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Unformatted text preview: 09/16/09 Professor Philip S. Marcus ME106 Problem Set 3 All problems due in class Wednesday September 23, 2009 Do Munson (6 th Edition) problems: 2.67, 2.73, 2.82, 2.87, and 2.95. O1) Figure a shows a tank with bottom cross-sectional area α is filled with a fluid of density ρ 1 ( z ) = ρ- b ( z- z ), where ρ , b and z are constants. The pressure P ( z ) in the tank obeys dP dz =- ρ 1 g . Outside the tank the pressure is P out and is constant. The shaded plate of area A is symmetrical about the two dashed lines parallel to the x and z axes, The total force on the plate due to the fluids inside and outside the tank is F =- f ˆ y . The geometric center C of the plate (the place where the dashed lines cross) is at ( X C ,Y C ,Z C ), and the point labeled G is at ( X G ,Y G ,Z G ). The torque at C is Γ C , so by Lecture 8, the torque at G is Γ G = Γ C + [( X G- X C ) ˆ x + ( Y G- Y C ) ˆ y + ( Z G- Z c ) ˆ z ] × F . (1) We now add a layer of lighter fluid with density ρ 2 ( z ) = ρ L e- az and with total mass 1 M...
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- Fall '08
- Force, zt, Patm, shaded plate