Question 2:

For a thin walled cylindrical tube with an internal radius of ri, wall thickness of t, and length of L, answer the following

a) Show that the minimum mass of the tube is given by: m = 2N * L * * P * ri^2 * /y

Where N is the design safety factor, P is the pressure difference , ri is the internal radius, is the density, and y is the yield strength. The working stress (w) of the tube will always be w y / N

b) For the data given below, select the allow which will produce the lightest vessel. Assume L = 1 m.

c) Using the data given below, select the allow which will produce the minimum cost vessel. Assume L = 1 m.

Allow

1040 Carbon Steel y = 600 MPa Density = 7.8 g/cm3 Cost = 0.63 $/kg

304 Stainless Steel y = 205 MPa Density = 7.8 g/cm3 Cost = 3.70 $/kg

Ti-5Al-2.5Sn y = 827 MPa Density = 4.46 g/cm3 Cost = 15.00 $/kg

3003-H14 aluminim y = 145 MPa Density = 2.73 g/cm3 Cost = 3.00 $/kg