  A recent study on axisymmetric ideal magnetohydrodynamic equilibria with
incompressible flows [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas {\bf
5}, 2378 (1998)] is extended to the generic case of helically symmetric
equilibria with incompressible flows. It is shown that the equilibrium states
of the system under consideration are governed by an elliptic partial
differential equation for the helical magnetic flux function $\psi$ containing
five surface quantities along with a relation for the pressure. The above
mentioned equation can be transformed to one possessing differential part
identical in form to the corresponding static equilibrium equation, which is
amenable to several classes of analytic solutions. In particular, equilibria
with electric fields perpendicular to the magnetic surfaces and
non-constant-Mach-number flows are constructed. Unlike the case in axisymmetric
equilibria with isothermal magnetic surfaces, helically symmetric $T=T(\psi)$
equilibria are over-determined, i.e., in this case the equilibrium equations
reduce to a set of eight ordinary differential equations with seven surface
quantities. In addition, it is proved the non-existence of incompressible
helically symmetric equilibria with (a) purely helical flows (b) non-parallel
flows with isothermal magnetic surfaces and the magnetic field modulus being a
surface quantity (omnigenous equilibria).
