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# lecture15 - 2.20 Marine Hydrodynamics Spring 2005 Lecture...

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Lecture 15 - Marine Hydrodynamics Lecture 15 Chapter 4 - Real Fluid Effects ( ν = 0 ) Potential Flow Theory Drag = 0. Observed experiment (real ﬂuid ν << 1 but = 0) Drag = 0. In particular the total drag measured on a body is regarded as the sum of two components: the pressure or form drag, and the skin friction or viscous drag. Total Drag = Pressure Drag + Skin Friction Drag Profile Drag or Form Drag or Viscous Drag Drag Force due to Pressure �� �� p ˆ nds Drag Force due to Viscous Stresses �� �� τ ˆ tds S S where ˆ n and t ˆ are the normal and tangential unit vectors on the body surface respectively. The pressure and the viscous stresses on the body surface are p and τ respectively. The form drag is evaluated by integrating the pressure along the surface of the body. For bluff bodies that create large wakes the form drag is total drag. The skin friction drag is evaluated by integrating the viscous stresses on and along the body boundary. For streamlined bodies that do not create appreciable wakes, friction drag is dominant. 1 2.20 - Marine Hydrodynamics, Spring 2005 2.20

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� �� � 4.1 Form Drag 4.1.1 Form Drag on a Bluff Body Consider a sphere of diameter d : D (Drag) ρ ν U d If no DBC apply then we have seen from Dimensional Analysis that the drag coeﬃcient is a function of the Reynolds number only: C D = C D ( R e ) The drag coeﬃcient C D is defined with respect to the body’s projected area S : D D = = C D 1 ρU 2 S 1 ρU 2 πd 2 / 4 2 2 Projected area The Reynolds number R e is defined with respect to the body’s diameter d : Ud R e = ν The following graph shows the
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lecture15 - 2.20 Marine Hydrodynamics Spring 2005 Lecture...

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