Momentum kinematical

Mutual Diffusivity, Mass Diffusivity, Interdiffusion Coefficient Diffusivity is denoted by D g and is defined by Tick s first law as the ratio of the flux to the concentration gradient, as in Eq. (5-181). It is analogous to the thermal diffusivity in Fourier s law and to the kinematic viscosity in Newton s law. These analogies are flawed because both heat and momentum are conveniently defined with respec t to fixed coordinates, irrespective of the direction of transfer or its magnitude, while mass diffusivity most commonly requires information about bulk motion of the medium in which diffusion occurs. For hquids, it is common to refer to the hmit of infinite dilution of A in B using the symbol, D°g. 

Having established that these assumptions are reasonable, we need to consider the relationship between the parameters of the actual offset jet and the equivalent wall jet that will produce the same (or very similar) flow far downstream of the nozzle. It can be shown that the ratio of the initial kinematic momentum per unit length of nozzle of the wall jet to the offset jet,, and the ratio of the two nozzle heights,, depend on the ratio D/B, where D is the offset distance betw een the jet nozzle and the surface of the tank, and h, is the nozzle height of the offset jet. The relationship, which because of the assumptions made in the analysis is not valid at small values of D/hj, is shown in Fig 10.72. 

Figures 10.75 and 10.76 show the initial kinematic momentum required to meet this criterion as a function of the buoyancy velocity and the length of the tank, for different values of the allowable concentration Qj. , and critical veloc-ity As we would expect, the required momentum increases both as the length of the tank increases and as the buoyancy of the contaminant increases.

FIGURE 10.75 Required initial kinematic momentum, f/p, as a function of the length of the tank, L, and the buoyancy velocity, v, when the critical contour criterion is applied with the critical concentration, C ,j, equal to 5% and the cross-drafts equal to 0.05 m s". ... 

In kinetics, Newton s second law, the principles of kinematics, conservation of momentum, and the laws of conservation of energy and mass are used to develop relationships between the forces acting on a body or system of bodies and the resulting motion. 

It will be shown that the momentum and thermal boundary layers coincide only if the Prandtl number is unity, implying equal values for the kinematic viscosity (p./p) and the thermal diffusivity (DH = k/Cpp). 

It is thus seen that the kinematic viscosity, the thermal diffusivity, and the diffusivity for mass transfer are all proportional to the product of the mean free path and the root mean square velocity of the molecules, and that the expressions for the transfer of momentum, heat, and mass are of the same form. 

An analogy exists between mass transfer (which depends on the diffusion coefficient) and momentum transfer between the sliding hquid layers (which depends on the kinematic viscosity). Calculations show that the ratio of thicknesses of the diffnsion and boundary layer can be written as... 

The Reynolds number Re = vl/v, where v and l are the characteristic velocity and length for the problem, respectively, gauges the relative importance of inertial and viscous forces in the system. Insight into the nature of the Reynolds number for a spherical particle with radius l in a flow with velocity v may be obtained by expressing it in terms of the Stokes time, t5 = i/v, and the kinematic time, xv = l2/v. We have Re = xv/xs. The Stokes time measures the time it takes a particle to move a distance equal to its radius while the kinematic time measures the time it takes momentum to diffuse over... 

In Section III we discuss the applicability of these models for kinematically complete experiments on target single ionization in ion-atom collisions, which have been performed using the technique of recoil-ion momentum spectroscopy. The examples illustrated will include the pioneering experiments [2,4,5] of... 

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