Velocity characteristic

It can be shown that c is dependent only on Tg, Mg, and y and that it is independent of the pressure and the physical dimensions of the combustion chamber and exhaust nozzle r, as defined in Eq. (1.74), is a parameter used to describe the energetics of combustion. 

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To generate characteristic velocities and bring a molecular system toequillbrium at th e sim illation temperature, atom s are allowed to in teract W ith each other through the equation s of motion. For isothermal simulations, a temperature bath" scales velocities to drive the system towards the simulation temperature,. Scaling occurs at each step of a simulation, according to equation 2S. 

Adsorption Chromatography. The principle of gas-sohd or Hquid-sohd chromatography may be easily understood from equation 35. In a linear multicomponent system (several sorbates at low concentration in an inert carrier) the wave velocity for each component depends on its adsorption equihbrium constant. Thus, if a pulse of the mixed sorbate is injected at the column inlet, the different species separate into bands which travel through the column at their characteristic velocities, and at the oudet of the column a sequence of peaks corresponding to the different species is detected. 

Davies (Turbulence Phenomena, Academic, New York, 1972) presents a good discussion of the spectrum of eddy lengths for well-developed isotropic turbulence. The smallest eddies, usually called Kolmogorov eddies (Kolmogorov, Compt. Rend. Acad. Sci. URSS, 30, 301 32, 16 [1941]), have a characteristic velocity fluctuation given by... 

The concepts of shp velocity and characteristic velocity are useful in defining the Flooding point and operational regions of different types of column contactors. The shp (or relative) velocity is given by the equation ... 

From this has been derived the concept of characteristic velocity which is defined by the general equation ... 

The value of may be identified with the average terminal velocity of the droplets within the contactor. Each different type of contactor will have a different and unique characteristic velocity. 

Figure 7-15 shows plots of Pumping number Nq and Power number Np as functions of Reynolds number Np for a pitched-blade turbine and high-efficiency impeller. Hicks et al. [8] further introduced the scale of agitation, S, as a measure for determining agitation intensity in pitched-blade impellers. The scale of agitation is based on a characteristic velocity, v, defined by... 

In geometrically similar systems, the characteristic velocity becomes... 

Thus, during geometric scale-up, the characteristic velocity is held constant by holding NqND constant. Qp is determined from the Pumping number and Figure 7-15. is a linear function of the characteristic velocity and is determined by... 

A particular fluid flow problem must have an associated characteristic length L and characteristic velocity V. These values may be more or less arbitrarily specified, with the only constraint being that they represent some typical scales. For example, if the problem involves a flow past a sphere, L could be the diameter of the sphere and V could be the velocity of the fluid at infinity. The characteristic length and characteristic velocity also fix a characteristic time scale T = L/V. 

Choose the characteristic velocity m so, that total heat flux on the wall is fully expended for liquid evaporation (the heating without any losses of heat r = 1). We conclude that... 

The fractional dispersed phase holdup, h, is normally correlated on the basis of a characteristic velocity equation, which is based on the concept of a slip velocity for the drops, VgUp, which then can be related to the free rise velocity of single drops, using some correctional functional dependence on holdup, f(h). 

Under normal circumstances, the use of a characteristic velocity equation of the type shown above can cause difficulties in computation, owing to the existence of an implicit algebraic loop, which must be solved, at every integration step length. In this the appropriate value of L or G satisfying the value of h generated in the differential mass balance equation, must be found as shown in the information flow diagram of Fig. 3.54. 

As explained in Sec. 3.3.1.11, in order to avoid difficulties in the IMPLICIT LOOP solution of the characteristic velocity equation for dispersed phase... 

If the length scales associated with changes in velocity are normalized by Vv (characteristic length scale for Stokes flow), length scales associated with changes in curvature are normalized by Ss (typical striation thickness) and velocities normalized by V (a characteristic velocity), then the normal stress condition becomes,... 

In this section, we consider flow-induced aggregation without diffusion, i.e., when the Peclet number, Pe = VLID, where V and L are the characteristic velocity and length and D is the Brownian diffusion coefficient, is much greater than unity. For simplicity, we neglect the hydrodynamic interactions of the clusters and highlight the effects of advection on the evolution of the cluster size distribution and the formation of fractal structures. 

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 forced convection, the velocity of the liquid must be characterized by a suitable characteristic value Vih e.g. the mean velocity of the liquid flow through a tube or the velocity of the edge of a disk rotating in the liquid, etc. For natural convection, this characteristic velocity can be set equal to zero. The dimension of the system in which liquid flow occurs has a certain characteristic value /, e.g. the length of a tube or the longitudinal dimension of the plate along which the liquid flows or the radius of a disk rotating in the liquid, etc. Solution of the differential equations (2.7.5), (2.7.7) and (2.7.8) should yield the value of the material flux at the phase boundary of the liquid with another phase, where the concentration equals c. ... 

The Cartesian coordinates of the system, x, y and z, are referred to the characteristic length / and the components of the velocity vx> vy and vz within the Prandtl layer are referred to the characteristic velocity V0>... 

In convective diffusion to a rotating disk, the characteristic velocity V0 is given by the product of the disk radius r, as a characteristic dimension of the system, and the radial velocity co, so that the Reynolds number is given by the equation... 

For the flow induced by the rotating hemisphere, the leading edge of the flow boundary layer occurs at the pole of rotation. The surface distance, x, from the leading edge is equal to ad. One may also take aQsinff as the characteristic velocity for every local point on the spherical surface. Thus, the quantities, Shx, Rex, and fx can be expressed as... 

In each of these groups, the characteristic length is the cyclone diameter, D, and the characteristic velocity is V = AQ/tzD1. Various empirical hydrocyclone models indicate that the relationship between these groups is... 

This simple calculation gives a result close to that obtained by integrating over the three-dimensional Maxwell velocity distributions for both A and B. In this case, the same expression is obtained with the characteristic velocity of approach between A and B... 

In some cases, the characteristic velocity can cause difficulties in solution, owing to the presence of an implicit equation. In this the appropriate value of L or Gn satisfying the value of hn generated by the differential material balance equation must be found by root finding algorithms increasing computation time required. 

The transition from a laminar boundary layer to a turbulent boundary layer occurs at the value Rex = 3.2 x 105. In the Reynolds number Rex the free stream velocity vand the distance x from the leading edge of the plate are used as the characteristic velocity and linear dimension. 

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