We continue with the 1997 work of Noca et al. and o!er some additional closed-form expressions (and their derivations) for the evaluation of time-dependent forces on a body in an incompressible, viscous, and rotational #ow, which require only the knowledge of the velocity "eld (and its derivatives) in a "nite and arbitrarily chosen region enclosing the body. In particular, we o!er an expression for the force which only depends on the velocity "eld (and its derivatives) on the surface of an arbitrary control volume. These expressions are particularly useful for experimental techniques like Digital Particle Image Velocimetry (DPIV) which provide time sequences of 2-D velocity "elds but not pressure "elds. For some common #ow situations (freely moving objects, #exible bodies, #ying and swimming animals, low Reynolds number #ows, soap "lm tunnels), these techniques may be more viable than traditional methods (strain gages). The formulations can also be of some interest to the Computational Fluid Dynamics (CFD) community, especially when pressure is not evaluated explicitly, such as in vorticity-based algorithms. From a theoretical point of view, they provide an explicit relation between loading and #ow structure. In the present work, the formulations are tested on a numerical #ow simulation using a high-resolution vortex method and experimentally with DPIV on a circular cylinder #ow.