Class method conditional velocity

The theory of kinematic waves, initiated by Lighthill Whitham, is taken up for the case when the concentration k and flow q are related by a series of linear equations. If the initial disturbance is hump-like it is shown that the resulting kinematic wave can be usually described by the growth of its mean and variance, the former moving with the kinematic wave velocity and the latter increasing proportionally to the distance travelled. Conditions for these moments to be calculated from the Laplace transform of the solution, without the need of inversion, are obtained and it is shown that for a large class of waves, the ultimate wave form is Gaussian. The power of the method is shown in the analysis of a kinematic temperature wave, where the Laplace transform of the solution cannot be inverted. 

Let us now consider continuous flows of premixed combustible gases and address the question of conditions necessary to retain a flame in the system [2]. This question is of practical significance for many power-production devices. To achieve high power densities, gas velocities in combustors exceed flame velocities, and so means must be found to stabilize flames against blowout, a condition at which the flames are transported through the exit of the burner so that combustion ceases. There are two main classes of stabilization techniques, stabilization by fluid streams and stabilization by solid elements. Although other stabilization methods may be envisioned, such as continuous or intermittent deposition of radiant or electrical energy, in the vast majority of practical continuous-flow systems, stabilization is obtained by techniques that fall within one of the two main classes. Stabilization by solid elements will be discussed first then stabilization by fluid streams will be considered. ... 

However, there is no clear distinction between the above-mentioned classes of devices, because under certain hydrodynamic conditions, the character and method of interface formation may change. For example, in plate absorbers, at high velocities of the gas stream, inversion of phases occurs resulting in ablation of liquid from the plates results in direct flow and the absorbers begin to operate as high-velocity, direct-flow spray absorbers. Operation of absorbers with mobile orifices at low gas velocities is not different from operation of devices with motionless orifices. It is possible to give many other similar examples. 

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