Why is the continuity equation called the continuity equation?

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Main Question or Discussion Point

Most of you are probably familiar with the continuity equation, but what does the term "continuity" mean? I mean, what is continous in the context of the continuity eq.?

Just wondering...
 

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"Continuity" is similar in this sense to "conservation." Since the continuity equation (I'm guessing you're talking about the one in fluid dynamics) models an incompressible fluid, a certain volume of fluid must pass a section of a pipe in the same time everywhere in the pipe. You can see this from the units of each side of the equation: [itex]m^3/s[/itex], or "volume per unit time" (the flow rate) is always the same everywhere in the pipe.
 
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