Normalized velocity

For normal velocity distribution in straight circular pipes at locations preceded by runs of at least 50 diameters without pipe fittings or other obstructions, the graph in Fig. 10-7 shows the ratio of mean velocity V to velocity at the center plotted against the Reynolds number, where D = inside pipe diameter, p = flmd density, and [L = fluid viscosity, all in consistent units. Mean velocity is readily determined from this graph and a pitot reading at the center of the pipe if the quantity Du p/ I is less than 2000 or greater than 5000. The method is unreliable at intermediate values of the Reynolds number. 

The dimensionless numbers are important elements in the performance of model experiments, and they are determined by the normalizing procedure ot the independent variables. If, for example, free convection is considered in a room without ventilation, it is not possible to normalize the velocities by a supply velocity Uq. The normalized velocity can be defined by m u f po //ao where f, is the height of a cold or a hot surface. The Grashof number, Gr, will then appear in the buoyancy term in the Navier-Stokes equation (AT is the temperature difference between the hot and the cold surface) ... 

FIGURE I 2.28 Normalized velocity versus Reynolds number in a ventilated room. ... 

A reduced scale of the model requires an increased velocity level in the experiments to obtain the correct Reynolds number if Re < Re for the prob lem considered, but the experiment can be carried out at any velocity if Re > RCj.. The influence of the turbulence level is shown in Fig. 12.40. A velocity u is measured at a location in front of the opening and divided by the exhaust flow rate in order to obtain a normalized velocity. The figure show s that the normalized velocity is constant for Reynolds numbers larger than 10 000, which means that the flow around the measuring point has a fully developed turbulent structure at that velocity level. The flow may be described as a potential flow with a normalized velocity independent of the exhaust flow rate at large distances from the exhaust opening— and far away from surfaces. 

FIGURE 12.40 Normalized velocity versus Reynolds number for a vortex exhaust. The location of the measuring point is indicated in the figure. 

By combining the result (32) for the step velocity (v t A/(i) with results (22) and (41) for the step separation far away from the center (i rsj the normal velocity is determined as... 

No slip Is used as the velocity boundary conditions at all walls. Actually there Is a finite normal velocity at the deposition surface, but It Is Insignificant In the case of dilute reactants. The Inlet flow Is assumed to be Polseullle flow while zero stresses are specified at the reactor exit. The boundary conditions for the temperature play a central role in CVD reactor behavior. Here we employ Idealized boundary conditions In the absence of detailed heat transfer modelling of an actual reactor. Two wall conditions will be considered (1) adiabatic side walls, l.e. dT/dn = 0, and (11) fixed side wall temperatures corresponding to cooled reactor walls. For the reactive species, no net normal flux Is specified on nonreacting surfaces. At substrate surface, the flux of the Tth species equals the rate of reaction of 1 In n surface reactions, l.e. 

Figure 3. Normal velocity profile in cm/sec for the 9.3% (mole fraction) hydrogen air fiame with a strain rate of a = 200 sec ...

Figure 2.25 Normalized velocity distributions over 20 micro channels obtained by Commenge et al. [116] for a specific class of flow chamber geometries.

The spin-displacement density function, c (z, Z), and the normalized displacement distribution function, P(z, Z), can be converted readily into the joint spin-velocity density function, q(z, vn), and the normalized velocity distribution function, P(z, vn), respectively, with the net velocity vn defined as vn = Z/A. Once the velocity density function is determined for each of the volume elements, the superficial average velocity, v, is calculated by [23] ... 

J. T. Hynes, R. Kapral, and M. Weinberg, Molecular theory of translational diffusion microscopic generalization of the normal velocity boundary condition, J. Chem. Phys. 70, 1456 (1970). 

Here r and v are respectively the electron position and velocity, r = —(e2 /em)(r/r3) is the acceleration in the coulombic field of the positive ion and q = /3kBT/m. The mobility of the quasi-free electron is related to / and the relaxation time T by p = e/m/3 = et/m, so that fi = T l. In the spherically symmetrical situation, a density function n(vr, vt, t) may be defined such that n dr dvr dvt = W dr dv here, vr and vt and are respectively the radical and normal velocities. Expectation values of all dynamical variables are obtained from integration over n. Since the electron experiences only radical force (other than random interactions), it is reasonable to expect that its motion in the v space is basically a free Brownian motion only weakly coupled to r and vr by the centrifugal force. The correlations1, K(r, v,2) and fc(vr, v(2) are then neglected. Another condition, cr(r)2 (r)2, implying that the electron distribution is not too much delocalized on r, is verified a posteriori. Following Chandrasekhar (1943), the density function may now be written as an uncoupled product, n = gh, where... 

The Vmax is a special point. At Vmax, the velocity does not depend on the concentration of substrate. Most assays are performed at substrate concentrations that are near saturating (the word near is usually used because Vmax, like Nirvana, is approached, not reached). For practical people, though, 99 percent of Vmax is as good as Vmax. The Vmax and v have exactly the same units. The Vmax conceals the dependence of the velocity on the concentration of enzyme. It s buried in there. If Vmax is expressed in units of micromolar per minute ((xM/min), then doubling the enzyme concentration doubles Vmax in contrast, if Vmax (and v) are given in units of micromoles per minute per milligram [p,mol/(min mg), i.e., specific activity], the normalized velocity and Vmax won t depend on enzyme concentration. 

For this reason, one utilizes a normalized velocity characteristic that is called the electrophoretic mobility (/, in cm2 V-1 s-1)... 

Because the length of the capillary and the applied voltage are typical for a specific system, the migration velocity is a characteristic specific for one system. It is therefore not possible to make comparisons between runs with different applied voltages or obtained with capillaries of different lengths. For this reason one utilizes a normalized velocity characteristic that is called the electrophoretic mobility (/t, in cm V s ) ... 

Though the velocity component parallel to the shock wave remains unchanged, Vi = V2, the velocity component normal to the shock wave, Ui — M2, changes through the shock wave. The change in the normal velocity component through the oblique... 

Since the Mach number of the inflow to the shock wave is given by Mj = wjui and that of the outflow from the shock wave is given by M2 = iV2/a2. the Mach number of the normal velocity perpendicular to the oblique shock wave, Mj, is represented by... 

The condition on the tangential velocity at the interface is not as obvious as that on the normal velocity. There is now ample experimental evidence that the fluid velocity at the surface of a rigid or noncirculating particle is zero relative to the particle, provided that the fluid can be considered a continuum. This leads to the so-called no-slip condition, which for a fluid particle takes the form... 

Burning rates can also be detd in an apparatus described in Ref 15, pp 120-21 and reproduced here as Fig A, using "highspeed photography . The "normal velocity in this case must be calcd by substracting from total velocity the rate of flow of gases from chamber A due to pressure... 

Detonation, Higher than Normal Velocity of. Same as Detonation, Supervelocity or Hypervelocity of... 

In Dunkle s Syllabus (Ref 7, p 259) it is stated that the overdriven wave can be defined as one "moving at higher than normal velocity ... 

At 77 K the velocity of a helium atom is 638 m sec i, so that in 1.91 xl0 3sec it will travel 1.91 x 10 3 x 638 x 10 or 1.2A. Thus, the condition that the adsorbate reside near the surface for one vibrational cycle is fulfilled by the normal velocity of helium and not by virtue of being adsorbed. Stated in alternate terms, the density of helium near a solid surface at 77 K is independent of the surface and is the same as the density remote from the surface. 

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