Underwater Vehicle Sphere Thickness Calculation

_______________________________________________________________________
PROBLEM (8.86) An underwater vehicle having a living space that can be approximated as a sphere
of radius r and thickness t is to operate at depths h (Fig. P8.81). It is filled with air at pressure p . The
material of the sphere is steel with yield strength y
σ
. The factor of safety is to be ns . Determine the
required thickness t of the sphere.
Given: r = 2.5 m, p = 4 MPa, y
σ
= 600 MPa, h = 1000 m,
s
n = 2.5
Assumptions: Sea water weighs about
γ
= 10 kN/m3. Buckling of the vessel will not occur.
SOLUTION
600 240
2.5
y
all s
M
Pa
n
σ
σ == =
The maximum pressure acting on the sphere is
awa
p
pp p h
γ
=−=−
63
4(10 ) (10 10 )(1000) 6
M
Pa=− × =−
where the minus sign means outer pressure. Hence
6(2.5)
; 240
all pr
tt
σ
−
=−=
This gives
0.0625 62.5
req
tm==mm
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