Velocity calculations for

However, it was Maxwell in 1848 who showed that molecules have a distribution of velocities and that they do not travel in a direct line. One experimental method used to show this was that ammonia molecules are not detected in the time expected, as derived from their calculated velocity, but arrive much later. This arises l om the fact that the ammonia molecules tnterdiffuse among the air moixules by intermolecular collisions. The molecular velocity calculated for N-ls molecules from the work done by Joule in 1843 was 5.0 xl02 meters/sec. at room temperature. This implied that the odor of ammonia ought to be detected in 4 millisec at a distance of 2.0 meters from the source. Since Maxwell observed that it took several minutes, it was fuUy obvious that the molecules did not travel in a direct path. 

Detonation velocities calculated for densities of 0.73-1.80 are compared with those determined at Bruceton. Values calculated for TNT from the LSZK equation of state at densities of 1.00-1.625 are given for the following detonation parameters ... 

For both fluences, only one front was visible until about 100 ns, after which two fronts became distinguishable. As can be seen in Figs. 41a and b, the velocity of this initial shock wave rapidly decays well below the velocity at which the blast wave next appears. This leads to the conclusion that this initial shock is separate from the blast wave or product front. Therefore, the first velocities calculated for both the blast wave and product front in both the 50 and 250 mjcm 2 fluence laser can be questioned, since they are based on the final position of the initial shock. Because of this doubt, these points have been left open in contrast to the filled points used for the remainder of the blast wave and product front points. The apparently separate initial shock is of particular interest, because it appears in both fluence cases and persists for a similar duration even though the propagation distance is quite different. This indicates that a relatively strong material ejection occurs near the peak of the laser pulse and then abruptly stops. In both fluence... 

Collision efficiency was calculated by the method proposed for the first time by Dukhin Derjaguin (1958). To calculate the integral in Eq. (10.25) it is necessary to know the distribution of the radial velocity of particles whose centre are located at a distance equal to their radius from the bubble surface. The latter is presented as superposition of the rate of particle sedimentation on a bubble surface and radial components of liquid velocity calculated for the position of particle centres. Such an approximation is possibly true for moderate Reynolds numbers until the boundary hydrodynamic layer arises. At a particle size commensurable with the hydrodynamic layer thickness, the differential of the radial liquid velocity at a distance equal to the particle diameter is a double liquid velocity which corresponds to the position of the particle centre. Such a situation radically differs from the situation at Reynolds numbers of the order of unity and less when the velocity in the hydrodynamic field of a bubble varies at a distance of the order ab ap. At a distance of the order of the particle diameter it varies by less than about 10%. Just for such conditions the identification of particle velocity and liquid local velocity was proposed and seems to be sufficiently exact. In situations of commensurability of the size of particle and hydrodynamic boundary layer thickness at strongly retarded surface such identification leads to an error and nothing is known about its magnitude. 

War local value of the gas velocity calculated for the whole column cross-section, m/s ... 

The data obtained by the spherical flame model are in close agreement with the aforementioned results. The model has been used for the laminar flame velocity calculation for the finite radius of the 3-cm sphere for 70% H2 mixture at elevated... 

Power consuiTmtion has also been measured and correlated with impeller Reynolds number. The velocity head for a mixing impeller can be calculated, then, from flow and power data, by Eq. (18-3) or Eq. (18-5). 

A slide surface is a surface where the tangential velocity can be discontinuous as shown in Fig. 9.9. Separate velocities are calculated for each side. Slide lines are useful for modeling phenomena such as sliding friction or flow through pipes. 

Free energy calculations rely on the following thermodynamic perturbation theory [6-8]. Consider a system A described by the energy function = 17 + T. 17 = 17 (r ) is the potential energy, which depends on the coordinates = (Fi, r, , r ), and T is the kinetic energy, which (in a Cartesian coordinate system) depends on the velocities v. For concreteness, the system could be made up of a biomolecule in solution. We limit ourselves (mostly) to a classical mechanical description for simplicity and reasons of space. In the canonical thermodynamic ensemble (constant N, volume V, temperature T), the classical partition function Z is proportional to the configurational integral Q, which in a Cartesian coordinate system is... 

The functional B[(2(r)] actually depends only on the velocity dQ/dr at the moment when the non-adiabaticity region is crossed. If we take the path integral by the method of steepest descents, considering that the prefactor B[(2(r)] is much more weakly dependent on the realization of the path than Sad[Q(A]> we shall obtain the instanton trajectory for the adiabatic potential V a, then B[(2(t)] will have to be calculated for that trajectory. Since the instanton trajectory crosses the dividing surface twice, we finally have... 

Flow coefficients and pressure coefficients can be used to determine various off-design characteristics. Reynolds number affects the flow calculations for skin friction and velocity distribution. 

An important practical question is, what is the representative pipe diameter in loading circuits comprising different sizes of pipe This has a large effect on the values calculated for velocity and velocity-diameter product. As an example, static ignition of ester mist in a rail car (5-1.3.1) involved 1450 gpm through a 6-in. pipe (v = 5 m/s and vd = 0.76 mVs) followed by a short 4-in. dip pipe assembly (y = 11 m/s and vd = 1.15 mVs). Were nonconductive liquid flow rate restrictions applied to the semiconductive ester (time constant —0.01 s) involved in this fire, the flow rate based on the 4-in. pipe would be unacceptably large based either on a 7 m/s maximum velocity or a 0.80 mVs maximum vd product. However, based on the 6-in. pipe upstream the flow velocity is less than 7 m/s and also meets API s vd < 0.80 mVs criterion. 

The silica dispersion showed the smallest retention volume. It should be noted, however, that the authors reported that the silica dispersion required sonicating for 5 hours before the silica was sufficiently dispersed to be used as "pseudo-solute". The retention volume of the silica dispersion gave the value of the kinetic dead volume, /.e., the volume of the moving portion of the mobile phase. It is clear that the difference between the retention volume of sodium nitroprusside and that of the silica dispersion is very small, and so the sodium nitroprusside can be used to measure the kinetic dead volume of a packed column. From such data, the mean kinetic linear velocity and the kinetic capacity ratio can be calculated for use with the Van Deemter equation [12] or the Golay equation [13]. 

The results obtained were probably as accurate and precise as any available and, consequently, were unique at the time of publication and probably unique even today. Data were reported for different columns, different mobile phases, packings of different particle size and for different solutes. Consequently, such data can be used in many ways to evaluate existing equations and also any developed in the future. For this reason, the full data are reproduced in Tables 1 and 2 in Appendix 1. It should be noted that in the curve fitting procedure, the true linear velocity calculated using the retention time of the totally excluded solute was employed. An example of an HETP curve obtained for benzyl acetate using 4.86%v/v ethyl acetate in hexane as the mobile phase and fitted to the Van Deemter equation is shown in Figure 1. 

Table 1, values for the optimum velocity can be calculated for different values of the separation ratio of the critical pair. The results are shown in Figure 3. 

Cross-draft velocity was normalized by dividing the measured cross-draft ve-locit by the capture velocity calculated at the tatik centerline. Capture velocity at the tank centerline was calculated using Silverman s - centerline velocity (Eq. (JO.l)) for unflanged slot hoods. There was considerable scatter in the data, show ing chat cross-draft velocity alone is not responsible for low capture efficiency. 

Rectangular Flanged Openings- C i Jhe velocity fields for these openings must be calculated for each direction individually. Here and are the nondimensional velocities parallel to rhe opening plane and v. is the nondimensional velocity perpendicular to the opening plane directed toward the opening plane ... 

Figure 6.33 can be used to calculate the initial velocity Vj for bursting pressurized vessels filled with ideal gas. The quantities to be substituted, in addition to those already defined (p, po, and V), are... 

Thus, is 20% of the energy calculated for nonideal gases or for flash-vaporization situations. For scaled energies ( ) larger than about 0.8 as calculated by Eq. (9.3.5), the calculated velocity is too high, so method 3 should be applied. 

For cylinders with horizontal axes, the initial trajectory will be low, typically 5° or 10°. Table 9.10 shows maximum ranges for initial velocities calculated by each method with various low trajectory angles assumed. 

Assuming an eluent viscosity of 1 cP, K can be read from Table 2.1 and the theoretical linear velocity of an eluent at any given pressure can be calculated. For the less rigid Sephadex G types, the maximum operating pressures at which the relation between superficial velocity and applied pressure is still linear are given in Table 2.1. Exceeding the pressures listed will result in bead compression, a reduction in pore volume, and a decreased flow rate. 

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