Momentum gain

The improvement of the flow distribution by increasing the value of DJD results from the decrease of momentum gain in the combining header. 

This consists of an impeller and turbine mounted adjacently within a pipeline. The impeller is rotated at a constant angular velocity at which imparts the same angular velocity to the fluid as it flows past. On leaving the impeller, the fluid immediately enters the turbine where the angular momentum gained by the fluid is used to drive the turbine. If a mass of fluid dm enters the impeller during time dr, then ... 

Hamiltonian, the wavepacket immediately starts to move away from its origin. When it has reached the asymptotic region where the potential is zero, the center of the wavepacket travels with constant velocity to infinity. The oscillations in i -space reflect the momentum gained during the breakup. 

The momentum lost by the wall is equal to the momentum gained by the bead. And from conservation of kinetic energy, we see... 

Rate of momentum gain by convection + pressure difference acting on flow = 0 pudu+ dp= 0 (1.19)... 

Chen [61] conducted a boundary layer analysis of this problem and included the momentum gain of the condensate in dropping from tube to tube and the condensation that takes place directly on the subcooled condensate film between tubes. His numerical results for the average coefficient of N tubes can be approximated to within 1 percent by ... 

According to the power balance, Eq. (38), the mean power gain from the electric field is compensated for by the mean power loss in collisions, and this happens for any given gas and its specific atomic or molecular data and for any reduced field strength E/N. An analogous compensation occurs in the momentum balance, Eq. (39), between the mean momentum gain from the field and the mean momentum loss in collisions. 

Fig. 10, Temporal evolution of the power and momentum gain-to-loss ratios in neon.

However, the representation of the momentum gain-to-loss ratio at the bottom of Fig. 10 makes it obvious that the evolution of this quantity toward the value 1 takes place much faster. The almost complete compensation of the momentum gain and loss is reached much earlier, at about 10 s, and this happens nearly independent of the field strength. This evolution is largely in agreement with the magnitude and the weak energy dependence of the lumped frequency for momentum dissipation by collisions in neon presented above in Fig. 8. 

The behavior of the individual terms in the momentum balance (right) is similar to that in the power balance. Now the normalized momentum loss in elastic collisions r (z)/I oo) oscillates around the oscillating momentum gain /(z)// (oo), and the somewhat lesser deviations between these quantities are compensated for to a large extent by the normalized source term d/dz) [(2/3m )u z)]/P oQ) of the momentum balance (dotted-dashed curve) containing the spatial derivative of the mean energy density , (z). 

The law of momentum conservation can be stated as follows For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by object 1 is equal to the momentum gained by object 2. 

In the development of the GLRDVE a reduced form of the momentum balance is considered. We assume a pseudo steady state and negligible viscous contribution. Moreover, the gradient of pressure is assumed to be much larger than the rate of momentum gain by convention of the fluid. Thus, the resulting momentum balance is of the form. 

The average value of the momentum gained during the pulse by the inner part of the lower- or excited-state wavepacket, that is, the momentum kick, can be evaluated from the mass current and the partial population by... 

Since most releases are in the form of a jet rather than a plume, it is important to assess the effects of initial momentum and air entrainment on the behavior of a jet. Near its release point where the jet velocity differs gready from the wind velocity, a jet entrains ambient air due to shear (velocity difference), grows in size, and becomes diluted. For a simple jet (neutral buoyancy), its upward momentum remains constant while its mass increases. Therrfore, if vertically released, the drag forces increase as the surface area increases and eventually horizontal momentum dominates. The result is that the jet becomes bent over at a certain distance and is dominated by the wind momentum. If the jet has positive buoyancy (buoyant jet), the upward momentum will increase and the initial momentum will become negligible compared to the momentum gained due to the buoyancy. Then, the jet will behave like a plume. The rises of simple or buoyant jets, collectively called plume rises, have been smdied by many researchers and their formulas can be found in Briggs (1975, 1984) or most reviews on atmospheric diffusion (including Hanna et al., 1982). 

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