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For problems with multiple bodies, the current integral approach needs theuse of auxiliary potential functions in order to have an individual forceformula for each body. While the singularity approach, based on an extension ofthe unsteady Lagally theorem, is restricted to multibody and multivortex flowswithout bound vortex and vortex production. In this paper, we considermultibody and multivortex flow and derive force formulas, in both forms ofsingularity approach and integral approach but without auxiliary function, thatgive individual forces of each body for unsteady two dimensional potential flowwith vortex production on the surface of bodies. A number of problems,including Karman vortex street, Wagner problem of impulsively starting flow,interaction of two circular cylinders with circulation, and interaction of anairfoil with a bound vortex, are used to validate the force formulas.

Explicit force formlulas for two dimensional potential flow with multiple bodies and multiple free vortices