{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

chap0050 - Darcy-Weisbach Friction Factors for Laminar and...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Darcy-Weisbach Friction Factors for Laminar and Turbulent Pipe Flows: Formulas and Moody Diagram By M.S. Ghidaoui, Spring 2002 The Darcy-Weisbach wall shear stress formula is as follows (See CIVL 151, Chapter on Dimensional Analysis): 8 2 0 V f ρ τ = where f = friction factor ; V=Q/A= cross sectional average velocity (see Figure 1); ρ = density of the fluid; τ 0 =wall shear stress. To apply this formula, the friction factor needs to be determined; thus, the objective of this chapter. From dimensional analysis you found that (See CIVL 151, Chapter on Dimensional Analysis): ) , ( D e R f e Ψ = where R e =VD/v = Reynolds number; D= pipe diameter; e= pipe roughness (in some books the symbols ε or k are used instead of e ); and e/D= relative roughness. The values of e can be found in tables and from pipe manufacturers. For example (Source: Fluid Mechanics by Streeter and Wylie, 1981): Riveted Steel e= 0.99 mm Concrete e= 0.3 to 3 mm Wood Stave e= 0.18 to 0.9 mm Cast Iron e= 0.25 mm Galvanized Iron e= 0.15 mm Asphalted Cast Iron e= 0.12 mm Commercial Steel or Wrought Iron e= 0.046 mm Drawn Tubing e= 0.0015 mm Essentially, the objective of this chapter is to determine the function Ψ for laminar and turbulent flows. Frictional Velocity * 0 u : Thus far, we have introduced and used * 0 u but we did not mention how we relate this velocity to the cross sectional average velocity in the pipe V. Using the Darcy- Weisbach formula we have: 2 * 0 2 0 8 u V f ρ ρ τ = = 8 * 0 f V u e o = = τ
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
V u (r) Remark : Other empirical formulas such as Manning equation and Chezy equation can be used to estimate * 0 u . In fact, in open channel, either the Manning equation or
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern