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# quiz1 - 2.25 ADVANCED FLUID MECHANICS QUIZ 1 Fall 2005...

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2.25 ADVANCED FLUID MECHANICS Fall 2005 QUIZ 1 THURSDAY, October 13, 2005, 7:00-9:00 P.M. OPEN QUIZ WHEN TOLD AT 7:00 PM THERE ARE TWO PROBLEMS OF EQUAL WEIGHT Please answer each question in SEPARATE books You may use FOUR (4) pages of handwritten notes as well as the handout on Bernoulli equation plus any tables you feel are necessary

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. ± ² ³ Consider a channel of height 2 R with rectangular cross-section as shown in the sketch. A hinged plank of a length L < R and at an angle θ is located at the center of the channel. (You may assume that L is small compared to the length perpendicular to the sketch.) The plank has a mass per unit width, m . A constant volume ﬂux per unit width, Q , of an inviscid, incompressible ﬂuid is applied at the inlet of the channel. a.) Find all equilibrium values for θ (include BOTH stable and unstable equilibria!) To simplify your calculation, you may assume that we have chosen the mass, m , and volume ﬂux, Q , such that for at least one equilibrium state, θ is small. b.) Which values of θ from part (a) represent stable equilibria? Which are unstable? Justify your answers.
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quiz1 - 2.25 ADVANCED FLUID MECHANICS QUIZ 1 Fall 2005...

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