Material Derivative: Finding P for Steady State Flow

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The discussion focuses on calculating the material derivative of density P in a steady state flow, specifically for the equation P = -1 - 2xy - 3z^3 and velocity field u = (3x - z, y + 3z, x - y). The user expresses confusion about how to apply the material derivative to the given density function and seeks clarification on its definition. After some explanation, the user believes they understand the concept and requests verification of their calculated material derivative, which is -8xy + 8zy - 12xz. The conversation highlights the importance of understanding the material derivative in fluid dynamics.
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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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