Show that the force acting on a control surface of any arbitrary control volume is equal to the force on a larger regularly shaped control volume enclosing the given body. In order to do this you need a control volume that is multiply connected by surfaces \(S_{1}\) and \(S_{2}\). Then apply the divergence theorem in reverse to show that the forces on \(S_{1}\) and \(S_{2}\) are the same.

You should also write the Stokes equation in the following stress-divergence form:

\[abla \cdot \tilde{\sigma}=0\]

where \(\tilde{\sigma}\) is the total stress tensor defined as \(-\tilde{p I}+\tilde{\tau}\).

Show that the torque acting on any arbitrary control volume is again given as the torque on a larger regularly shaped control volume enclosing the given body.