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Unformatted text preview: 2.016 HW #5 Out: October 18, 2005 Due: October 25, 2005 1) Expand the following for i=1,2,3, j=1,2,3, and k=1,2,3, and write them in vector into a vector, and repeated letters imply summation. For example: a. b. u i = u 1 , u 2 , u 3 [ ] = r u notation. Recall for tensor notation, letters that appear only once imply expansion c. d. e. u i u i v i " u i " x i u i " v k " x i " ijk # u k # x j 2) Consider a submarine built very poorly, such that the axis of the propeller makes an angle " with the axis of the cylindrical submarine fuselage, as shown. If the propeller generates thrust, T, to drive the sub at steadystate speed, U, use inviscid flow theory (e.g. added mass) to find the trim angle, " . (Note: despite my misleading artwork, " # $ ) Assume the length of the sub is much greater than the radius, . ( R << L ) 3) The equation, ¡ = a cos( kx # ¢ t ) , is for a plane progressive wave moving to the [left] [right]. Draw a picture of the wave at time t = 0 sec and time t = 1 sec, and label the [right]....
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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.
 Fall '05
 AlexandraTechet

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