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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 steady-state 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