Material Derivative: Finding P for Steady State Flow

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SUMMARY

The discussion focuses on calculating the material derivative of the density function P = -1 - 2xy - 3z^3 for a steady state flow characterized by the velocity vector u = (3x - z, y + 3z, x - y). The material derivative is defined as the total derivative of a quantity as it moves with the flow. The user initially struggled with the application of the material derivative to the given density but ultimately proposed an answer of -8xy + 8zy - 12xz, which requires verification.

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material derivative?

I have to find the material derivative of the density P for the following steady state flow:

P = -1-2xy-3z^3 and u = (3x-z, y+3z, x-y)

I have looked at previous examples but I am not sure what i have to do with the density -1-2xy-3z^3 ... ?

please help.
 
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What's the DEFINITION of the material derivative?
 
I think iv got my head round it now. If someone has a spair few minutes could they check my answer of -8xy +8zy -12xz
 

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