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Unformatted text preview: 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 v k = characteristic roughness height To account for roughness we first define an equivalent sand roughness coecient k (units: [ L ]), a measure of the characteristic roughness height. The parameter that determines the significance of the roughness k is the ratio k We thus distinguish the following two cases, depending of the value of the ratio k on the actual surface- e.g., ship hull. 1. Hydraulically smooth surface For k < v << , where 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 ) 1 2.20 - Marine Hydrodynamics, Spring 2005 2.20 2. Hydraulically rough surface For k >> >> v , the ow will resemble what is sketched in the following figure. separation v k In terms of sand grains: each sand grain can be thought of as a bluff body. The ow, 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....
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.20 taught by Professor Dickk.p.yue during the Spring '05 term at MIT.
- Spring '05