  In this paper we investigate the velocity dispersion profiles of clusters of
galaxies for seven cosmological models. One model is the SCDM model, and the
others are six low-density models with the density parameter $\Omega=0.1$, 0.2
or 0.3 and with or without a cosmological constant $\Lambda=1-\Omega$. We find
that the velocity dispersion profiles depend both on $\Omega$ and on $\Lambda$.
For $\Lambda=0$, the profiles are steeper in a lower-$\Omega$ model than in a
higher-$\Omega$ one. The cosmological constant significantly weakens the
dependence on $\Omega$: the difference in the profile distributions between two
flat models is much smaller than that between the two corresponding open models
with the same $\Omega$. These results in principle can be used to constrain the
cosmological parameters when a large sample of the velocity dispersion profiles
is available. Motivated by the practical situation that a sample of $\sim 100$
clusters with $\sim 100$ measured redshifts per cluster is still the best
sample available in the foreseen future, we examine carefully to what degree
the cosmological parameters can be constrained with the velocity dispersion
profiles of such a sample of clusters. The limited sampling around clusters and
the limited number of clusters seriously degrade the discriminative power of
the velocity dispersion profiles among cosmological models. We find that the
five models of $\Omega\ge 0.2$ cannot be distinguished by this type of
observation. Due to the limited sampling, one should be very cautious in
extracting information about the density profile and/or the dynamics around
single clusters from the diluted velocity dispersion profiles
