manner as the single-stage. 

More eomplex forms ean be derived e.g. allowing for a ehange in radial position of the slurry (as in bateh operation), or allowing for the resistanee of the filter eloth. 

Hydrodynamic Dispersion Macroscopic dispersion is produced in a capillar) even in tlie absence of molecular diffusion because of the velocity profile produced by the adherence of the fluid to tlie wall. Tlris causes fluid particles at different radial positions to move relative to one anotlier, witli tlie result tliat a series of mixing-cup samples at tlie end of tlie capillary e.xhibits dispersion. 

Under the steady-state flow conditions, there is an increasing tendency of this fiberlike structure moving toward the capillary wall as shear stress, flow flux, and radial position increase. In fact, we often obtained extru-dates with a very thin TLCP-rich skin layer from the capillary test [8]. 

Consider a uniform cylindrical bar or tube to which some balanced torque T is applied (Figure 2-28). The bar will be subject to a torsional stress, or shear stress which increases with the radial position within the bar. 

The boundary between the two regions and the radius rc of the core is determined by the position in the cross-section at which the shear stress is exactly equal to the yield stress Ry of the fluid. Since the shear stress is linearly related to the radial position ... 

A power law fluid is flowing under laminar conditions through a pipe of circular cross-section. At what radial position is the fluid velocity equal to the mean velocity in the pipe Where does this occur for a fluid with an n-value of 0.2 ... 

Traditional analysis methods on these measurements have been based around recording the movement of the radial position of the boundary r y with time t, from which a sedimentation coefficient, 5 (sec or Svedbergs, S, where 1 S = 10 sec) can be obtained (see, e.g. [30]) ... 

The simplest way computationally of obtaining a sedimentation coefficient distribution is from time derivative analysis of the evolving concentration distribution profile across the cell [40,41]. The time derivative at each radial position r is d c r,t)/co /dt)r where cq is the initial loading concentration. Assuming that a sufficiently small time integral of scans are chosen so that Ac r t)/At= dc r t)ldt the apparent weight fraction distribution function g (s) n.b. sometimes written as (s ) can be calculated... 

The fundamental equation of sedimentation equihbrium can be manipulated to define a new function with dimensions of molar mass (g/mol) called M r). M (r) at a radial position r is defined by... 

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