Question

A parcel of mass m moving with an initial velocity 'u' collides inelastically with a particle of mass m initially at rest if the collision is completely inelastic, then find the expression for final velocity of combined entity and loss in kinetic energy

Answer 1

linear momentum conservation is applicable to all types of collisions!

Answer 2

The value of stiffness constant for which results for hard and soft particles are identical is found to be k≥2×106mg/d , where m is the mass of a particle, g is the acceleration due to gravity, and d is the particle diameter. We compare the simulation results to constitutive relations obtained from the kinetic theory of Jenkins and Richman [J. T. Jenkins and M. W. Richman, Arch. Ration. Mech. Anal. 87, 355 (1985)] for pressure, dissipation, viscosity, and thermal conductivity. We find that all the quantities are very well predicted by kinetic theory for volume fractions ν<0.5 . At higher densities, obtained for thicker layers ( H=15d and H=20d ), the kinetic theory does not give accurate prediction. Deviations of the kinetic theory predictions from simulation results are relatively small for dissipation and heat flux and most significant deviations are observed for shear viscosity and pressure. The results indicate the range of applicability of soft particle simulations and kinetic theory for dense flows.

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