Divergence in cylindrical coordinate system

In summary, the conversation is about understanding the derivation of the divergence formula in cylindrical coordinates. The paper provided does a good job of explaining it, but the speaker is having trouble understanding two specific things that the author does. These are the equations \frac{\partial\hat{\rho}}{\partial\phi} = \hat{\phi} and \frac{\partial\hat{\phi}}{\partial\phi} = \hat{\rho}, which can be found in the derivation on page 3. The speaker is asking for help in understanding these equations. Additionally, they mention a unit vector \overline{\rho} that can be found on page 1 of the link provided.
  • #1
Sesse
5
0
I am trying to understand the derivation of the divergence formula in cylindrical coordinates. www.csupomona.edu/~ajm/materials/delcyl.pdf paper does a good job of explaining it but I don't understand 2 things that the author does.
[tex]\frac{\partial\hat{\rho}}{\partial\phi} = \hat{\phi}[/tex] and [tex]\frac{\partial\hat{\phi}}{\partial\phi} = \hat{\rho}[/tex]
Derivation is on page 3.
Can anyone help me understand this?
 
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  • #2
go back to page 1: "derivation of unit vectors with the coordinates"
 
  • #3
Sesse said:
I am trying to understand the derivation of the divergence formula in cylindrical coordinates. www.csupomona.edu/~ajm/materials/delcyl.pdf[/URL] paper does a good job of explaining it but I don't understand 2 things that the author does.
[tex]\frac{\partial\hat{\rho}}{\partial\phi} = \hat{\phi}[/tex] and [tex]\frac{\partial\hat{\phi}}{\partial\phi} = \hat{\rho}[/tex]
Derivation is on page 3.
Can anyone help me understand this?[/QUOTE]

As note below, one finds z^ etc (unit vector), in variation vectors does the differentiation with respect to [tex]\rho[/tex],[tex]\phi[/tex], z

OK
Now my question is how do you find

[tex]\overline{}[/tex][tex]\rho[/tex] (line above, could not get that to work)= x [tex]\widehat{}[/tex]x+ y [tex]\widehat {}[/tex]y
 
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  • #4
that one is found in page 1 of the link
 

Related to Divergence in cylindrical coordinate system

1. What is divergence in cylindrical coordinate system?

Divergence in cylindrical coordinate system is a measure of the rate at which a vector field is flowing outward or inward from a given point in space. It is represented by the symbol ∇ ⋅ F and is calculated by taking the partial derivatives of the vector field with respect to each coordinate in the cylindrical coordinate system.

2. What is the formula for calculating divergence in cylindrical coordinate system?

The formula for calculating divergence in cylindrical coordinate system is:

∇ ⋅ F = 1/r * (∂(rFr)/∂r + ∂Fθ/∂θ + ∂Fz/∂z)

Where r, θ, and z are the coordinates in the cylindrical coordinate system and Fr, Fθ, and Fz are the components of the vector field in the r, θ, and z directions, respectively.

3. How is divergence related to the flow of a vector field?

Divergence is directly related to the flow of a vector field as it represents the net flux or flow of the vector field through a given point. A positive divergence indicates that the vector field is flowing outward from the point, while a negative divergence indicates that the vector field is flowing inward towards the point.

4. What does it mean if the divergence of a vector field is zero?

If the divergence of a vector field is zero, it means that the vector field is neither flowing outward nor inward at that point. This can also be thought of as the vector field having a balanced flow or no net flux through the point.

5. How is divergence used in physics and engineering?

Divergence is used in physics and engineering to analyze the flow of vector fields and to understand the behavior of fluid and electric fields. It is also used in the study of fluid dynamics, electromagnetism, and other fields where vector fields play a significant role.

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