Why is the continuity equation called the continuity equation?

In summary, the continuity equation models an incompressible fluid and ensures that the flow rate of fluid is consistent throughout the pipe. The term "continuity" is similar to "conservation" and refers to the concept that the volume of fluid passing through a section of the pipe must remain constant. This is reflected in the units of the equation, which measure volume per unit time and remain the same throughout the pipe.
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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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  • #2
"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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  • #3


The continuity equation is called the continuity equation because it represents the principle of continuity, which states that matter cannot be created or destroyed, only transferred or transformed. In the context of the equation, continuity refers to the continuous flow of a fluid or substance through a particular system. This means that the amount of fluid entering a system must be equal to the amount of fluid exiting the system, ensuring that there is no accumulation or depletion of the substance. In simpler terms, the continuity equation ensures that there is a balance in the flow of a substance, maintaining its continuity. This concept is important in various fields such as fluid mechanics, thermodynamics, and electromagnetism, making the continuity equation a fundamental law in physics.
 

1. What is the continuity equation?

The continuity equation is a fundamental principle in physics that states that the amount of a conserved quantity within a specified region of space can only change through the flow of that quantity into or out of the region.

2. Why is it called the continuity equation?

The continuity equation is called so because it describes the continuity of a conserved quantity, meaning that the quantity remains constant as it flows through a system.

3. What quantities does the continuity equation apply to?

The continuity equation applies to any conserved quantity, such as mass, energy, or momentum. It is a universal principle that can be applied to various physical systems.

4. How is the continuity equation used in fluid mechanics?

In fluid mechanics, the continuity equation is used to describe the conservation of mass in a fluid. It states that the rate of change of mass within a system is equal to the net flow of mass into or out of the system.

5. Is the continuity equation always true?

Yes, the continuity equation is a fundamental principle in physics and is always true as long as the quantities involved are conserved. It is a mathematical representation of the law of conservation of mass.

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