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chap0050

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

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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

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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
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