Velocity, constant

Figure C2.9.2 Shear force versus time during (a) sliding and (b) stick-slip motion. The motion of the surface beneath the sliding block of figure C2.9.1 is at constant velocity.

A body continues to move in a straight line at constant velocity unless a force acts upon it. 

It is helpful to distinguish three different types of problem to which Newton s laws of motion may be applied. In the simplest case, no force acts on each particle between collisions. From one collision to the next, the position of the particle thus changes by v,5f, where v, is the (constant) velocity and 6t is the time between collisions. In the second situation, the particle experiences a constant force between collisions. An example of this type of motion would be that of a charged particle moving in tr uniform electric field. In the third case, the force on the particle depends on its position relative to the other particles. Here the motion is often very difficult, if not impossible, to describe analytically, due to the coupled nature of the particles motions. 

The first molecular dynamics simulation of a condensed phase system was performed by Alder and Wainwright in 1957 using a hard-sphere model [Alder and Wainwright 1957]. In this model, the spheres move at constant velocity in straight lines between collisions. All collisions are perfectly elastic and occur when the separation between the centres of... 

Growth in the radial direction is assumed to occur at a constant velocity. There is ample experimental justification for this in the case of three-dimensional spherical growth. 

The picture of the electron in an orbit as a standing wave does, however, pose the important question of where the electron, regarded as a particle, is. We shall consider the answer to this for the case of an electron travelling with constant velocity in a direction x. The de Broglie picture of this is of a wave with a specific wavelength travelling in the x direction as in Figure 1.4(a), and it is clear that we cannot specify where the electron is. 

Consistent with this model, foams exhibit plug flow when forced through a channel or pipe. In the center of the channel the foam flows as a soHd plug, with a constant velocity. AH the shear flow occurs near the waHs, where the yield stress has been exceeded and the foam behaves like a viscous Hquid. At the waH, foams can exhibit waH sHp such that bubbles adjacent to the waH have nonzero velocity. The amount of waH sHp present has a significant influence on the overaH flow rate obtained for a given pressure gradient. 

The terminal velocity in the case of fine particles is approached so quickly that in practical engineering calculations the settling is taken as a constant velocity motion and the acceleration period is neglected. Equation 7 can also be appHed to nonspherical particles if the particle size x is the equivalent Stokes diameter as deterrnined by sedimentation or elutriation methods of particle-size measurement. 

With vertical zone melting and horizontal zone melting without a gas bubble, simple tube rotation at a constant moderate velocity does not significantly influence 5. In those cases, accelerated cmcible rotation or spin up—spin down could be used (72—75). The tube is spun more rapidly than described above, but not at constant velocity. It may, for example, be spun rapidly, suddenly stopped, spun rapidly, etc, resulting in very vigorous stirring. 

The development of combustion theory has led to the appearance of several specialized asymptotic concepts and mathematical methods. An extremely strong temperature dependence for the reaction rate is typical of the theory. This makes direct numerical solution of the equations difficult but at the same time accurate. The basic concept of combustion theory, the idea of a flame moving at a constant velocity independent of the ignition conditions and determined solely by the properties and state of the fuel mixture, is the product of the asymptotic approach (18,19). Theoretical understanding of turbulent combustion involves combining the theory of turbulence and the kinetics of chemical reactions (19—23). 

An initially clean activated carbon Led at 320 K is fed a vapor of benzene in nitrogen at a total pressure of 1 MPa. The concentration of benzene in the feed is 6 mol/m. After the Led is uniformly saturated with feed, it is regenerated using benzene-free nitrogen at 400 K and 1 MPa. Solve for Loth steps. For sim-phcity, neglect fluid-phase acciimiilation terms and assume constant mean heat capacities for stationary and fluid phases and a constant velocity. The system is described by... 

Measuring rollers unwind and measure the precise length of packaging material at constant velocity. 

Figure 2.8. An x-t diagram of a piston interacting with a compressible fluid. At the origin, the piston begins moving at constant velocity, generating a shock wave. At tj, the piston stops abruptly, generating rarefaction fan. Snapshots of wave profiles at times t2 and 3 are shown.

Here, AujAt is the acceleration of the vehicle. When it travels at constant velocity, this term becomes zero. So then... 

Coefficient A and exponent a must be evaluated experimentally. Experiments have shown that A and a are themselves functions of the Reynolds number. Equation 47 shows that the resistance force increases with increasing velocity. If the force field (e.g., gravity) has the same potential at all points, a dynamic equilibrium between forces P and R develops shortly after the particle motion begins. As described earlier, at some distance from its start the particle falls at a constant velocity. If the acting force depends on the particle location in space, in a... 

In this apparatus the plastic to be tested is heated in a barrel and then forced through a capillary die as shown in Fig. 5.16, Normally the ram moves at a constant velocity to give a constant volume flow rate, Q. From this it is conventional to calculate the shear rate from the Newtonian flow expression. 

Along with a constant velocity zone (Zone 1), there is a constant temperature zone in a jet. Heat diffusion in a jet is more intense than momentum diffusion therefore the core of constant temperatures fades away faster than that of constant velocities and the temperature profile is flatter than the velocity profile. Thus the length of the zone with constant temperature (Fig. 7.23) is shorter than the length of the constant velocity zone (Zone I... 

Constant velocity method. This is a simple but not very cost effective approach for systems with a wide range of duct diameters. 

Isovel A line in a flow system or on a graph connecting points with constant velocity. 

Liquids are able to flow. Complicated stream patterns arise, dependent on geometric shape of the surrounding of the liquid and of the initial conditions. Physicists tend to simplify things by considering well-defined situations. What could be the simplest configurations where flow occurs Suppose we had two parallel plates and a liquid drop squeezed in between. Let us keep the lower plate at rest and move the upper plate at constant velocity in a parallel direction, so that the plate separation distance keeps constant. Near each of the plates, the velocities of the liquid and the plate are equal due to the friction between plate and liquid. Hence a velocity field that describes the stream builds up, (Fig. 15). In the simplest case the velocity is linear in the spatial coordinate perpendicular to the plates. It is a shear flow, as different planes of liquid slide over each other. This is true for a simple as well as for a complex fluid. But what will happen to the mesoscopic structure of a complex fluid How is it affected Is it destroyed or can it even be built up For a review of theories and experiments, see Ref. 122. Let us look into some recent works. 

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