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lecture19

# lecture19 - 2.20 Marine Hydrodynamics Spring 2005 Lecture...

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Lecture 19 - Marine Hydrodynamics Lecture 19 Turbulent Boundary Layers: Roughness Effects So far, we have assumed a ‘hydraulically smooth’ surface. In practice, it is rarely so, due to fouling, rust, rivets, etc. . . . U o Viscous sublayer δ v k = characteristic roughness height To account for roughness we first define an ‘equivalent sand roughness’ coeﬃcient k (units: [ L ]), a measure of the characteristic roughness height. The parameter that determines the significance of the roughness k is the ratio k δ We thus distinguish the following two cases, depending of the value of the ratio k δ on the actual surface - e.g., ship hull. 1. Hydraulically smooth surface For k < δ v << δ , where δ v is the viscous sub-layer thickness, k does not affect the turbulent boundary layer significantly. k << 1 C f C f , smooth C f = C f ( R e L ) δ 1 2.20 - Marine Hydrodynamics, Spring 2005 2.20

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2. Hydraulically rough surface For k >> δ >> δ v , the ﬂow will resemble what is sketched in the following figure. separation δ v k In terms of sand grains: each sand grain can be thought of as a bluff body. The ﬂow, thus separates downstream of each sand grain. Recalling that drag due to ‘separation’ = form drag >> viscous drag we can approximate the friction drag as the resultant drag due to the separation behind each sand grain. k k δ >> 1 C f C f , rough C f ���� = C f ( , R e L ) L weak dependence k/l C f C D F (Re L ) k/l = constant C f rough R L C f smooth C f , rough has only a weak dependence on R e L , since for bluff bodies C D ) = F ( R e L 2

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lecture19 - 2.20 Marine Hydrodynamics Spring 2005 Lecture...

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