lab1 - Object Impact on the Free Surface and Added Mass...

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Object Impact on the Free Surface and Added Mass Effect 2.016 Laboratory Fall 2005 Prof. A. Techet Introduction to Free Surface Impact Free surface impact of objects has applications to ocean engineering such as ship slamming hydrodynamics. The simplest geometric object to study is a sphere. The hydrodynamics are three dimensional, but several basic concepts can be observed using high speed video sequences. The main focus of Part A of this laboratory exercise is to determine the terminal velocity of a sphere that impacts the free surface of a tank of water at high speeds. When an object which is falling under the influence of gravity or subject to some other constant driving force is subject to a resistance (drag force) which increases with velocity, it will ultimately reach a maximum velocity where the drag force equals the driving force. This final, constant velocity of motion is called a "terminal velocity", a terminology made popular by skydivers. For objects moving through a fluid at low speeds so that turbulence is not a major factor, the terminal velocity is determined by viscous drag. F drag F buoyancy = ρ gV F g = mg M drag buoyancy gravity F F F + = 2 1 2 drag d F U C A ! = (1.1) The drag force is (1.2) where U is the speed of the object, A is the frontal area of the object, and C d = 0.5 is the coefficient of drag for a sphere.
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The buoyancy force is buoyancy F g ! = " gravity F mg = (1.3) and force of gravity is simply (1.4) Two photos removed for copyright reasons. Flow about a sphere in a wind tunnel. Lab part A: In this section of the lab you will observe objects impacting the free surface at two speeds and continuing down into the tank. You are asked to qualitatively consider the behavior of the sphere at the moment of impact: the splash formation (height and shape), wave generation, bubble/cavity formation behind the sphere, etc. You will take high speed video of the objects and use a software package to determine the position of the ball as a function of time, x(t) . A graduate student will show you how to operate the image recognition software. You will then use the data to determine the velocity of the ball as a function of time. As the ball approaches the bottom of the tank it may reach terminal velocity. Using the
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.016 taught by Professor Alexandratechet during the Fall '05 term at MIT.

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lab1 - Object Impact on the Free Surface and Added Mass...

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