Control Volume and Control Surfaces
Consider a control volume surrounding the cylinder as shown in the previous slide. Assume the flow around the cylinder is symmetric, therefore, only half of the control volume is needed as shown below. There are a total of five control surfaces in this problem.
- Surface 4 is the symmetric plane, therefore, does not contribute since no flow (therefore momentum) going through it.
- Surface 5 is the surface surrounding the cylinder, and the integration of the pressure and shear stresses on 5 will give the total force the cylinder is acting on the fluid: Rx. This force should balance with the forces acting on surfaces (1), (2) & (3) plus the momentum flow in & out of those surfaces. (Note: the force in y direction will be zero, why?)
- The surface forces on surfaces (1) & (3) will be free-stream pressure and they should cancel.
- Momentum flow in & out of (1) & (3) can be determined by integration.
- Question: Is there momentum flow out of surface (2)?