We rederive and expand upon a method for finding solutions to the two-dimensional irrotational (inviscid) flow equations in the presence of a free surface, found by Hopkinson. This method allows the flow to be driven by placing singularities, like sources or vortices, in the interior of the flow domain. We then apply the method to find a number of novel solutions: separated flow driven by a source, vortices behind a plate and free-surface flow stirred by a double vortex. Free surfaces generically exhibit cusp singularities with a 2/3 power index, similar to those found in very viscous flow.
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