  The High Altitude Water Cherenkov (HAWC) observatory is an array of large
water Cherenkov detectors sensitive to gamma rays and hadronic cosmic rays in
the energy band between 100 GeV and 100 TeV. The observatory will be used to
measure high-energy protons and cosmic rays via detection of the energetic
secondary particles reaching the ground when one of these particles interacts
in the atmosphere above the detector. HAWC is under construction at a site 4100
meters above sea level on the northern slope of the volcano Sierra Negra, which
is located in central Mexico at 19 degrees N latitude. It is scheduled for
completion in 2014. In this paper we estimate the sensitivity of the HAWC
instrument to point-like and extended sources of gamma rays. The source fluxes
are modeled using both unbroken power laws and power laws with exponential
cutoffs. HAWC, in one year, is sensitive to point sources with integral
power-law spectra as low as 5x10^-13 cm^-2 sec^-1 above 2 TeV (approximately 50
mCrab) over 5 sr of the sky. This is a conservative estimate based on simple
event parameters and is expected to improve as the data analysis techniques are
refined. We discuss known TeV sources and the scientific contributions that
HAWC can make to our understanding of particle acceleration in these sources.
