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midterm-1-Fall-09

midterm-1-Fall-09 - In class Monday Professor Philip S...

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In class, Monday, September 28, 2009 Professor Philip S. Marcus ME 106 Mid-term Exam I The large tank in the Figure is filled with a static fluid with a density ρ ( z ) that is linear in the vertical direction z : ρ ( z ) = a + b z , where a and b are constants. Gravity g points in the downward ( - ˆ z ) direction. The unit vector ˆ y points into the paper. Attached to the interior of the left wall is a suction cup, inside of which there is a vacuum, so the pressure inside the suction cup is zero. The shape of the suction cup is quite irregular, and I have lost the equation used to generate it! However, I do know that the volume of the vacuum inside the suction cup has a value of V . I also remember that the suction cup is symmetric with respect to the x y plane at z = 0. (That is, if we put a mirror in the x y plane at z = 0, the image of the top of the suction cup in the mirror looks exactly like the bottom of the suction cup.) The cross-sectional area of the vacuum inside the suction cup in the x y plane at z = 0 is AA . The total surface area of the suction cup is AAA . I also remember the values of A 0 integraltext S dy dz , A 2 integraltext S z 2 dy dz , and A 3 integraltext S z 3 dy dz , where S is that portion of the area of the left-edge wall that is exposed to the vacuum (i.e., covered by the suction cup).

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midterm-1-Fall-09 - In class Monday Professor Philip S...

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