Semi-empirical procedures for estimation of residual velocity and ballistic limit for impact on mild steel plates by projectiles

This paper deals with the development of simplified semi-empirical relations for the prediction of residual velocities of small calibre projectiles impacting on mild steel target plates, normally or at an angle, and the ballistic limits for such plates. It has been shown, for several impact cases for which test results on perforation of mild steel plates are available, that most of the existing semi-empirical relations which are applicable only to normal projectile impact do not yield satisfactory estimations of residual velocity. Furthermore, it is difficult to quantify some of the empirical parameters present in these relations for a given problem. With an eye towards simplicity and ease of use, two new regression-based relations employing standard material parameters have been discussed here for predicting residual velocity and ballistic limit for both normal and oblique impact. The latter expressions differ in terms of usage of quasi-static or strain rate-dependent average plate material strength. Residual velocities yielded by the present semi-empirical models compare well with the experimental results. Additionally, ballistic limits from these relations show close correlation with the corresponding finite element-based predictions.

Velocity-Space Contours of Collision Integrals

Based on the recently found closed-form expressions of the Boltzmann collision integrals in a rigid-sphere gas for multi-Maxwellian distributions, a few typical sets of contour surfaces of the integrals in the space of molecular velocities are presented. These show graphically the tendency toward equilibrium under the influence of collisions. A brief preliminary comparison with Monte Carlo results is also given.

Sound Velocity Anomaly at the Mott Transition: Application to Organic Conductors and V2O3

Close to the Mott transition, lattice degrees of freedom react to the softening of electron degrees of freedom. This results in a change of lattice spacing, a diverging compressibility, and a critical anomaly of the sound velocity. These effects are investigated within a simple model, in the framework of dynamical mean-field theory. The results compare favorably to recent experiments on the layered organic-conductor kappa-(BEDT-TTF)(2)Cu[N(CN)(2)]Cl. We predict that effects of a similar magnitude are expected for V2O3, despite the much larger value of the elastic modulus of this material.

Studies in bubble formation — III

Bubble formation from single horizontal orifices submerged in Newtonian liquids has been investigated for such chamber volumes that both the pressure inside the chamber and flow rate into the bubble are time dependent. The data collected show that under these conditions the bubble volume decreases exponentially with increase in orifice submergence. The equations for the generalized two stage model of bubble formation, taking the variation of gas flow rate with time into account, have been derived. These equations reduce to the cases of constant gas flow rate and constant pressure when adequate constraints are imposed. The results obtained under intermediate conditions have been quantitatively explained on the basis of these equations.

Studies in bubble formation—II bubble formation under constant pressure conditions

Bubble formation under constant pressure conditions has been investigated for wide range of variation of liquid properties.Air bubbles were formed from single horizontal orifices submerged in liquids whose viscosity varied from 1·0 to 600 cPs and surface tension from 37 to 72 dyn/cm. Air flow rate was varied from 2 to 250 cm3/sec and the orifice diameter from 0·0515 to 0·4050 cm.

Studies in bubble formation—I bubble formation under constant flow conditions

A model based on two step mechanism of bubble formation is proposed. The resulting equations are used to explain the discrepancies existing in the literature. Data have been collected over a wide range of variables to test the model.

Effect of impulsive change of wall velocity and wall temperature in viscous heat-conducting gas

A study of compression waves produced in a viscous heat-conducting gas by the impulsive start of a one-dimensional piston and by the inpulsive change of piston wall temperature is made using Laplace Transform Technique for Prandt1 number unity. Expressions for velocity, temperature and density have also been obtained using small-time expansion procedure in this case. For arbitrary Prandt1 number solutions have been developed using large-time expansion procedure. A number of graphs exhibiting the distribution of the fluid velocity, temperature and density have been drawn.

The effect of viscosity and surface tension on the Taylor instability of the surface of a cavitation bubble*

This paper is devoted to a consideration of the following problem: A spherical mass of fluid of density varrho1, viscosity μ1 and external radius R is surrounded by a fluid of density varrho2 and viscosity μ2.The fluids are immiscible and incompressible. The interface is accelerated radially by g1: to study the effect of viscosity and surface tension on the stability of the interface. By analyzing the problem in spherical harmonics the mathematical problem is reduced to one of solution of the characteristic determinant equation. The particular case of a cavity bubble, where the viscosity μ1 of the fluid inside the bubble is negligible in comparison with the viscosity μ2 of the fluid outside the bubble, is considered in some detail. It is shown that viscosity has a stabilizing role on the interface; and when g1 > T(n − 1) (n + 2)/R2(varrho2 − varrho1) the stabilizing role of both viscosity and surface tension is more pronounced than would result when either of them is taken individually.

Studies in bubble formation - IV: bubble formation at porous discs

Bubble formation from porous discs submerged in liquids of different physical properties has been investigated. It is found the number of sites effective for bubble formation is much smaller than the total potentially available sites. The number of effective sites is found to be a function of the surface tension, viscosity, and density of the liquid and the gas flow rate through the disc. A model proposed on the basis of bubble formation from an isolated nozzle and the close packed arrangement of the formed bubbles, explains the phenomenon adequately. © 1970.

A unified approach to bubble and drop formation

An approach, starting with the bubble formation model of Khurana and Khumar, has been presented, which is found to be reasonably applicable to the formation of both bubbles and drops from single submerged nozzles. The model treats both the phenomena jointly as the formation of a dispersed phase entity resulting from injection, whose size depends upon operating parameters and physical properties.