Overall Mass Balance and Continuity Equation

6 OVERALL MASS BALANCE AND CONTINUITY EQUATION 2.6A Introduction and Simple Mass Balances 

In fluid dynamics fluids are in motion. Generally, they are moved from place to place by means of mechanical devices such as pumps or blowers, by gravity head, or by pressure, and flow through systems of piping and/or process equipment. The first step in the solution of flow problems is generally to apply the principles of the conservation of mass to the whole system or to any part of the system. First, we will consider an elementary balance on a simple geometry, and later we shall derive the general mass-balance equation. 

Simple mass or material balances were introduced in Section 1.5, where 

in fluid flow, we are usually working with rates of flow and usually at steady state, the rate of accumulation is zero and we obtain 

In Fig. 2.6-1 a simple flow system is shown where fluid enters section 1 with an 

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