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# hw_06 - Name(s(up to three students per homework set Due In...

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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. Cimbala Total: 100 1 . (15 pts) Consider a vertical rectangular flat plate of height h and width w exposed to stagnant water of depth h on 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 2 h /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, P below = P above + ρ g| z |. Integrate to prove that the center of pressure is located at water depth 2 h /3. Hint : Integrate to calculate the actual moment about the top of the plate, and set it equal to the moment generated by the resultant force acting at the center of pressure. (You will also need to integrate to find the resultant force.)
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