Question

A spherical balloon is filled with a gas. The outer diameter of the balloon is 20 in. and the thick-ness is 0.012 in. Calculate the maximum permissible pressure in the balloon if the allowable tensile stress and the allowable shear stress in the balloon are 1 ksi and 0.3 ksi, respectively.

Answer 1

1.4 psi

Step-by-step explanation:

Before diving into the solution to the question above, let's pick out the parameters needed in solving this problem from the question.

=> The measurement for the outer diameter of the balloon = 20 inches, the measurement for the thickness = 0.012 in, the allowable tensile stress = 1ksi and the allowable shear stress in the balloon = 0.3 ksi.

The first thing to determine is the inner diameter = 20 - 2 × 0.012 in = 19.976 in.

Therefore, the tensile stress:

1000 = k × [19.976/2]÷ 2 × 0.012 = 2.4 psi.

Also, the sheer stress which is also the maximum permissible pressure in the balloon can be calculated below as:

0.3 × 1000 = k × [19.976/2]/ 4 × 0.012 = 1.4 psi.