Question

Estimate the maximum diameter to which a thin walled spherical shell can be expanded. If the diameter of the shell prior to expansion is 180 mm and material have an allowable strain of 35 percentage. A - 743 mm B-6480 mm C-243 mm D-Insufficient data.​

Answer 1

Answer:

which parallel and meridians should be used to describe the extinction of river Sao Francisco

Answer 2

Suppose, thickness of the shell before expansion = t mm.

Radius of the spherical shell before expansion = (180 / 2) mm = 90 mm.

Therefore, volume of the material used in the construction of the spherical shell = {4 * π * (90^2) * t} mm^3 = (32400 * π * t) mm^3.

Now, this volume will remain unchanged even after expansion; since, no thermal element is involved here. What all the mechanical stress can do is to expand its radius at the cost of reduction in thickness.

Now, maximum allowable strain = 35%. This means, the maximum allowable reduction in thickness = (0.35 * t) mm.

So, minimum thickness of the spherical shell after expansion = (0.65 * t) mm.

Let, r be the maximum radius of the spherical shell after expansion.

As, volume of the material that the shell was made up of remains unchanged under mechanical stress.

So, 4 * π * (r^2) * (0.65 * t) = 4 * π * (90^2) * t

(r^2) = (90^2) / 0.65

r ≈ 111.63 mm.

So, maximum diameter of the spherical shell after expansion ≈ 223.26 mm.