Divergence Explained: Velocity & Density in Fluid Flow

  • Thread starter Thread starter ehrenfest
  • Start date Start date
  • Tags Tags
    Divergence
Click For Summary

Homework Help Overview

The discussion revolves around the concept of divergence in fluid dynamics, particularly focusing on its interpretation in relation to velocity and density within fluid flow. Participants are exploring how divergence relates to the flow of fluid and the implications of density in this context.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the relationship between velocity and density in the context of divergence, with some suggesting that divergence should relate to acceleration rather than density. Others are discussing the implications of fluid flow towards a central point and how this affects the interpretation of velocity. There is also a query about how making the volume infinitesimal relates to deriving the equation for divergence.

Discussion Status

The discussion is active, with participants raising various interpretations and clarifications regarding the concept of divergence. There is no explicit consensus, but several lines of reasoning are being explored, particularly around the relationship between velocity, density, and the mathematical formulation of divergence.

Contextual Notes

Participants are navigating assumptions about fluid flow, including the distinction between mass and volume flow rates, and the implications of spatial versus temporal changes in velocity.

ehrenfest
Messages
2,001
Reaction score
1
My book says that divergence can be understood in the context of fluid flow as the rate at which density flows out of a given region. It says that if F(x,y,z) is the velocity of a fluid, then that is the interpretation of the divergence. I fail to understand where the density comes in when we are only dealing with velocities at first and we only take a spatial derivative. It seems like the interpretation should be the rate of change of velocity i.e. acceleration.
 
Physics news on Phys.org
"Acceleration" implies a velocity changing with time. If you have a fluid flowing toward a central drain, for example, the velocity may vary with position but not time. A single molecule of the fluid could move toward the drain with constant velocity while different particles, around the drain, move with the same speed but different velocities.
 
Rate of fluid flow is related to volume, and not mass so the density doesn't enter...

Do you see how over a closed volume... the rate at which fluid is leaving the the volume is F.A (dot product of velocity with the area) over the volume... ie the flux of F through the area enclosing the volume...
 
OK and you just make that volume infinitesimal? How does making the volume infinitesimal get you the equation for the divergence? Is
 

Similar threads

  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 9 ·
Replies
9
Views
17K
Replies
3
Views
2K
Replies
0
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 1 ·
Replies
1
Views
1K