Module 5: Reynolds Transport Theorem
  Lecture 11: Control mass, control volume, mass-, momentum-, kinetic energy balance
 
 
Mathematical analysis of fluid motion and associated properties

There are two ways to carry out the analysis:

  • Control mass: In such an analysis, a fixed mass of fluid element in the flow-field is identified and conservation equations for properties such as momentum, energy or concentration are written. The identified mass moves around in the flow-field. Its property may change from one location to another; however, the property must correspond to the same contents of the identified fluid element. In general, such approach is mathematically or experimentally difficult to apply.
  • Control volume: This approach is popular and widely applied in the analysis. An arbitrary fixed volume located at a certain place in the flow-field is identified and the conservation equations are written. The property under consideration or analysis may change with time.
    • If  is a general property associated with fluid, then  and   may be considered to describe change in the property,  of the fluid, following the control mass (CM) and control volume (CV)approach, respectively.
    • The surface which bounds CV is called control surface (CS). In the CV approach, the co-ordinate axis is first fixed. A ‘CV’ is then marked in the flow-field. Choice of location and shape of CV are important for mathematical formulation.