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final_solutions - DEPARTMENT OF OCEAN ENGINEERING...

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±±±± D EPARTMENT OF O CEAN E NGINEERING M ASSACHUSETTS I NSTITUTE OF T ECHNOLOGY 2.20 Marine Hydrodynamics SAMPLE FINAL EXAM THREE HOURS CLOSED BOOKS INSTRUCTIONS: For the problems in section A, fill in the required answers where indicated by ______________, (or in the provided space). When a list of options, [ . . . ] [ . . . ] [ . . . ], is provided select (by circling) all (none, one or more of) the options which apply. For problems in section B, write your solutions in the exam book provided. Unless otherwise indicated, use gravitational acceleration g = s m 10 2 , water density = ρ 10 3 kg m 3 , and 2 2 kinematic viscosity = ν 10 6 m s ; and air density = ρ kg 1 m 3 , and kinematic viscosity = ν 10 5 m s . Give all your numerical results in SI ( s , m , kg ) units. For numerical answers, you MUST give also the proper units (e.g., m 5 2 s not 5). There are a large number of problems and each individual answer can only be worth that many points, do NOT spend a disproportionate amount of time on any one problem. YOUR NAME: If you want us to post your course grade so that you can know it next week, please provide a nontrivial alphanumeric code here (don’t forget your code): 2.20 - SAMPLE FINAL EXAM Page 1
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SECTION A [35%] A1. A 2D point vortex of circulation Γ is placed at a point A (1, 1) in a corner created by the two walls x = 0 and y = 0. The horizontal force on the vortex (in terms of ρ and Γ ) is F = _____________________ Neglecting gravity, the pressure difference between the two points O(0,0) and B(1,0) is: ( P O P B )/ ρ =_______________________ A2. A thin square plate (density ρ s = 2 ρ ) of dimension 1cm × 1cm and thickness 1mm is released in water from rest. If the plate falls parallel to the square side (figure (a) below), its terminal velocity is U p = ____________________________________ (use friction coefficient C f = 1.328 R L -1/2 for laminar, and C f = 0.0725 R L -1/5 for turbulent boundary layer). A teardrop-shaped streamlined body has the same length (1cm) and total wetted area ( S =2cm 2 ) as the flat plate above, and has a weight in water (weight minus buoyancy) W =1.5·10 -3 N. When dropped from rest vertically (figure (b) below), the terminal velocity of this body is found to be U b = 0.25m/s. Based on this information, the form drag (total drag minus friction drag) of the teardrop-shaped body can be estimated to be D = _______________________. A3. A 2D circle has an unsteady horizontal velocity U(t) in an infinite fluid. The fluid itself has a uniform horizontal acceleration (to the right) of A = 1m/s 2 . At some instant t = τ , the total horizontal & hydrodynamic force on the circle is zero. Assuming potential flow, at t = τ , U ( τ ) = ____________m/s 2 to the [right] [left].
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