  Long-duration gamma-ray bursts (LGRBs) are generally considered to originate
from the massive collapsars. It is believed that the central engine of
gamma-ray bursts (GRBs) is a neutrino-dominated accretion flow (NDAF) around a
rotating stellar-mass black hole (BH). The neutrino annihilation above the NDAF
is a feasible mechanism to power GRB. In this work, we analyse the
distributions of the isotropic gamma-ray radiated energy and jet kinetic energy
of 48 LGRBs. According to the NDAF and fireball models, we estimate the mean
accreted masses of LGRBs in our sample to investigate whether the NDAFs can
power LGRBs with the reasonable BH parameters and conversion efficiency of
neutrino annihilation. The results indicate that most of the values of the
accreted masses are less than $5~M_\odot$ for the extreme Kerr BHs and high
conversion efficiency. It suggests that the NDAFs may be suitable for most of
LGRBs except for some extremely high energy sources.
