lecture5

lecture5 - 2.20 Marine Hydrodynamics Spring 2005 Lecture 5...

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Lecture 5 - Marine Hydrodynamics Lecture 5 Chapter 2 - Similitude (Keyword: EQUAL RATIOS) Similitude: Similarity of behavior for different systems with equal similarity parameters. Prototype Model (real world) (physical/ analytical/ numerical . . . experiments) Similitude Similarity Parameters (SP’s) Geometric Similitude Length ratios, angles Kinematic Similitude Displacement ratios, velocity ratios Dynamic Similitude Force ratios, stress ratios, pressure ratios . . . Internal Constitution Similitude ρ, ν Boundary Condition Similitude . . . For similitude we require that the similarity parameters SP’s (eg. angles , length ratios , velocity ratios , etc) are equal for the model and the real world. Example 1 Two similar triangles have equal angles or equal length ratios . In this case the two triangles have geometric similitude . Example 2 For the ﬂow around a model ship to be similar to the ﬂow around the prototype ship, both model and prototype need to have equal angles and equal length and force ratios . In this case the model and the prototype have geometric and dynamic similitude . 1 2.20 - Marine Hydrodynamics, Spring 2005 2.20

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2.1 Dimensional Analysis (DA) to Obtain SP’s 2.1.1 Buckingham’s π theory Reduce number of variables derive dimensionally homogeneous relationships. 1. Specify (all) the (say N) relevant variables (dependent or independent): x 1 , x 2 , . . . x N e.g. time, force, ﬂuid density, distance. . . We want to relate the x i ’s to each other I ( x 1 , x 2 , . . . x N ) = 0 2. Identify (all) the (say P) relevant basic physical units (“dimensions”) e.g. M,L,T (P = 3) [temperature, charge, . . . ].
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