  In this paper, we consider the steady irrotational Euler flows in
multidimensional nozzles. The first rigorous proof on the existence and
uniqueness of the incompressible flow is provided. Then, we justify the
corresponding low Mach number limit, which is the first result of the low Mach
number limit on the steady Euler flows. We establish several uniform estimates,
which does not depend on the Mach number, to validate the convergence of the
compressible flow with extra force to the corresponding incompressible flow,
which is free from the extra force effect, as the Mach number goes to zero. The
limit is on the Holder space and is unique. Moreover, the convergence rate is
of order $\varepsilon^2$, which is higher than the ones in the previous results
on the low Mach number limit for the unsteady flow.
