(1)
Assuming an ideal gas and neglecting viscous and heat conduction effects the terminal velocity can be determined. These are good approximations for high-speed flow when the characteristic flow time is short compared with the diffusion times for such nonequilibrium processes (Ref. 21). The flow is assumed to be a reversible and adiabatic process, and thus the state of the gas changes isentropically.
The terminal translational velocity V_(terminal) can be obtained, assuming an ideal gas and substantial cooling upon expansion (T<<T_o), as well as constant gamma and C_p over the temperature range of interest, by:
(2) 
with:
(3) 
and 
where X_i is the number or mole fraction and W_i the molecular weight of each gas specie in a mixture (see Table 3). As can be seen high temperatures are desired to obtain high translational energies, and the velocity (energy) only depends on the initial temperature T_o and the properties of the gas specie used.
One concern is the issues if the terminal velocity V_(infinity) is reached or some other velocity due to rotational and vibrational states contributing to V_(infinity) in the case of polyatomic molecules. Miller (Ref. 21) found that the temperature, density, and collision frequency drop rapidly with distance from the nozzle, but the translational velocity reaches the terminal translational velocity V_(infinity) within a very short distance from the nozzle, namely several nozzle diameters in distance. This is a very important feature in understanding the properties of beams extracted from free jets. The velocity is fairly independent of the quitting surface distance, while all other parameters are very sensitive to where the transition from continuum to molecular flow occurs. Those findings are experimentally supported by Sibener et. al. (Ref. 65) which found that the terminal velocity V_(infinity) stays constant with nozzle pressure P_o (except for velocity slip at low P_o for his gas mixtures).
Note also equation (10), which gives an estimate of the terminal parallel temperature T_(parallel),_(infinity), which can be neglected for typical jet operating conditions in the determination of the terminal velocity V_(infinity) (see equation (23) in the appendix).
Table 3: Properties of Gases (Ref. 21 except for NH_3)
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