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University of Michigan - Ann Arbor
Mechanical Engineering
Donald Siegel

THE UNIVERSITY OF MICHIGAN Department of Mechanical Engineering ME 235 Thermodynamics I / Winter 2014 / Section 002 HW 1 Due date: Jan. 16 2014 1.41 A tank has two rooms separated by a membrane. Room A has 1 kg air and volume 0.5 m , room B 3 3 has 0.75 m air with density 0.8 kg/m . The membrane is broken and the air comes to a uniform state. Find the final density of the air. 1.50 A piston/cylinder with cross sectional area of 0.01 m has a piston mass of 100 kg resting on the stops, as shown in Fig. P1.50. With an outside atmospheric pressure of 100 kPa, what should the water pressure be to lift the piston? Po g P1.50 1.53 A 5-kg cannon-ball acts as a piston in a cylinder with a diameter of 0.15 m. As the gun-powder is burned a pressure of 7 MPa is created in the gas behind the ball. What is the acceleration of the ball if the cylinder (cannon) is pointing horizontally? 2 1.59 A steel tank of cross sectional area 3 m and 16 m tall weighs 10 000 kg and it is open at the top, as shown in Fig. P1.59. We want to float it in the ocean so it sticks 10 m straight down by pouring concrete into the bottom of it. How much concrete should we use? P1.59 1.61 Liquid water with density ρ is filled on top of a thin piston in a cylinder with cross-sectional area A and total height H, as shown in Fig. P1.61. Air is let in under the piston so it pushes up, spilling the water over the edge. Derive the formula for the air pressure as a function of piston
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