  Future weak lensing surveys potentially hold the highest statistical power
for constraining cosmological parameters compared to other cosmological probes.
The statistical power of a weak lensing survey is determined by the sky
coverage, the inverse of the noise in shear measurements, and the galaxy number
density. The combination of the latter two factors is often expressed in terms
of $n_{\rm eff}$ -- the "effective number density of galaxies used for weak
lensing measurements". In this work, we estimate $n_{\rm eff}$ for the Large
Synoptic Survey Telescope (LSST) project, the most powerful ground-based
lensing survey planned for the next two decades. We investigate how the
following factors affect the resulting $n_{\rm eff}$ of the survey with
detailed simulations: (1) survey time, (2) shear measurement algorithm, (3)
algorithm for combining multiple exposures, (4) inclusion of data from multiple
filter bands, (5) redshift distribution of the galaxies, and (6) masking and
blending. For the first time, we quantify in a general weak lensing analysis
pipeline the sensitivity of $n_{\rm eff}$ to the above factors.
  We find that with current weak lensing algorithms, expected distributions of
observing parameters, and all lensing data ($r$- and $i$-band, covering 18,000
degree$^{2}$ of sky) for LSST, $n_{\rm eff} \approx37$ arcmin$^{-2}$ before
considering blending and masking, $n_{\rm eff} \approx31$ arcmin$^{-2}$ when
rejecting seriously blended galaxies and $n_{\rm eff} \approx26$ arcmin$^{-2}$
when considering an additional 15% loss of galaxies due to masking. With future
improvements in weak lensing algorithms, these values could be expected to
increase by up to 20%. Throughout the paper, we also stress the ways in which
$n_{\rm eff}$ depends on our ability to understand and control systematic
effects in the measurements.
