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fall_2003_pset13

# fall_2003_pset13 - Massachusetts Institute of Technology...

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Unformatted text preview: Massachusetts Institute of Technology Department of Aeronautics and Astronautics Cambridge, MA 02139 16.01/16.02 Unified Engineering I, II Fall 2003 Problem Set 13 Time Spent (min) F16 Name: F17 Due Date: 12/2/03 M17 M18 Study Time Announcements: Fall 2003 Uniﬁed Engineering Fluids Problems F16–F17 F16. �1 (x, y ) and �2 (x, y ) are known to be physically-possible ﬂows (i.e. satisfy mass con­ servation), and their corresponding pressure ﬁelds p1 (x, y ) and p2 (x, y ) are known via the Bernoulli equation. a) A third ﬂow is now deﬁned by �3 (x, y ) = �1 + �2 . Explain how you would obtain its corresponding pressure ﬁeld p3 . b) Yet another ﬂow �4 = � �1 /�x is deﬁned. Is this a physically-possible ﬂow? F17. A vortex ﬂow is given by u1 (x, y ) = x2 y + y2 v1 (x, y ) = −x + y2 x2 A uniform ﬂow in the x-direction is given by u2 (x, y ) = V� v2 (x, y ) = 0 Superimpose these two ﬂows, determine the pressure ﬁeld, and ﬁnd the x, y location of the p oint of maximum pressure. Unified Engineering I Problem M17 In question M16. You had a state of strain: Fall 2003 Given a state of plane strain: e11 = -0.000200, e22 = +0.000400, e12 = -0.000200, do the following: a) If a strain gauge rosette, with three gauges at 60° to each other was placed with one of the gauges orientated along the x1 direction. What strains would the three gauges read? b) By representing the strains as a matrix calculate the principal strains and principal directions via the eigenvalue and eigenvectors of the matrix. Show that this is consistent with the values you calculated in M16. c) If the state of strain was no longer plane strain, and was now e11 = -0.000200, e22 = +0.000400, e12 = -0.000200, e33 = 0.000300, e23 = 0, e123 = 0. What would the principal strains now be? Problem M18 Read Ashby and Jones Chapters 4, 5 and 6. Answer the following short questions (each answer should be one or two sentences only, the important task is the reading, the questions are to focus your attention): i) What are the two principal factors that contribute to the Young’s modulus of a homogeneous material? ii) What is the glass transition temperature of a polymer and what is the underlying cause for this? iii) Why do metals tend to have higher densities than ceramics or polymers? iv) What is the relationship between the force exerted by an interatomic bond as a function of separation of the atoms and the potential energy associated with the same separation of the atoms? ...
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