lecture7

# lecture7 - 2.20 Marine Hydrodynamics Spring 2005 Lecture 7...

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Lecture 7 - Marine Hydrodynamics Lecture 7 Chapter 3 Ideal Fluid Flow The structure of Lecture 7 has as follows: In paragraph 3.0 we introduce the concept of inviscid ﬂuid and formulate the governing equations and boundary conditions for an ideal ﬂuid ﬂow. In paragraph 3.1 we introduce the concept of circulation and state Kelvin’s theorem (a conservation law for angular momentum). In paragraph 3.2 we introduce the concept of vorticity. Inviscid Fluid ν =0 + Ideal Fluid Flow Incompressible Flow ( § 1.1) or ∇· ±v Dt 1 2.20 - Marine Hydrodynamics, Spring 2005 2.20

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3.0 Governing Equations and Boundary Conditions for Ideal Flow Inviscid Fluid, Ideal Flow Recall Reynolds number is a qualitative measure of the importance of viscous forces compared to inertia forces, UL inertia forces R e = = ν viscous forces For many marine hydrodynamics problems studied in 13.021 the characteristic lengths and velocities are L 1m and U 1m/s respectively. The kinematic viscosity in water is ν water =10 6 m 2 /s leading thus to typical Reynolds numbers with respect to U and L in the order of R e = 10 6 >>> 1 ν 1 viscous forces ± 0 R e inertia forces This means that viscous eﬀects are << compared to inertial eﬀects - or conﬁned within very small regions. In other words, for many marine hydrodynamics prob- lems, viscous eﬀects can be neglected for the bulk of the ﬂow. Neglecting viscous eﬀects is equivalent to setting the kinematic viscosity ν = 0, but ν =0 inviscid ﬂuid Therefore, for the typical marine hydrodynamics problems we assume incompressible ﬂow + inviscid ﬂuid ideal ﬂuid ﬂow which turns out to be a good approximation for many problems.
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lecture7 - 2.20 Marine Hydrodynamics Spring 2005 Lecture 7...

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