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Part 3: Derivation of the Continuity Equation
Consider an incompressible fluid (water is almost incompressible) flowing along a pipe, as in Figure 1. Its volume (V) is given by: Therefore the volume passing per second (the volumetric flow rate Q) is given by: But we can write velocity as distance moved/time (see Equation (1)), so we can replace L/t by v: (9) This is the FLOW EQUATION. Now consider pipes of different areas A1 and A2 as shown in Figure 2. The volumetric flow rate (Q) must be the same for both pipes, because we cannot gain or lose any fluid. Therefore from Equation (8) above: (10) This is the CONTINUITY EQUATION and it is true for any number of changes in pipe diameter for a single pipe arrangement (a single flow...
Read MorePart 4: The Continuity Equation for Multiple Pipe System
The rule for multiple flow paths for incompressible fluids is: This is written mathematically as: (10) Consider the pipe system shown below (in section) in Figure 3: In this case the flow in is given by: And the flow out is given by: So from Equation X we can write: (11) This is true for any number of flows in and...
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