Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

The Beads on a Wire Model

The basic concepts of shock and particle velocities are well illustrated by an example first introduced by Duvall and Band (1968). Here we assume that a string of beads of diameter d, mass m, and spaced a fixed distance / apart on a smooth (frictionless) wire is impacted by a rigid, massive piston at velocity v. Each bead is assumed to undergo perfectly elastic, rigid-body motion upon impact with its neighbor. [Pg.12]

After impact the first bead assumes a velocity 2v, due to its rigid elastic response. This is the instantaneous particle velocity that the bead acquires. The first bead travels across the gap d and impacts the second bead. The only way by which momentum and energy can be simultaneously conserved is for the first bead to come to rest at the instant the second bead acquires a velocity [Pg.12]

This process proceeds sequentially down the wire. The time between collisions is defined to be r, which is the separation distance divided by the bead velocity, 2v. The first bead remains at rest until impacted again by the piston. It accelerates to velocity 2v, and again collides with the second bead (now at rest), again giving up its momentum and kinetic energy. The velocity history of the first bead is illustrated in Fig. 2.4. Its velocity alternates between zero and 2v at equal intervals, so its mean (or drift) velocity is v. The same is true for all the other beads that have been disturbed. [Pg.13]

This simple example Illustrates the important kinematic properties of shock waves, particularly the concepts of particle velocity and shock velocity. The particle velocity is the average velocity acquired by the beads. In this example, it is the piston velocity, v. The shock velocity is the velocity at which the disturbance travels down the string of beads. In general, at time n//2v, the disturbance has propagated to the nth bead. The distance the disturbance has traveled is therefore n d -b /), and the shock velocity is [Pg.13]

Note that this is faster than the particle velocity u = v. [Pg.13]


See other pages where The Beads on a Wire Model is mentioned: [Pg.12]   


SEARCH



Bead model

Wire models

© 2024 chempedia.info