The direction of flux vectors in derivation of conservation of mass

In summary, the conservation law of mass states that the net mass entering a control volume must be equal to any variation of mass within the control volume during a given time interval. This applies to control volumes of any size and can change during the time interval.
  • #1
Mart1234
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In the derivation of the conservation law of the conservation of mass, the flux on one side enters and the flux on the other side leaves the control volume. I presume this is due to the assumption that the volume is infinitesimally small and hence v(x,y,z,t) will not change directions dramatically within the control volume. Is this the correct way of thinking about this or am I missing something?
 
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  • #2
:welcome:

That sounds plausible, but without the context it's difficult to say.
 
  • #3
No, what the law of conservation of mass says is that, during a given time interval, any variation of mass inside a control volume must be equal to the net mass that traverses the control surface during that same time interval. Not only the control volume can be of any size, but it can also increase or decrease during that time interval.
 

What is the meaning of "flux vectors" in the derivation of conservation of mass?

Flux vectors refer to the flow of a physical quantity, such as mass or energy, through a surface or boundary. In the derivation of conservation of mass, flux vectors are used to understand the movement of mass in and out of a system.

Why is the direction of flux vectors important in the derivation of conservation of mass?

The direction of flux vectors is important because it determines the sign of the mass flow rate and whether mass is entering or leaving the system. This is crucial in understanding the overall change in mass within a system and whether it is conserved or not.

How are flux vectors calculated in the derivation of conservation of mass?

Flux vectors are calculated using the dot product of the velocity vector and the normal vector of the surface or boundary. This gives the magnitude and direction of the flux through that surface.

What is the significance of the conservation of mass in scientific research?

The conservation of mass is a fundamental principle in physics and is applicable in many scientific fields, such as chemistry, biology, and engineering. It allows us to understand and predict the behavior of mass in various systems, and is crucial in developing new technologies and solving real-world problems.

Can the direction of flux vectors change in the derivation of conservation of mass?

Yes, the direction of flux vectors can change if the system is dynamic or if there are external forces acting on it. However, the overall principle of conservation of mass still holds true, as the total mass within the system remains constant regardless of the direction of flux vectors.

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