Integral expression is derived for aerodynamic forces in unsteady separated flows of an incompressible Newtonian fluid via the characteristics of the flow on the body surface including the vortex flux generated by it. The expression obtained is valid for unsteady and steady flows under the no-slip or the partial slip boundary conditions in a viscous fluid as well as for complete slip in the case of an ideal fluid including the flows with tangential discontinuity of the velocity field. Unlike the number of existing formulas, the expression does not contain the volume integrals and is applicable for the case of multiple bodies. The expression greatly simplifies a calculation of the hydrodynamic force when using vortex meshless methods. The formula obtained satisfies the fundamental law of hydrodynamic momentum conservation. It is derived mathematically rigorously without any assumptions.