The vapor-liquid, two-phase, inviscid, compressible how in a converging-diverging nozzle is computed by high accuracy total variation diminishing and Newton-Raphson schemes. A homogeneous speed of sound definition based on flow quality and void Fraction is presented, along with some gas dynamic relations. Analytical two phase mass-flow expressions are also derived, and solutions are compared with those obtained from the numerical schemes. The computational results of void-fraction and Mach-number relation obtained for the Laval nozzle compare favorably with both schemes. Equilibrium and nonequilibrium numerical results for cryogenic nitrogen how are also presented. Numerical mass flux at both choked and unchoked throat conditions agrees with experimental data, but some discrepancy is observed in the pressure profiles at the diffusing portion of the nozzle.