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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