Development of Microscopic Mechanical Energy Equation and Its Application

9 DEVELOPMENT OF MICROSCOPIC MECHANICAL ENERGY EQUATION AND ITS APPLICATION 

For isothermal problems of fluid dynamics, it is usually advisable to use a form of the energy balance that involves only mechanical energy terms. By taking the scalar product of the equation of motion, equation (6.6.3), with the velocity vector (v) we arrive at the mechanical energy balance (Bird et al., 1960). 

This scalar equation describes the rate of change of kinetic energy per unit mass for an element of fluid moving downstream. 

As discussed by Bird et al. (1960), we can rewrite this equation with the help of the equation of continuity as 

Rate of Increase in Kinetic Energy = Per Unit Volume 

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