  Gamma-ray bursts (GRB) are the most powerful events in the universe. They are
capable of accelerating particles to very high energies, so are strong
candidates as sources of detectable astrophysical neutrinos. We study the
effects of particle acceleration and escape by implementing a two-zone model in
order to assess the production of high-energy neutrinos in GRBs associated with
their prompt emission. Both primary relativistic electrons and protons are
injected in a zone where an acceleration mechanism operates and dominates over
the losses. The escaping particles are re-injected in a cooling zone that
propagates downstream. The synchrotron photons emitted by the accelerated
electrons are taken as targets for $p\gamma$ interactions, which generate pions
along with the $pp$ collisions with cold protons in the flow. The distribution
of these secondary pions and the decaying muons are also computed in both
zones, from which the neutrino output is obtained. We find that for escape
rates lower than the acceleration rate, the synchrotron emission from electrons
in the acceleration zone can account for the GRB emission, and the production
of neutrinos via $p\gamma$ interactions in this zone becomes dominant for
$E_\nu>10^5$ GeV. For illustration, we compute the corresponding diffuse
neutrino flux under different assumptions and show that it can reach the level
of the signal recently detected by IceCube.
