  We revisit the relation between the stellar surface density, the gas surface
density, and the gas-phase metallicity of typical disk galaxies in the local
Universe with the SDSS-IV/MaNGA survey, using the star formation rate surface
density as an indicator for the gas surface density. We show that these three
local parameters form a tight relationship, confirming previous works (e.g., by
the PINGS and CALIFA surveys), but with a larger sample. We present a new local
leaky-box model, assuming star formation history and chemical evolution is
localized except for outflowing materials. We derive closed-form solutions for
the evolution of stellar surface density, gas surface density and gas-phase
metallicity, and show that these parameters form a tight relation independent
of initial gas density and time. We show that, with canonical values of model
parameters, this predicted relation match the observed one well. In addition,
we briefly describe a pathway to improving the current semi-analytic models of
galaxy formation by incorporating the local leaky-box model in the cosmological
context, which can potentially explain simultaneously multiple properties of
Milky Way-type disk galaxies, such as the size growth and the global stellar
mass-gas metallicity relation.
