- #1

SebastianRM

- 39

- 4

- Homework Statement
- In class we derive a relationship through the analysis of infinitesimal displacement.

- Relevant Equations
- $$\frac{1}{V}\frac{dV}{dt}= \nabla \cdot \vec{v}$$

in class we derived the following relationship:

$$\frac{1}{V}\frac{dV}{dt}= \nabla \cdot \vec{v}$$

This was derived though the analysis of linear deformation for a fluid-volume, where:

$$dV = dV_x +dV_y + dV_z$$

I understood the derived relation as: 1/V * (derivative wrt time) = div (velocity).

However, my professor recently told me that the $d/dt$ operator before V, stood for the material derivative and not the common derivative. I am very confused as to how is that the case, given that we did an infinitesimal analysis of linear deformation, in a way I could call analogous to any other infinitesimal analysis that results in the common derivative.

I also tried deriving the equation by taking the material derivative of V, and dividing by V. But I was unable to reach derive the result.

I hope you can help me understand guys.

Thank you for your time.

$$\frac{1}{V}\frac{dV}{dt}= \nabla \cdot \vec{v}$$

This was derived though the analysis of linear deformation for a fluid-volume, where:

$$dV = dV_x +dV_y + dV_z$$

I understood the derived relation as: 1/V * (derivative wrt time) = div (velocity).

However, my professor recently told me that the $d/dt$ operator before V, stood for the material derivative and not the common derivative. I am very confused as to how is that the case, given that we did an infinitesimal analysis of linear deformation, in a way I could call analogous to any other infinitesimal analysis that results in the common derivative.

I also tried deriving the equation by taking the material derivative of V, and dividing by V. But I was unable to reach derive the result.

I hope you can help me understand guys.

Thank you for your time.