Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

592
PRESSuRE VESSELS
For the outer surface of a cylindrical pressure vessel, Equations (13.24) can be rewritten in
terms of the longitudinal and hoop stresses:
1 1
ε = σ − υσ =
⎛ pr pr
−υ ⎞
υ
E
E⎝
t t ⎠ = pr
( ) (1
2 2tE
− 2 )
long long hoop (14.10)
1 1
ε = σ − υσ =
⎛ pr pr
−υ ⎞
υ
E
E⎝
t t ⎠ = pr
( ) (2
2 2tE
− )
hoop hoop long (14.11)
These equations assume that the pressure vessel is fabricated from a homogeneous, isotropic
material that can be described by E and ν.
mecmovies
ExAmpLES
m14.1 Derivation of
equations for tangential
normal stress due to pressure
in a spherical pressure
vessel.
m14.2 Derivation of
equations for longitudinal
and circumferential stress
due to pressure in a cylindrical
pressure vessel.
ExAmpLE 14.1
Standpipe
30 ft
y
A standpipe with an inside diameter of 108 in. contains water, which has a weight
density of 62.4 lb/ft 3 . The column of water stands 30 ft above an outlet pipe, which
has an outside diameter of 6.625 in. and an inside diameter of 6.065 in.
(a) Determine the longitudinal and hoop stresses in the outlet pipe at point B.
(b) If the maximum hoop stress in the standpipe at point A must be limited to
2,500 psi, determine the minimum wall thickness that can be used for the
standpipe.
A
B
x
Outlet
Plan the Solution
The fluid pressure at points A and B is found from the unit weight and the height of
the fluid. Once the pressure is known, the equations for the longitudinal stress and
the hoop stress will be used to determine the stresses in the outlet pipe and the
minimum wall thickness required for the standpipe.
SolutioN
Fluid Pressure
The fluid pressure is the product of the unit weight and the height of the fluid:
p = γ h = (62.4 lb/ft 3 )(30 ft) = 1,872 lb/ft 2 = 13lb/in. 2 = 13psi