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- Assuming the velocity vector for the radial direction is not zero, how do I get it? And other questions.

Pardon if the answers to my questions are obvious, because as usual I am trying to decipher everything on my own (as the material has not been taught to us quite well; then again it's graduate school). I just need someone to reassure me that I am understanding this correctly.

Say for example I have a pipe where the 2D advection dispersion equation applies on the flowing fluid (assume tangential/angular gradients are negligible), I will have the quantity u

1. Am I correct to assume that the 'true' velocity would be the resultant of these two? ergo, u = √(u

2. Assuming that there are density differences (due to temperature), obviously there will be differences to the point velocities as velocity = volumetric rate / area; and that volumetric rate and density are inversely related. If say for example, u

3. Also, if I want to calculate u

4. I know this is so undergraduate and stupid (pardon me, lol). I have a quantity D

So if I intend to calculate ∂D

Thank you so much in advance.

Say for example I have a pipe where the 2D advection dispersion equation applies on the flowing fluid (assume tangential/angular gradients are negligible), I will have the quantity u

_{r}for the velocity along the radial direction and u_{z}for the axial direction.1. Am I correct to assume that the 'true' velocity would be the resultant of these two? ergo, u = √(u

_{r}^{2}+ u_{z}^{2}), where u is the 'true entrance velocity' of the fluid in the pipe (and that u = u_{z}because it is a general assumption that u_{r}is zero since this is a pipe, and that radial velocities are near inexistent?)2. Assuming that there are density differences (due to temperature), obviously there will be differences to the point velocities as velocity = volumetric rate / area; and that volumetric rate and density are inversely related. If say for example, u

_{z}is zero, I am assuming that ∂u_{z}/∂z is not necessarily zero due to these density differences in different points along the fluid region (change in densities will cause change in volumetric rate). Is this correct?3. Also, if I want to calculate u

_{r}from the point volumetric rate, then it's u_{r}= volumetric rate / radial area, and I am assuming the radial area = 2πrL?4. I know this is so undergraduate and stupid (pardon me, lol). I have a quantity D

_{i}for diffusivity coefficient which is a function of flow rate F_{i}of two components, temperature T, and pressure P, and that D_{i}returns a vector containing the diffusivities of two components. If I intend to calculate ∂D_{i}/∂z, I can use chain rule. I am assuming this is correct, lol.So if I intend to calculate ∂D

_{i}/∂z, I can calculate (∂D_{i}/∂F_{i}) (∂F_{i}/∂z), which would probably be inefficient since I have to keep calling the diffusion function one by one to calculate the derivative for the first component and the second component. I thought of just chaining it to ∂D_{i}/∂T such that (∂D_{i}/∂T) (∂T/∂z) so that the returning vector would automatically be derivatives of the diffusion coefficient of each component. I am actually thinking this is allowable since I did not exactly break any mathematical law, lol. It's just that I want to make sure because manipulating my program with respect to T is so taxing.Thank you so much in advance.

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