  The first stages of planet formation take place in protoplanetary disks that
are largely made up of gas. Understanding how the gas affects planetesimals in
the protoplanetary disk is therefore essential. In this paper, we discuss
whether or not gas flow can erode planetesimals. We estimate how much shear
stress is exerted onto the planetesimal surface by the gas as a function of
disk and planetesimal properties. To determine whether erosion can take place,
we compare this with previous measurements of the critical stress that a
pebble-pile planetesimal can withstand before erosion begins. If erosion takes
place, we estimate the erosion time of the affected planetesimals. We also
illustrate our estimates with two-dimensional numerical simulations of flows
around planetesimals using the lattice Boltzmann method. We find that the wall
shear stress can overcome the critical stress of planetesimals in an eccentric
orbit within the innermost regions of the disk. The high eccentricities needed
to reach erosive stresses could be the result of shepherding by migrating
planets. We also find that if a planetesimal erodes, it does so on short
timescales. For planetesimals residing outside of $1 \ \rm{au}$, we find that
they are mainly safe from erosion, even in the case of highly eccentric orbits.
