258 A Textbook of Machine Design EXERCISES 1. A steel cylinder of 1 metre diameter is carrying a fluid under a pressure of 10 N/mm². Calculate the necessary wall thickness, if the tensile stress is not to exceed 100 MPa. [Ans. 50 mm] 2. A steam boiler, 1.2 metre in diameter, generates steam at a gauge pressure of 0.7 N/mm². Assuming the efficiency of the riveted joints as 75%, find the thickness of the shell. Given that ultimate tensile stress 385 MPa and factor of safety -5. exceed 88 MPa. [Ans. 7.3 mm] 3. Find the thickness of a cast iron cylinder 250 mm in diameter to carry a pressure of 0.7 N/mm². Take maximum tensile stress for cast iron as 14 MPa. [Ans. 6.25 mm] 4. A pressure vessel has an internal diameter of I m and is to be subjected to an internal pressure of 2.75 N/mm² above the atmospheric pressure. Considering it as a thin cylinder and assuming the efficiency of its riveted joint to be 79%, calculate the plate thickness if the tensile stress in the material is not to [Ans. 20 mm] 5. A spherical shell of 800 mm diameter is subjected to an internal pressure of 2 N/mm². Find the [Ans. 4 mm] thickness required for the shell if the safe stress is not to exceed 100 MPa. 6. A bronze spherical shell of thickness 15 mm is installed in a chemical plant. The shell is subjected to an internal pressure of 1 N/mm². Find the diameter of the shell, if the permissible stress for the bronze [Ans. 2.64 m] is 55 MPa. The efficiency may be taken as 80%. 7. The pressure within the cylinder of a hydraulic press is 8.4 N/mm². The inside diameter of the cylinder is 25.4 mm. Determine the thickness of the cylinder wall, if the allowable tensile stress is 17.5 MPa. [Ans. 8.7 mm] 8. A thick cylindrical shell of internal diameter 150 mm has to withstand an internal fluid pressure of 50 N/mm². Determine its thickness so that the maximum stress in the section does not exceed 150 MPa. [Ans. 31 mm] 9. A steel tank for shipping gas is to have an inside diameter of 30 mm and a length of 1.2 metres. The [Ans. 4.5 mm] gas pressure is 15 N/mm². The permissible stress is to be 57.5 MPa. 10. The ram of a hydraulic press 200 mm internal diameter is subjected to an internal pressure of 10 N/mm². If the maximum stress in the material of the wall is not to exceed 28 MPa, find the external [Ans. 265 mm] diameter. 11. The maximum force exerted by a small hydraulic press is 500 kN. The working pressure of the fluid is 20 N/mm². Determine the diameter of the plunger, operating the table. Also suggest the suitable thickness for the cast steel cylinder in which the plunger operates, if the permissible stress for cast [Ans. 180 mm; 20 mm steel is 100 MPa. 12. Find the thickness of the flat end cover plates for a 1 N/mm² boiler that has a diameter of 600 mm. The [Ans. 38 mm limiting tensile stress in the boiler shell is 40 MPa. This vessel holds oll at high pressure.