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STRESS ON THIN-WALLED THIN-WALLED PRESSURE VESSELS A tank or pipe carrying a fuid or gas under a pressure is subjected to tensile orces, which resist bursting, developed across longitudinal and transverse sections. A.TANGENTIAL STRESS (CIRCUMFERENTIAL STRESS)
Consider the tank shown being subjected to an internal pressure p. The length o the tank is L and the wall thickness is t. Isolating the right hal o the tank, !"#$ ! # %T &where'
! # pressure(Area) ! # p*L T # Tension Tension T # Tensile Tensile +tress(Area) +tress(Area) σ T # ( t tL)
p*L#%(
σ t
tL)
pD σt= 2 t
&where' p
#pressure t # thickness * # diaeter I there e-ist an e-ternal pressure po and an internal pressure pi, the orula ay be e-pressed as'
( pi− po ) D σt=
2 t
LONGITUDINAL STRESS, σL
Consider the ree body section o the tank' The total orce orce acting at the rear o o the tank ! ust e/ual to the total longitudinal stress on the wall 0 T # 1LAwall. +ince t is so sall copared to *, the area o the wall is close to 2*t
I there e-ist an e-ternal pressure po and an internal pressure p i, the orula ay be e-pressed as'
( pi − po ) D σL=
2 t
3-. 4.) A cylindrical steel pressure vessel 5$$ in diaeter with a wall thickness o %$ , is subjected to an internal pressure o 5.6 789 %. (a) Calculate the tangential and longitudinal stresses in the steel. (b) To what value ay the internal pressure be increased i the stress in the steel is liited to 4%$ 789 %: (c) I the internal pressure were increased until the vessel burst, sketch the type o racture that would occur. +;L
b.) Longitudinal +tress(Tangential +ection)
c.)
3-. %.) A cylindrical pressure vessel is abricated ro steel plating that has a thickness o %$ . The diaeter o the pressure vessel is 56$ and its length is %.$ . *eterine the a-iu internal pressure that can be applied i the tensile stress is liited to =$ 70a. +;L
pD σt= 2 t
>.) Calculate the iniu wall thickness or a cylindrical vessel that is to carry a gas at a pressure o 45$$ psi. The diaeter o the vessel is % t, and the stress is liited to 4% ksi. +;L
Republic of the Philippines Aurora State College of Technology ENGINEERING DEPARTMENT FINAL TERM QUIZ CE 411: Mechanics of Fluid Name: ____________________________________ ec!ion: ______________________
"a!e: ______________
+3AT?;@' I.
BUOYANCY
4.) An object having a sp.gr. o $.=$ foats in a li/uid having a sp.gr. o $.B$. a.) ?hat is the percentage o the volue below the li/uid surace to the total volue o the body: b.) I the total volue above the li/uid surace is $.$%5, what is the weight o the object: c.) ?hat is the total load that will cause the object to be ully suberged: %.) A block with a horiDontal s/uare section >$c - >$c has a depth o %6c. It is allowed to foat on a body o li/uid which consist o %$c. o layer o water above a layer o ercury. The speciEc weight o the block is 4BB6$ 89. *eterine the position o the block. II.
HYDROSTATIC FORCE ACTING ON PLANE SURFACES
4.) A rectangular plate suberged in water is 4.6 by 4.B, the 4.6 side being horiDontal and the 4.B side being vertical. *eterine the agnitude o the orce on one side o the plate and the depth to its center o pressure i the top edge is $.> below the water surace.