26 this equation relates hf to the wall shear stress

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Unformatted text preview: e problem of head loss in pipe flow. Functionally, we can assume that w | v v where | F( , V, , d, ) is the wall-roughness height. Then dimensional analysis tells us that e-Text Main Menu | Textbook Table of Contents | Study Guide (6.28) 340 Chapter 6 Viscous Flow in Ducts 8w V2 f F Red, (6.29) d The dimensionless parameter f is called the Darcy friction factor, after Henry Darcy (1803 – 1858), a French engineer whose pipe-flow experiments in 1857 first established the effect of roughness on pipe resistance. Combining Eqs. (6.27) and (6.29), we obtain the desired expression for finding pipehead loss hf f L V2 d 2g (6.30) This is the Darcy-Weisbach equation, valid for duct flows of any cross section and for laminar and turbulent flow. It was proposed by Julius Weisbach, a German professor who in 1850 published the first modern textbook on hydrodynamics. Our only remaining problem is to find the form of the function F in Eq. (6.29) and plot it in the Moody chart of Fig. 6.13. Equations of Motion For eithe...
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