HNC Mechanical Engineering

Question

A thin walled pressure vessel which has an internal diameter of 100mm and a length of 200mm is made from a material 1.5mm thick. If it is subjected to and internal pressure of 5MPa calculate the circumferential and longitudinal stress.

Answer 1

Use the basic strength of materials relationships for thin walled cylindrical tanks.

 

L = length

r = radius = d/2 = (100 x 10^-3 m)/2

t = thickness of tank wall = 1.5 x 10^-3 m

P = pressure inside tank = 5 x 10⁶ Pa

 

Longitudinal stress:

 

σ_l = Pr / 2t = P(d/2) / 2t = Pd / 4t = (5 x 10⁶ Pa)(100 x 10^-3 m) / [4(1.5 x 10^-3 m)]

 

σ_l ≅ 8.333 x 10⁷ Pa = 83.33 MPa

 

Circumferential stress:

 

σ_c = Pr/t = P(d/2)/t = Pd / 2t = (5 x 10⁶ Pa)(100 x 10^-3 m) / [2(1.5 x 10^-3 m)]

 

σ_c ≅ 1.667 x 10⁸ Pa = 166.7 MPa

 

By the way, if you compare the formulas for longitudinal and circumferential stress, you will note that

 

σ_c = 2σ_l,

 

which is the result we just got. Also note the stresses do not depend on the tank length.