Concepts of System and Control Volume

The common approaches for handling the properties in a flow field are discussed in the previous section. So, one can either look at individual particles and find out how the properties associated with it change as it moves. The other approach is to concentrate on a finite region of flow and find out how the flow properties change in that region. Based on above descriptions, the concepts of system and control volume are introduced here to tackle the mathematical model of the basic laws in fluid flows.

In fluid mechanics, a system is defined as the chunk of fluid particles whose identity does not change during the course of flow. Here, the identity means that the chunk is composed of same fluid particles as it flows. The natural consequence of this definition is that the mass of the system is invariable since it is composed of the same fluid particles. The shaded oval shown in Fig. 2.1.2(a), is considered as the system which moves towards left as indicated by an arrow. Although, the particles inside the oval do not change as it moves, but the shape and size of this oval may change during the course of the flow because different particles have different velocities, Moreover, Lagrangian approach will be more appropriate for this method of description.

A control volume is a volume or region in space whose identity is not same as fluid can enter and leave through the control surface which encloses this volume (Fig. 2.1.2-b). The shape and size of the control volume may be fixed or can change depending upon the choice of coordinate system used to analyze the flow situation. Here, the Eulerian variables are more suitable for analysis of flow field.

 

Fig. 2.1.2: Concept of system and control volume.