Profile initial velocity

An analytical solution of the interaction in the case of isothermal main and directing jets, assume that the main stream (Fig. 7.57), supplied with initial velocity (t oi) through a nozzle that has internal diameter (Tqj), is developing within a zone ( -/q, 0) as a free jet. The momentum (/,) of the jet within the zone ( -Iq -F /, 0) remains equal to the initial momentum (/oi)> the velocity distribution in the cross-section of interaction in the plane XY remains the same within the zone (0, X ). The axisymmetric main stream within the zone (0, X j) is substituted by the linear flow with velocity profile that can be described by the formula... 

The initial conditions for the velocity components are set up so that there is a tubular shear layer aligned along the 2 -direction at time t = 0. The tv-velocity has a top-hat profile with a tan-hyperbolic shear layer. Stream wise and azimuthal perturbations are introduced to expedite roll-up and the development of the Widnall instability. The details can be found in [7]. The initial velocity field is made divergence-free using the Helmholtz decomposition. The size of the computational domain (one periodic cubical box) is 4do on each side. 

The time-dependent simulations of free jets discussed here focus on the vortex dynamics and transition to turbulence downstream of the jet exit. For the sake of computational efficiency, the author concentrates on the study of jet flow initialized with laminar conditions with a thin rectangular vortex sheet having slightly rounded-off corner regions and uniform initial momentum thickness [9]. Initial conditions for the simulated jets involve top>-hat initial velocity profiles... 

Enzyme kinetics is an important tool for assaying enzyme activities and for determining enzyme mechanisms. Although other techniques can provide useful information on enzyme mechanisms, the kinetics has to be the ultimate arbiter because it looks at the reaction while it is taking place. Initial velocity patterns, inhibition patterns, patterns of isotopic exchange, pH profiles, and isotope effects are all kinetic tools that allow one to determine kinetic mechanisms, chemical mechanisms, and transition state structures. 

The simulations were performed assuming that the flow is laminar. Additionally, the contact angle is assumed to be known. The initial velocity is assumed to be zero everywhere in the domain. The initial fluid temperature profile is taken to be linear in the natural convection thermal boundary layer and the thermal boundary layer thickness, 5j, is evaluated using the correlation for the turbulent natural convection on a horizontal plate as, Jj. =1. 4(vfiCil ... 

Relationship between the initial velocity (v) and the substrate concentration [S] for an allosteric enzyme that shows a homotropic effect. The substrate functions as a positive modulator. The profile is sigmoidal, and during the steep part of the profile, small changes in [S] can cause large changes in v. Ko.i represents the substrate concentration corresponding to half-maximal velocity. 

Early work by Keilin and Hartree (1948) demonstrated a bellshaped profile for the pH-dependence of the initial velocity with a peak at pH 5.6. The enzyme is specific for -D-glucose ... 

The sensitivity of the axisymmetric combustor flow dynamics to the actual choice of inlet velocity conditions was also examined. Figure 11.3 compares the results of initializing the simulations with the turbulent-pipe or LM-6000 swirling conditions and otherwise identical initial conditions S = 0.56, Uo — 100 m/s, STP). The flow visualizations depict the significant effects on the combustor vortex dynamics of changing the specifics of the velocity profiles used to initialize the LES, with noticeably more-axisymmetric features observed in the flow features for the LM-6000 case. The LM-6000 initial velocity conditions (Fig. 11.2a) involve a peak tangential velocity component located farther away from the axis and a more moderate radial gradient of the axial velocity. A clear consequence of these initial condition specifics, apparent in Fig. 11.3a, is that the LM-6000... 

In analyzing initial velocity or inhibition patterns, one considers separately the effects on the slopes of such reciprocal plots (which represent effects on VIK) and on the intercepts (which represent effects on V). Similarly, one considers isotope effects on V or VIK separately, and one plots the logarithms of V or VIK versus pH for pH profiles. 

This may change the initial velocity pattern, as in the case of fructose-6-sulfate, which is a slow substrate for phosphofructokinase. This substrate has lost sufficient affinity for the enzyme that it binds only when MgATP is present, and thus the mechanism changes from a random one with both substrates sticky with fructose 6-phosphate (fructose-6-P) to an equilibrium ordered one with MgATP adding first (19). Slow alternate substrates give cleaner and more easily interpreted pH profiles, and isotope effects are often (but not always) more fully expressed (see Sections VII,A and VII,B below). 

Amylase has been prepared from defatted hawk eye soybean flour. The enzyme-concentration dependence of the initial velocity for the hydrolytic reaction was investigated at pH 5.4 in a range of the enzyme concentrations and it was found that the initial velocity was proportional to the enzyme concentration in this range. The hydrolyses of maltodextrin (DPn = 74.4) and soluble starch catalysed by soybean /3-amylase were investigated in the pH range from 3.0 to 9.1 at 25 C, and and kjnax each substrate were determined at each pH. The pH-rate profile showed a bell-shaped curve, and the pH optimum was at 5.85. From Dixon plots of V and the pAT values were found to be 3.5 and... 

When two gas streams collide, the initial velocity profiles characteristic of a free flow deform in the vicinity of the impingement plane and additional components of velocity (radial, axial, or circumferential, depending on the impinging streams configuration) appear as a result of this deformation (Figures 21.28 and 21.29). 

Abstract This chapter relates to the liquid sheets and their instabihty. Liquid sheet instability is due to the interaction between the hquid and its surrounding fluid. When the amplitude of a perturbation grows and reaches a critical value, sheet is disintegrated forming liquid ligaments. Here, the linear and nonlinear instability of an inviscid and viscous liquid sheet is discussed, showing the effect of the aerodynamic forces on the growth rate of the initially small perturbations. Other effects, such as the effect of initial velocity profile on the instability are also discussed. 

For all fluids entering a small pipe from either a very much larger one or from a reservoir, the initial velocity profile will be approximately flat, and will then imdergo a progressive change until fully developed flow is established, as shown schematically in Figure 3.24. 

In fitting pH profiles for For V/K, the parameters vary by a factor 10 per pH unit above or below the which causes loss of activity. In such cases, it is better to assume that the variance of the initial rates is proportional to the square of the initial velocity. This corresponds to a constant percent error (i.e, 1 0.1 and 10 1), and requires weights in reciprocal plots. 

When the initial velocity profile is uniform and there are no abrupt contraction (Zc = 0) and expansion = 0), one can take into account the effects of momentum change in the entrance region by using K (x>) which includes the increased wall shear in the entrance region but separates out the downstream fully developed flow pressure drop due to wall shear to give... 

A setup wizard that takes the user though a defined set of questions to generate the initial velocity and pressure profiles. 

Fig. 9.10. Observed and simulated TOF profiles of a molecular beam of OH radicals exiting the Stark decelerator when the deceierator is operated at a phase angie of 70° for a synchronous molecule with an initial velocity of 470m/s (o), 450m/s (6), 430 m/s (c) and 417 m/s (d). The molecules that are accepted by the decelerator are split off from the molecular beam and arrive at later times, and with the final velocities as indicated, in the detection region. (Reproduced from S.Y.T. van de Meerakker et with permission. 2006 by Annual Reviews www.annuaireviews.org.)...

The calculated PBX-9502 results are presented in Tables 4.5 and 4.6. The effects of jet composition, diameter, and velocity were examined. The calculated profiles for a 0.4 cm diameter Copper jet with a 0.7 cm/ijsec initial velocity are shown in Figure 4.30. The Copper jet initiates an overdriven detonation smaller than the critical diameter, which enlarges to greater than the critical diameter of self-confined PBX-9502 when shocked by a 0.7 cm/ps Copper jet. When the PBX-9502 is shocked by a 0.5 cm/psec Copper jet, the detonation is decayed by side and rear rarefactions before it enlarges to the critical diameter, as shown in Figure 4.31. 

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