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1. A spherical tank for storing gas under a pressure is 20 m in diameter and is made of steel 20 mm thick. The yield point of the material is 240 MPa. If a factor of safety of 2 is desired, what is the maximum permissible internal pressure that the tank can hold? 2. A water tank 2 m in diameter and 5 m high is made from steel having a thickness of 10 mm. A) Determine the circumferential stress when the tank is fully filled with water. B) Determine the longitudinal stress at the bottom of the tank when it is fully filled with water. C) If the tangential stress is limited to 3 MPa, what maximum height to which the tank may be filled with water? 3. A large pipe called penstock in hydraulic work is 1.5 m in diameter. Here it is composed of wooden staves bound together by steel hoops each 300 mm2 in cross sectional area, and is used to conduct water from a reservoir to a powerhouse. If the maximum tensile stress permitted in the hoops is 130 MPa, what is the maximum spacing between hoops under a head of water of 30m? Use density of water equal to 1000 kg/m3.