Overall Mass Balance and Continuity Equation
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 any part of the system.
InpUT – OUTPUT = ACCUMULATION
At steady state, the rate of accumulation is zero
∴ INPUT = OUTPUT
In the following Figure a simple flow system is shown where fluid enters section
1 with an average velocity (u1) and density (ρ1) through the cross-sectional area (A1).
The fluid leaves section 2 with an average velocity (u2) and density (ρ1) through the
cross-sectional area (A2).
Thus,
At steady state ṁ1=ṁ2
Q1 ρ1 = Q2 ρ2
u1 A1 ρ1 = u2 A2 ρ2
For incompressible fluids at the same temperature [ρ1 = ρ2]
∴ u1 A1 = u2 A2
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