We present new calculations of the mass inflow and outflow rates around the Milky Way, derived from a catalog of ultraviolet metal-line high velocity clouds (HVCs). These calculations are conducted by transforming the HVC velocities into the Galactic Standard of Rest (GSR) reference frame, identifying inflowing (v_GSR < 0 km/s) and outflowing (v_GSR > 0 km/s) populations, and using observational constraints on the distance, metallicity, dust content, covering fractions, and total hydrogen column density of each population. After removing HVCs associated with the Magellanic Stream and the Fermi Bubbles, we find inflow and outflow rates in cool (T~10^4 K) ionized gas of dM_in/dt >~ 0.53+/-0.17 (d/12 kpc) (Z/0.2 Z_sun)^-1 M_sun/yr and dM_out/dt >~ 0.16+/-0.06 (d/12 kpc) (Z/0.5 Z_sun)^-1 M_sun/yr. The excess of inflowing over outflowing gas suggests that the Milky Way is currently in an inflow-dominated phase, but the presence of substantial mass flux in both directions supports a Galactic fountain model, in which gas is constantly recycled between the disk and the halo. We also find that the metal flux in both directions (in and out) is indistinguishable. By comparing the outflow rate to the Galactic star formation rate, we present the first estimate of the mass loading factor (etc_HVC) of the disk-wide Milky Way wind, finding eta_HVC >~ 0.10+/-0.06 (d/12 kpc) (Z/0.5 Z_sun)^-1. Including the contributions from low- and intermediate-velocity clouds and from hot gas would increase these inflow and outflow estimates.
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