Time-Averaged Characteristics

As described above, the plume becomes wider and more dilute as it evolves in the streamwise direction, thus ccenteriine and a are changing with x. The decrease of the time-averaged concentration along the centerline of the plume follows a v 1 profile for x/H 2 (Fig. 5.8). This power law decrease agrees well with the time-averaged concentration field predicted by modeling efforts that assume 

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Laminar and Turbulent Flow, Reynolds Number These terms refer to two distinct types of flow. In laminar flow, there are smooth streamlines and the fuiid velocity components vary smoothly with position, and with time if the flow is unsteady. The flow described in reference to Fig. 6-1 is laminar. In turbulent flow, there are no smooth streamlines, and the velocity shows chaotic fluctuations in time and space. Velocities in turbulent flow may be reported as the sum of a time-averaged velocity and a velocity fluctuation from the average. For any given flow geometry, a dimensionless Reynolds number may be defined for a Newtonian fluid as Re = LU p/ I where L is a characteristic length. Below a critical value of Re the flow is laminar, while above the critical value a transition to turbulent flow occurs. The geometry-dependent critical Reynolds number is determined experimentally. 

Hydrodynamic effects on suspended particles in an STR may be broadly categorized as time-averaged, time-dependent and collision-related. Time-averaged shear rates are most commonly considered. Maximum shear rates, and accordingly maximum stresses, are assumed to occur in the impeller region. Time-dependent effects, on the other hand, are attributable to turbulent velocity fluctuations. The relevant turbulent Reynolds stresses are frequently evaluated in terms of the characteristic size and velocity of the turbulent eddies and are generally found to predominate over viscous effects. 

The derivation of the equations of the Debye-Huckel theory did not require differentiation between a solution of a single electrolyte and an electrolyte mixture provided that the limiting law approximation Eq. (1.3.24), was used, which does not contain any specific ionic parameter. If, however, approximation (1.3.29) is to be used, containing the effective ionic diameter ay it must be recalled that this quantity was introduced as the minimal mean distance of approach of both positive and negative ions to the central ion. Thus, this quantity a is in a certain sense an average of effects of all the ions but, at the same time, a characteristic value for the given central... 

The reaction is monitored by TLC (silica gel, 6 1 hexanes ethyl acetate). Typical characteristics are Rf- 0.15, a yellow spot [tris(acetonitrile)chromium tricarbonyl intermediate], and Rf = 0.51, a red spot (product complex). Total reaction time averaged 180 hr. 

One of the more important aspects of external flows is that the solid flow boundary is of finite extent (in the downstream direction) so that the flow must be treated as developing boundary layers in which time average steady-state conditions cannot be reached before the solid surface terminates. Another characteristic of such flows is... 

The whole volume of oceanic water is considered as a single biocenosis in which the flux of organic matter produced in surface layers then descending to the bottom of the ocean is the main connecting factor. All model parameters are assumed to be able to change as functions of place and time, and their parametric description is made by average characteristics (i.e., deterministic models). 

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