Navier Stokes: Homework Q&A on Solution & Equations

[driven4rhythm]

Homework Statement

Solution and question are here: http://i51.tinypic.com/bg63qb.png

Homework Equations

Equations listed in image.

The Attempt at a Solution

I made several assumptions and there's one that I made that isn't correct but I don't understand why. My textbook lists an assumption for an example as "fully developed flow, so no properties vary in the x direction; δ/δx=0" So I would assume that -δP/δx=0 but it doesn't. Why is this?

 

[KataKoniK]

I would like to address your question regarding the assumption made in the textbook example. While it is true that fully developed flow implies that no properties vary in the x direction, this does not necessarily mean that the pressure gradient (-δP/δx) is equal to zero. The assumption in this case is that the velocity profile is fully developed, which means that the velocity distribution along the x direction does not change. However, the pressure gradient is still present and can be calculated using the Navier-Stokes equation. This assumption simplifies the problem and allows for easier calculations, but it is not always true in all cases. In some situations, the pressure gradient may also be affected by other factors such as changes in fluid properties or external forces. Therefore, it is important to carefully consider the assumptions made in a problem and verify their validity in each specific case. I hope this helps clarify your question.