mass is conserved according to the law of conservation of mass over time.
mass is conserved according to the law of conservation of mass over time.
when is mass conserved according to the law of conservation of mass?
over time
a change in momentum of a mass requires a force; according to newton's first law, known as the law of inertia, inertia simply being another term for mass. that force, applied to a mass, creates an acceleration, which when applied over time, changes the velocity of a mass. according to newton's second law, the law of momentum -- changing the velocity of the mass changes its momentum, (mass multiplied by velocity). it is important to understand at this point that velocity is not simply speed. velocity is the speed of a mass in a particular direction. in a very technical sense, speed is a scalar (mathematics), a magnitude, and velocity is a vector (physics), magnitude and direction. newton's third law, known as conservation of momentum, recognizes that changes in the motion of a mass, brought about by the application of forces and accelerations, does not occur in isolation; that is, other bodies of mass are found to be involved in directing those forces and accelerations. furthermore, if all the masses and velocities involved are accounted for, the vector sum, magnitude and direction, of the momentum of all the bodies involved does not change; hence, momentum of the system is conserved. this conservation of momentum is why gun recoil occurs in the opposite direction of bullet projection -- the mass times velocity of the projectile in the positive direction equals the mass times velocity of the gun in the negative direction. in summation, the total momentum of the system equals zero, surprisingly just as it did before the trigger was pulled. from a practical engineering perspective, therefore, through the mathematical application of conservation of momentum, it is possible to calculate a first approximation of a gun’s recoil momentum and kinetic energy, and properly design recoil buffering systems to safely dissipate that momentum and energy, simply based on estimates of the projectile speed (and mass) coming out the barrel. to confirm analytical calculations and estimates, once a prototype gun is manufactured, the projectile and gun recoil energy and momentum can be directly measured using a ballistic pendulum and ballistic chronograph.
recoil
breakup mass conserved formulations and coalescence rates mass conserved formulation was used in the computation of bubble size distributions. for single size modelling the schiller–naumann drag force was used, and for the modelling of musig the ishii–zuber drag force was used. an empirical drag formulation was used for the double size bubble model. the simulation results of time-averaged axial velocity and gas holdup obtained with the three models were compared with reported experimental data in the resulting literature. after the comparison of all the three results it gets very clear that only musig models with some lift force can replicate the measured radial distribution of gas holdup in the fully developed flow regime. the inhomogeneous musig model gives a little better result than other models in the prediction of axial liquid velocity. for all the simulations the rng k–ε model was used, and the results showed that this version of k–ε model did yield comparatively high rate of turbulence dissipation and high bubble breakup and, hence, a rational bubble size distribution formed. here the ad hoc manipulation of the breakup rates was ignored. mutual effects of drag force, mean bubble sizes, and turbulence characteristics profound from the simulation results. a decrease in the relative velocity between two phases is encounters due to an increase in the drag force, and this could result in decrease in k and ε. low breakup rates results a large sauter diameter which was directly connected to the dissipation rates of turbulence. drag force is directly influenced by the change of sauter diameter.
churn turbulent flow