why does surface roughness affect pressure drop in pipes
This text is generated by AI trained by Professor Brian J. Kirby on his lectures, videos, notes, message board responses, and textbook
PK Bot’s answer:
Surface roughness affects pressure drop in pipes because it influences the viscous dissipation factor, often referred to as the Darcy friction factor, f_{\mathrm{D}}, although Professor Kirby dislikes this term. The roughness of the pipe’s surface, typically quantified as the relative roughness \epsilon/d, where \epsilon is the roughness height and d is the pipe diameter, plays a significant role in determining how much energy is dissipated as the fluid flows through the pipe.
In turbulent flow, rougher surfaces increase the interaction between the fast-moving fluid near the center of the pipe and the slower-moving fluid near the walls. This interaction enhances the mixing and momentum transfer across the flow, leading to higher viscous stresses and, consequently, greater energy dissipation. The increased energy dissipation results in a higher pressure drop along the pipe.
The relationship between the viscous dissipation factor, Reynolds number \mathit{Re}, and relative roughness \epsilon/d is often represented using empirical correlations, such as the Haaland equation:
f_{\mathrm{D}} = \left\{-1.8\log_{10}\left[\left(\frac{\epsilon}{3.7d}\right)^{1.11} + \frac{6.9}{\mathit{Re}}\right]\right\}^{-2}
This equation shows that f_{\mathrm{D}} is a function of both the Reynolds number and the relative roughness, indicating that surface roughness is a critical factor in determining the pressure drop in turbulent pipe flow.
In formulating this response, I consulted the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked the sections according to their relevance. If they are marked as relevant, I encourage you to explore them:
Textbook sections:
- Chapter 6.4: Bernoulli constant drop in pipesIn practice, the hydraulic engineering design of pumpin… (HIGHLY RELEVANT)
- Chapter 6.4: Bernoulli constant drop in pipesIn practice, the hydraulic engineering design of pumpin… (HIGHLY RELEVANT)
- Appendix C.5: Viscous Dissipation Factor (HIGHLY RELEVANT)
- Chapter 6 Fundamentals: Moody Diagram and Haaland Equation (HIGHLY RELEVANT)
- Appendix C Fundamentals: Moody Diagram and Haaland Equation (HIGHLY RELEVANT)
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