Show that the force acting on a control surface of any arbitrary control volume is equal to
Question:
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.
Step by Step Answer:
Advanced Transport Phenomena Analysis Modeling And Computations
ISBN: 9780521762618
1st Edition
Authors: P. A. Ramachandran