PROBLEM 1 (100 points): An open cylindrical tank contains water at a depth of 2 m when at rest. The diameter of the tank is 2 m. The tank is then rotated about its vertical axis, and the center of the fluid surface is depressed (Fig. 1). a) h X dr*** Z 3 R H y Created in BioRender.com bio b) X dr** Z R H hmin y Created in BioRender.com bio Fig. 1: solutionspile.com

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PROBLEM 1 (100 points): An open cylindrical tank contains water at a depth of 2 m when at rest. The diameter of the tank is 2 m. The tank is then rotated about its vertical axis, and the center of the fluid surface is depressed (Fig. 1). a) h X dr*** Z 3 R H y Created in BioRender.com bio b) X dr** Z R H hmin y Created in BioRender.com bio Fig. 1: The cylindrical tank with water on it. Fig. la represents the scenario in which the bottom of the tank is exposed. Fig. 1b represents the scenario where the water will be spilled out of the tank. No water is spilled from the tank during its rotation movements. Assume that the grav- itational acceleration is 9.81 m/s². Answer the following questions: a) What is the angular velocity, in rev/min, that exposes the bottom of the tank? HINT: 1 rev = 27 rad. (50 points) b) If the tank is rotated with an angular velocity equal to 30 rev/min, what is the tank walls' minimum height, in m, to prevent water from spilling over the sides? (50 points)

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An open cylindrical tank contains water at a depth of

2 m

when at rest. The diameter of the tank is

2 m

. The tank is then rotated about its vertical axis, and the center of the fluid surface is depressed (Fig. 1). Fig. 1: The cylindrical tank with water on it. Fig. 1a represents the scenario in which the bottom of the tank is exposed. Fig. 1b represents the scenario where the water will be spilled out of the tank. No water is spilled from the tank during its rotation movements. Assume that the gravitational acceleration is

9.81 m / s^{2}

. Answer the following questions: a) What is the angular velocity, in rev/min, that exposes the bottom of the tank? HINT: 1 rev

= 2 ? rad

. (50 points) b) If the tank is rotated with an angular velocity equal to

30 rev / min

, what is the tank walls' minimum height, in

m

, to prevent water from spilling over the sides? (50 points)

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