  We report on the energetics of molecular outflows in 14 local Ultraluminous
Infrared Galaxies (ULIRGs) that show unambiguous outflow signatures (P-Cygni
profiles or high-velocity absorption wings) in the far-infrared lines of OH
measured with the Herschel/PACS spectrometer. Detection of both ground-state
(at 119 and 79 um) and one or more radiatively-excited (at 65 and 84 um) lines
allows us to model the nuclear gas (<~300 pc) as well as the more extended
components using spherically symmetric radiative transfer models. The highest
molecular outflow velocities are found in buried sources, in which slower but
massive expansion of the nuclear gas is also observed. With the exception of a
few outliers, the outflows have momentum fluxes of (2-5)xL_IR/c and mechanical
luminosities of (0.1-0.3)% of L_IR. The moderate momentum boosts in these
sources (<~3) suggest that the outflows are mostly momentum-driven by the
combined effects of AGN and nuclear starbursts, as a result of radiation
pressure, winds, and supernovae remnants. In some sources (~20%), however,
powerful (10^{10.5-11} Lsun) AGN feedback and (partially) energy-conserving
phases are required, with momentum boosts in the range 3-20. These outflows
appear to be stochastic strong-AGN feedback events that occur throughout the
merging process. In a few sources, the outflow activity in the innermost
regions has subsided in the last ~1 Myr. While OH traces the molecular outflows
at sub-kpc scales, comparison of the masses traced by OH with those previously
inferred from tracers of more extended outflowing gas suggests that most mass
is loaded (with loading factors of Mdot/SFR=1-10) from the central galactic
cores (a few x 100 pc). Outflow depletion timescales are <10^8 yr, shorter than
the gas consumption timescales by factors of 1.1-15, and are anti-correlated
with the AGN luminosity.
