  We study the hydrodynamic flow of electrons through a smooth potential energy
landscape in two dimensions, for which the electrical current is concentrated
along thin channels that follow percolating equipotential contours. The width
of these channels, and hence the electrical resistance, is determined by a
competition between viscous and thermoelectric forces. For the case of periodic
(moir\'{e}) potentials, we find that hydrodynamic flow provides a new route to
linear-in-$T$ resistivity. We calculate the associated prefactors for
potentials with $C_3$ and $C_4$ symmetry. On the other hand, for a random
potential the resistivity has qualitatively different behavior because
equipotential paths become increasingly tortuous as their width is reduced.
This effect leads to a resistivity that grows with temperature as $T^{10/3}$.
