Due: In class, Friday October 21, 2005 Name(s)(up to three students per homework set): 1. 2. 3. For instructor or TA use only: Problem Score Points 1 15 2 10 3 15 4 15 5 15 6 15 7 15 ME 33 Fall Semester, 2005 Homework Set # 6 Professor J. M. CimbalaTotal: 100 1. (15 pts) Consider a vertical rectangular flat plate of height hand width wexposed to stagnant water of depth hon one side, and to atmospheric pressure on the other side as in Figure 3-24 in the text. Using centroids and centroidal moments of inertia, it can easily be shown that the center of pressure is located at water depth 2h/3. Suppose you know nothing about centroids, but instead approach this problem from the basic fundamentals only. In other words, suppose that all you know is the hydrostatic pressure relation, Pbelow= Pabove+ ρg|∆z|. Integrate to prove that the center of pressure is located at water depth 2h/3. Hint: Integrate to calculate the actualmoment about the top of the plate, and set it equal to the moment generated by the resultant forceacting at the center of pressure. (You will also need to integrate to find the resultant force.)
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