Question

2. A submarine has an external diameter of 5.5m.  If the maximum stress allowed in the material is 160 MN/m², analyse and compare the maximum safe working depth given by both Thin and Thick Cylinder Theories for wall thicknesses of:
   1. 25mm,
   2. 35mm and
   3. 45mm.

        Ignore any internal pressure.

        Density of sea water = 1023 kg/m³.

        Which theory is preferred, and why?

Answer 1

assumptions :

1. The submarine is cylindrical in shape.

2. The pressure is almost same at the top and bottom of the submarine.

Thick cylinder is cylinder whose wall thickness is greater than 1/20 times of its internal diameter. ... Thin cylinder is cylinder whose wall thickness is lesser than 1/20 times of its internal diameter.

here in this case max wall thickness is 45mm and corresponding minimum internal dia is 5.455m

Hence, it is a case of thin cylinder

Assumptions in Thin Cylinders

1. It is assumed that the stresses are uniformly distributed throughout the thickness of the wall.

2. As the magnitude of radial stresses is very small in thin cylinders, they are neglected while analyzing thin cylinders i.e. r=0

Stresses in Thin Cylinder

1. Circumferential Stress ( h):- This stress is directed along the tangent to the circumference of the cylinder. This stress is tensile in nature. This stress tends to increase the diameter. here in this case as the pressure is outside the cylinder therefore this stress will try to crush the submarine

total crushing force = total resisting force

water pressure X area = max permissible stress X cross sectional area along the length

Date DELTA PONO S density of water - Diameter of submarine L+ length of submarine o circumferential stress Total crushing force = Resisting force Igh x 1023 x 9.8 x TDX hx 3.14 x 5.5 - = 2x ox tx X 2x 160x100 x t. h = 1848.2296 xt For For For t=25mm t= 35 mm t= 45 mm h= h- h = 46.20m 64.68 m 83.17 m