Material Derivative: Finding P for Steady State Flow

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In summary, material derivative is a concept in fluid dynamics that describes the change of a fluid particle's property as it moves through a flow field. It differs from ordinary derivative by taking into account the change of the property along the particle's path. In steady state flow, material derivative is important for finding the value of the pressure variable P, which is necessary for solving the governing equations. It is used in the continuity equation to set the material derivative of density to zero and solve for P. Moreover, material derivative can also be applied to other properties in steady state flow, but the specific equation used will depend on the governing equations.
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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 ... ?

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

What is material derivative?

Material derivative is a concept in fluid dynamics that is used to describe the change of a property of a fluid particle as it moves through a flow field.

How is material derivative different from ordinary derivative?

Material derivative takes into account the change of a fluid property as a particle moves through a flow field, while ordinary derivative only considers the change at a specific point in space.

What is the importance of material derivative in steady state flow?

In steady state flow, the material derivative is used to find the value of the pressure variable P, which is necessary for solving the governing equations of the flow.

How is the material derivative used to find P in steady state flow?

The material derivative is used in the continuity equation, which relates the change in density of a fluid particle to the divergence of the velocity field. By setting the material derivative of density to zero, the value of P can be solved for.

Can material derivative be applied to other properties besides pressure in steady state flow?

Yes, material derivative can be applied to other properties such as temperature or concentration in steady state flow. However, the specific equation used to find the value of the property will depend on the governing equations of the flow.

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