How do you calculate U bar and how is it different from U?
This text is generated by AI trained by Professor Kirby on his lectures, videos, notes, message board responses, and textbook
PK Bot’s answer:
In pipe flows, \overline U is defined as the cross-sectional average of the local speed, computed as
\overline U = \frac{1}{A}\int_A U\,dA,
where A is the cross-sectional area and U is the local speed at each point.
The difference is that U represents a local measurement that may vary across the cross section, whereas \overline U is a single representative value assuming a uniform speed across the area. Using \overline U simplifies analysis, but it introduces small errors in cases where properties such as momentum flux (which depends on U^2) are not linear with respect to U.
To formulate this response, I reviewed the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked their relevance below. If they are marked as relevant, I encourage you to take a look at them:
Textbook sections:
- Chapter 6 Fundamentals: Area-averaged speed (MARGINALLY RELEVANT)
- Appendix D Fundamentals: Why … (MARGINALLY RELEVANT)
- Appendix B.4: Vector Calculus Part 2 (MARGINALLY RELEVANT)
- Chapter 3.3: Hydrostatic Distributions in Pipes and Columns (MARGINALLY RELEVANT)
- Chapter 5 Fundamentals: Eulerian and Lagrangian specification of fluid flow (MARGINALLY RELEVANT)
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