Simplification of the right hand side of Eq. 3.3 gives:

However we know that,

Hence we get,

3.4

The first term in above equation is zero due to continuity equation. Hence the momentum equation (Eq. 3.1) reduces to

3.5

Equation 3.5 points out that the summation of all the forces acting on the elemental control volume leads to change in momentum of the element. However, these forces are of two types viz. body forces and surface forces. Examples of body forces are gravity and magnetic forces.. The only body force we shall be considering in the gravity for demonstration. The gravity force acting on the differential mass ρdxdydz within the control volume is

Body forces acting on the elements are pressure force and shear stress. The total stress tensor is,

3.6

The subscript notation for this stress tensor can be given as in Fig. 3.3,

Fig: 3.2 Notation for stresses in relation with the control volume