Why is the continuity equation called the continuity equation?

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SUMMARY

The continuity equation in fluid dynamics is named for its representation of the conservation of mass in an incompressible fluid. It asserts that a constant volume of fluid must flow through any cross-section of a pipe over time, maintaining a consistent flow rate measured in cubic meters per second (m³/s). This principle ensures that the mass flow rate remains unchanged throughout the pipe, highlighting the concept of continuity in fluid motion.

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  • Familiarity with the concept of mass conservation
  • Knowledge of flow rate calculations
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Students and professionals in engineering, particularly those specializing in fluid mechanics, as well as researchers interested in the principles of fluid flow and mass conservation.

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Most of you are probably familiar with the continuity equation, but what does the term "continuity" mean? I mean, what is continuous 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: m^3/s, or "volume per unit time" (the flow rate) is always the same everywhere in the pipe.
 
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