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OP warned about asking questions that can easily be Googled.

How does equation of continuity relate to conservation of mass principle? Laymans terms please.

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OP warned about asking questions that can easily be Googled.

How does equation of continuity relate to conservation of mass principle? Laymans terms please.

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DrClaude

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The ``continuity equation'' is a direct consequence of the rather trivial fact that what goes into the hose must come out. The volume of water flowing through the hose per unit time (i.e. theflow rate) at the left must be equal to the flow rate at the right or in fact anywhere along the hose. Moreover, the flow rate at [any] point in the hose is equal to the area of the hose at that point times the speed with which the fluid is moving:

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jbriggs444

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SteamKing

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Equation of continuity (in layman's terms):How does equation of continuity relate to conservation of mass principle? Laymans terms please.

What goes

This is analogous to Newton's Law of Gravity (also in layman's terms):

What goes

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Chestermiller

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Chet

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The equation of continuity reflects the volume concervation:How does equation of continuity relate to conservation of mass principle? Laymans terms please.

[itex]Q=\frac{V}{t}=\int_{0}^{S}w(s)ds[/itex]

where w is velocity and S is the cross section area,

and mass is related to volume as it is integral of dencity over the volume:

[itex]m=\int_{0}^{V}\rho (v)dv[/itex]

when

[itex]\rho =const(v)[/itex]

water at no very high pressure ie,

[itex]m=\int_{0}^{V}\rho (v)dv = \rho\cdot\int_{0}^{V}dv = \rho\cdot V[/itex]

the mass per time:

[itex]G=\frac{dm}{dt}= \rho\cdot Q[/itex]

and Q is shown at the 3-rd line of the post.

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Chestermiller

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$$\frac{\partial ρ}{\partial t}+\vec{∇}\centerdot (ρ\vec{v})=0$$

The rest of the posts in the thread are just specific examples of how this equation can be applied in practice.

Chet

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I'm interested too what OP mean. But I see that all who tried to answer tried to ralate the "continuity equation" and the "conservation of mass principle". And all tried to follow the paradigm "Laymans terms".I think that the form of the continuity equation he was referring to was

Is the nabla operator following that paradigm?

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Chestermiller

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My understanding was what that he was asking to explain what the equation was saying in layman's terms. So I guess the nabla operator is not inconsistent with that paradigm, if the equation he was referring to contained the nabla parameter.I'm interested too what OP mean. But I see that all who tried to answer tried to ralate the "continuity equation" and the "conservation of mass principle". And all tried to follow the paradigm "Laymans terms".

Is the nabla operator following that paradigm?

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I see that if you do not to see the:My understanding was what that he was asking to explain what the equation was saying in layman's terms. .

you will not see that what ever all we do.How does equation of continuity relate toconservation of mass principle

How much books it need to link showing that equation without the nabla symbol exist? That equation may be writen even in no differential form asif the equation he was referring to contained the nabla parameter

$$v_i \cdot s_i = const $$

To be honest it needs to say that the v is the velocity that is the output-averaging by the cross section (do not sure on how it must be said english).

And since that averaging is based on the law of conservation of mass, here, too, there is an opportunity to show this relationship "laymans terms".

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Chestermiller

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I have no idea what you are saying. The form of the continuity equation I wrote appears in every book on fluid mechanics and transport phenomena (exactly as I wrote it), and captures mathematically the principle of conservation of mass.I see that if you do not to see the:

you will not see that what ever all we do.

How much books it need to link showing that equation without the nabla symbol exist? That equation may be writen even in no differential form as

$$v_i \cdot s_i = const $$

To be honest it needs to say that the v is the velocity that is the output-averaging by the cross section (do not sure on how it must be said english).

- #12

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I see. I have a lot of sources but they are not english. That's why I show the first-google-paged links:I have no idea what you are saying.

http://theory.uwinnipeg.ca/mod_tech/node65.html

http://www.fsl.orst.edu/geowater/FX3/help/8_Hydraulic_Reference/Continuity_Equation.htm

and so on. Such links can be found by request

I am sorry that our doalog is so strange but I do not see the sence to continue. We have about a one hour after midnight now. Good by mr Chestermiller.

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Chestermiller

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I don't even know what we are arguing about, or even if we are arguing. Are you saying that the equation that I wrote is incorrect, or are you just saying that you don't think (based on some sort of sixth sense) that the standard continuity equation I wrote is what the OP was referring to?I see. I have a lot of sources but they are not english. That's why I show the first-google-paged links:

http://theory.uwinnipeg.ca/mod_tech/node65.html

http://www.fsl.orst.edu/geowater/FX3/help/8_Hydraulic_Reference/Continuity_Equation.htm

and so on. Such links can be found by requestequation of continuity.

I am sorry that our doalog is so strange but I do not see the sence to continue. We have about a one hour after midnight now. Good by mr Chestermiller.

My Warning finger is getting itchy.

Chet

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