Velocity relation between velocities

Relation between Velocities of Primary Collision Mechanism and Secondary Ions... 

The objective of the work of Wood Kirkwood described in Ref 36a is somewhat different, namely, to give an account of the relation between velocity and radius of curvature of the wave front, rather than the charge radius. The work of W K is closely related to the Curved Front Theory of Eyring et al, although the basic model, as well as the objective, is considerably different. 

CA 49, 2073 (1954) (Relation between velocity and radius of curvature of the deton wave) 36b) Anon, Military Explosives ,... 

See Fiscebeck, Zeitsch. anorg. Chem., 1926, 154, 261. For the relation between velocity of reaotion and composition of iron-sulphur mixtures, see Jorissen and Groeneveld, Bee. Trav. chim., 1928, 47, 737. 

For hydrates in ocean sediments, the technology for detecting the BSR was determined in 1953 with the development of a precision ocean depth recorder (Hamblin, 1985, p. 11). In this technique a sonic wave penetrates (and is reflected from) the ocean floor, with the time recorded for the return of the reflected wave to the source. Velocity contrasts beneath the ocean floor mark a change in material density, such as would be obtained by hydrate-filled sediments overlying a gas. BSRs related to hydrates are normally taken as indications of velocity contrasts between velocity in hydrated sediments and a gas, marked by a sharp decrease in sonic compressional velocity (Vp) and a sharp increase in shear velocity (Vs) (Ecker et al., 1996). 

Water flow s upward through a bed of sand, causing an expansion of the sand. Determine the condition for equilibrium and deduce a possible relation between velocity and porosity. 

The theoretical relation between velocity and end height has already been developed in Chapter 8 and we have exhibited a special form of this relationship in the first part of this chapter. Let us, however, return to the fundamental equation, Eq. (8-17)... 

Combining (29) and (30) we have Debye and Hiickel s relation between velocity and potential... 

Schuette and McCreery [34] demonstrated that with decreasing wire diameter there was a significant increase in current enhancement and modulation depth. This approached 100% modulation for a wire of diameter, d = 25 pm vibrated at 160 Hz. They showed that in these circumstances, for low Re numbers, the limiting current strictly followed the wire velocity and used [6] an empirical power-law correlation of mass-transfer coefficient to flow velocity /lim = /min(l + A/ cos(ft>.f)f) with s 0.7. They also noted that the frequency and amplitude dependence of the mean current, and the modulation depth, was linked to whether the flow was strictly laminar or not. Flow modelling indicated that for Re > 5 where Re = u dlv, there was separation of the boundary layer at the wire surface, when aid 1. For Re > 40 the flow pattern became very irregular. Under these circumstances, a direct relation between velocity and current should be lost, and they indeed showed that the modulation depth decreased steeply with increase of wire diameter, down to 10% for 0.8 mm diameter wire. 

The escape of hydrogen is caused by diffusion due to the high molecular velocity. The theory of molecular cinetics gives a relation between velocity v, molecular mass jl and temperature T of a gas ... 

Dilute solutions. In considering the velocity of reaction in dilute solutions, we have again to place in the foreground the relation between velocity and equilibrium, and first to pay attention to the displacement of equili-brium by pressure. According to Planck, this is given by the relation... 

Examination of the trajectories establishes that for both cases shown in Fig. 26, the molecule has not yet reached the surface. We have verified that the inverse relation between velocity and period of the shock front... 

Kinetic isotope effects take place under non-equihbrium physical or chemical conditions. Physically based isotope effects often occur because molecules of the same compormd, but containing different stable isotopes, move at different rates (owing to unequal masses). For example, carbon dioxide gas occurs in molecules containing C02 (molecular mass, m = 44) and C02 (T7Twt = 45), which must have the same kinetic energy (E = V2 Mv, where M is mass and v is velocity). Therefore the relation between velocity and mass at the same temperature is ... 

FIGURE 5.11 Examples of the relation between velocity gradient W and stress tr for liquidlike systems. ay is yield stress. See text. 

HPC the relation between velocity, feed and depth of cut, and the cutting tool properties the surface integrity of the machined workpiece as well as some phenomena concerning the technological process safety at high cutting speeds. 

Liquid-solid fluidised systems are generally characterised by the regular expansion of the bed which takes place as the liquid velocity increases from the minimum fluidisation velocity to a value approaching the terminal falling velocity of the particles. The general form of relation between velocity and bed voidage is found to be similar for both Newtonian and inelastic power-law liquids. For fluidisation of uniform spheres by Newtonian liquids, equation (5.21), introduced earlier to represent hindered settling data, is equally applicable ... 

Considering the Hagen-Poiseuille formula we find that the departures from the behavior expected from Newton s law can be represented, if we substitute for the Newtonian expression a more general relation between velocity gradient and shear stress. Many workers have endeavored to find an expression which would satisfy experimental facts. Rabino-witsch, Reiner and Weissenberg, particularly, have interested themselves recently in the anomalous behavior of viscous liquids. 

As in every energy variety, such an operator may reduce to a scalar in a restricted range of small operands, providing a simple linear relation between velocity and force. Another freqnently encountered case, especially in gases, is the proportionality of the friction resistance to the velocity, leading to a quadratic dependence of the force on the velocity ... 

In relation with the Fermi energy and wave vector one can introduces also other measures of interest, as Fermi velocity v calling the relation between velocity v and impulse p through the mass m,v = mp, so having... 

The conservation of volume provides a relation between (velocity in the x-direction) and ii ... 

Equation (13.4) is valid only at the initial stages of the relaxation process at which condition (13.2) is fulfilled. In order to describe the terminal stages, the motion of B must be taken into account. In this case, we assume for simplicity the following relations between velocities and momenta... 

Rao MR (1940) Relation between velocity of sound in liquids and molecule volume. Indian JPhys 14 109-116... 

Next, the time derivatives of r and s are substituted for the time derivatives of Xj and X2. The relation between velocities in the two coordinate systems comes about from taking the time derivative of the equations that relate r and s with Xi and X2 ... 

The velocity profile across the gap can be found by integrating the relation between velocity gradient and temperature (4.23) assuming the solution (4.25) and obvious symmetry consequences (i.e., the velocity must vanish on the centerline)... 

This part of our chapter has shown that the use of the two variables, moduli and phases, leads in a direct way to the derivation of the continuity and Hamilton-Jacobi equations for both scalar and spinor wave functions. For the latter case, we show that the differential equations for each spinor component are (in the nearly nomelativistic limit) approximately decoupled. Because of this decoupling (mutual independence) it appears that the reciprocal relations between phases and moduli derived in Section III hold to a good approximation for each spinor component separately, too. For velocities and electromagnetic field strengths that ate nomrally below the relativistic scale, the Berry phase obtained from the Schrddinger equation (for scalar fields) will not be altered by consideration of the Dirac equation. 

Ocily n. - 1 of the n equations (4.1) are independent, since both sides vanish on suinming over r, so a further relation between the velocity vectors V is required. It is provided by the overall momentum balance for the mixture, and a well known result of dilute gas kinetic theory shows that this takes the form of the Navier-Stokes equation... 

Then, knowing v one relation between the individual species velocities m... 

The method of solution is now straightforward, in principle. Equations (4.16) provide n-1 independent relations between the diffusion velocities, and another relation follows directly from their definition, namely ... 

Fig. 7. Relations between elastic constants and ultrasonic wave velocities, (a) Young s modulus (b) shear modulus (c) Poisson s ratio and (d) bulk...

Velocity Since most hquids are practicaUy incompressible, the relation between the quantity flowing past a given point in a given time and the velocity of flow is expressed as fohows ... 

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