Specific velocity

Figure 1.4 (a) The wave due to an electron travelling with specific velocity in the x direction, (b)... 

Table 22.4 Pipeline capacities at specific velocities (metric SI units)...

The mesh plots show different slopes of productivity, depending on i and qp, and the poly(3HB) content. How an increase in i or qp enhances productivity is presented in Fig. 5, starting from two different pairs of actual jli and qp values. Each of the initial values was increased by 20% or 40%. If both specific velocities are increased, then the productivity increases in the same way. Starting from jli = 0.35 h 1 and qp = 0.15 g g 1 h 1 (A) optimization of the growth rate has a stronger effect over a broader range of final poly(3HB) contents than starting from jli = 0.2 h 1 and qp = 0.05 g g 1 h 1 (B). 

The cells can be grown at high dilution rates in the first fermenter, usually under the limitation of a growth substrate which triggers poly(3HB) synthesis, to obtain cells at the beginning of the poly(3HB) accumulation phase when entering the second fermenter. Product formation in the second vessel can then take place at high specific velocity. 

A maximum value of the heat transfer coefficient is attained at some specific velocity which depends on the particle size. 

Let the rear boundary of reaction wave move with.a specific velocity Up along the line P in the x,t-plane as in Fig 9 of Ref 2 (our Fig 1). Then initial data are prescribed along two lines. One is the x-axis, which is spacelike with. respect to the material behind it and carries the quantity u = 0 (if. the material is initially at rest), and p=p0. The other line is P, which is timelike, or subsonic to the gas flow, since it is identical with the path of the adjacent gas particles it carries velocity Up. The discontinuity of the reaction wave is represented by the line W. The deductions on uniqueness which. can be Used for non-reactive flow (See Ref 2, pp 136-37) cannot be applied here directly because of the interference of the unknown discontinuity W. 

One can analyze the Jeffery-Hamel flow using a nondimensional velocity scaled by the maximum velocity at a radial location [429]. This approach permits determination of the local shape of the velocity profiles but still requires an integral mass-flow constraint to determine the local maximum velocity and hence the specific velocity profiles (i.e., in m/s). Nevertheless, using this approach and the limit of small angle, but large Reynolds number, permits the determination of the separation point as a function of the combined parameter Rea2 alone. 

In the patterns of reactivity treatment of polymer radicals, which was developed by Bamford and Jenkins (1963 Jenkins, 1967) from the earlier work of Alfrey and Price (1947) and Mayo and Walling (1950), the specific velocity constant ks for a radical reaction is given by (15), where /c3T is the rate... 

The manufactured 90 mm x 90 mm x 10 mm three-layered B4C/B4C-30wt%SiC tiles were tested as armor [67], The photographs of the experiment set-up of the ballistic test as well as a residual impression in the clay box that was used as one of the criteria in the ballistic performance of laminates are shown in Fig. 7.17. The ballistic penetration tests were performed to evaluate the ballistic performance of the laminates. Depth of penetration tests were used to evaluate the ballistic performance of the composite laminates. In addition, pure B4C monolithic ceramics were used as a standard for the test. Test panels were made using the three-layered B4C/B4C-SiC laminate and B4C monolithic ceramic material as the hard face. While the B4C monolithic tile had 100% of its theoretical density, the three-layered B4C/B4C-30wt%SiC laminates had about 3-4% of porosity. A commonly used Spectra fiber-reinforced polymer composite was used as backing plates. The targets were mounted on clay and the projectile was shot at the target at a specific velocity. 

With reference to a simple reaction with constant stoichiometric coefficients, and unless otherwise specified, the reaction rate R [moles time-1 volume-1] measures the specific velocity of destruction of those reactants (and of formation of those products) that appear with unitary stoichiometric coefficients. The reaction rates of each other component are proportional to R according to their stoichiometric coefficients. 

Two basic components of plate height in packed columns are Hf and HD, given by Eqs. 11.23 and 11.28, respectively. When these two terms are equal—which occurs at the specific velocity v c = AICm—we are at the transition point between a flow-controlled and diffusion-controlled random walk. (This transition, as it turns out, occurs near the minimum of each of the plate height curves shown in Figure 12.2.) The velocity u is a fundamental parameter characterizing every packed column system. Its value can be expressed by (see Eqs. 11.23 and 11.28)... 

For heterogeneous reactions, the observed reaction rate is determined by the amount of surface covered by reacting molecules and by the specific velocity of the surface reaction. The influence of temperature on the rate, therefore, must include two factors, the effect on the surface area covered, and the effect on the surface reaction itself. 

The mixture of molecular ion and fragments is accelerated to specific velocities using an electric field and then separated on the basis of their different masses by deflection in a magnetic or electrostatic field. Only the cations are detected and a mass spectrum is a plot of mass-to-charge ratio (w/z) on the x-axis against the number of ions (relative abundance, RA, %) on the y-axis. A schematic of the components of a mass spectrometer is shown in Fig. 30.2 and an example of a line-graph-type mass spectrum in Fig. 30.3. 

An allosteric dimer has an interaction factor, a, of 0.2 when analyzed according to the sequential interaction model (i.e., the binding of the first molecule of S increases the binding constant of the vacant site by a factor of 5—the dissociation constant of the vacant site decreases to 0.2 of the original value), (a) What is the relative distribution of enzyme species at [S] = 0.3 Ks (b) What is the specific velocity at [S] = 0.3 Ks (c) Will the calculated value of n,pp equal 2 ... 

The velocity constant k is expressed as the velocity constant per unit geometric surface area of the solid. Should the catalyst have internal surfaces and be characterized by a specific velocity constant referred to its total surface area of, say, k, = 10 cm./sec., this will have to be converted to refer to the geometric particle surface by multiplication by the specific surface area in cm. /g. and division by the external geometric particle surface area per gram of catalyst. For a high surface area of, say, 100 m. /g., a particle size of 0.25-cm. radius and a density of 1.2 g./cm., this would yield a constant k of the order of fc = 0.05. 

Let us examine the measured catalytic behavior of an assembly of different catalyst preparations (Weisz, 12), assumed to be of identical chemical composition and thus being associated with identical real specific velocity constants A , however differing in the diffusion modulus (p, due to any or all of the above-mentioned differences in mechanical properties such as particle size, diffusivity, and specific surface area. Tracing the reaction rates which would be observed over a wide temperature range of operation on such samples leads to a series of curves A, B, C, D as shown in Figure 14, ail of a similar shape but geometrically dis-... 

Under the assumption that Baker s mechanism is valid, Farkas and Flynn draw the following conclusions from their results. The rate of the catalyzed reaction depends on the concentration of the amine complex and on the specific velocity constant for the reaction which involves this complex and the alcohol. Since the diazabicyclooctane is free from steric hindrance and the nitrogen atoms are readily accessible to the reactants, the formation of the complex between this molecule and the isocyanate molecules takes place more readily than with an amine having a carbon-nitrogen bond capable of free rotation around the nitrogen. Related to the postulate of higher... 

Note that the preceding velocity is the interstitial injection velocity normalized by qt/(A( )), and that it is dimensionless. Lake (1989) and Green and Willhite (1998) used the term specific velocity for the dimensionless velocity. In this book, we follow their terminology. Corresponding to the front of the component C, we assume the water saturation is 8 3. According to the Buckley-Leverett theory (1942), the specific velocity of 8 3 is... 

Because 8 3 is the water saturation at the chemical front of Q, their specific velocities must be the same, resulting in... 

In the case of polymer flooding with a sharpening front, polymer concentration jumps from zero (its initial value) to its injection concentration Ciq. D, in Eq. 2.88 becomes Dp. In this case, the high polymer concentration solution flushes the initial zero polymer concentration solution. As discussed in Section 2.5 on types of fronts, there is a concentration shock. Corresponding to this concentration shock, there is a saturation shock from S p to Swi. The specific velocity of this saturation shock, (vd )as > is... 

These two specific velocities must travel at the same specific velocity. Thus,... 

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