sm8 83

_______________________________________________________________________
PROBLEM (8.83) The closed-ended cylindrical steel tank seen in Fig. P8.78 has a radius r and a
height h. It is completely filled with a liquid of density
γ
and is subjected to an additional internal gas
pressure of p. Calculate the wall thickness needed:
(a) At the top of the tank.
(b) At quarter-height.
(c) At mid-height.
Given: p = 400 kPa, h = 20 m, r = 5 m,
γ
= 15 kN/m3
Requirement: The allowable stress in cylinder walls is limited to 150 MPa.
SOLUTION
Total pressure at any depth:
3
400(10 ) ( )
p
hy γ
=
+−
y
p
t
r
h(a) At :
y
h
=
3
400(10 )
p
Pa=
x
Liquid
pressure
Thus, 3
6
400(10 )5000 13.33
150(10 )
all
pr
tm
σ
== = m
(b) At 4:
y
h=
33 3
400(10 ) 15(10 )(15) 625(10 )
p
Pa=+ =
3
6
625(10 )5000 20.8
150(10 )
tm==m
(c) At 2:
y
h=
33 3
400(10 ) 15(10 )(10) 550(10 )
p
Pa=+ =
3
6
550(10 )5000 18.3
150(10 )
tm==m
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or
instructional purposes only to students enrolled in courses for which the textbook has been adopted. Any other
reproduction or translation of this work beyond that permitted by Sections 107 or 108 of the 1976 United States
Copyright Act without the permission of the copyright owner is unlawful.