Question

You are tasked with designing a thin-walled vessel to contain a pressurized gas. You are given the parameters that the inner diameter of the tank will be 60 inches and the tank wall thickness will be 5/8" (0.625 inches). The allowable circumferential (hoop) stress and longitudinal stresses cannot exceed 30 ksi.

(1) What is the maximum pressure that can be applied within the tank before failure? = psi(2) If you had the opportunity to construct a spherical tank having an inside diameter of 60 inches and a wall thickness of 5/8" (instead of the thin-walled cylindrical tank as described above), what is the maximum pressure that can be applied to the spherical tank? = psi

Answer 1

Step-by-step explanation:

For cylinder

Diameter d = 60 inches

thickness t = 0.625 inches

circumferential (hoop) stress = 30 ksi

`hoop \ \ stress =\sigma_1=(P_1d)/(2t)\\\\\sigma_1=30ksi\\\\30000=(P_1* 60)/(2*0.625)\\\\P_1=624psi`

`longitudinal \ \ stress =\sigma_2=(P_2d)/(2t)\\\\\sigma_2=30ksi\\\\30000=(P_2* 60)/(4*0.625)\\\\30000=(P_2* 60)/(2.5)\\\\75000=P_2*60\\\\P_2=(75000)/(60) \\\\P_1=1250psi`

Therefore maximum pressure without failure is P₁ = 625 psi

ii) For Sphere

`\sigma_1=\sigma_2=(Pd)/(4t) \\\\P=(30000* 4 * 0.625)/(60) \\\\=(75000)/(60)\\\\=1250\ \ psi`