If ‘p’ is the pressure on the cylinder, ‘d’ and ‘t’ are the diameter and wall thickness, E is the Young’s Modulus and μ is the Poisson’s Ratio, the volumetric strain (εv ) in thin wall cylinder can be given by

$\frac{{pd}}{{6tE}} \times \left( {5+ 4\mu} \right)$

$\frac{{pd}}{{2tE}} \times \left( {5 - 4\mu} \right)$

$\frac{{pd}}{{4tE}} \times \left( {5 - 4\mu} \right)$

$\frac{{pd}}{{6tE}} \times \left( {5+ 4\mu} \right)$

$\frac{{pd}}{{8tE}} \times \left( {5 - 4\mu} \right)$

Internal and external radii of a thick cylinder are a and b. It is subjected to an internal pressure of pi. The radial stress at a radius r in the cylinder is

$\frac{{{b^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{a^2}}}{{{r^2}}}} \right)$

$\frac{{{a^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{a^2}}}{{{r^2}}}} \right)$

$\frac{{{a^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{b^2}}}{{{r^2}}}} \right)$

$\frac{{{b^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{a^2}}}{{{r^2}}}} \right)$

$\frac{{{b^2}{p_i}}}{{{b^2} - {a^2}}}\left( {1 - \frac{{{b^2}}}{{{r^2}}}} \right)$

In thick cylinders, the circumferential stress:

does not vary along the thickness

is related to none of the other options

70 + Mcqs in Cylinder Pressure Vessels in Machine Design Page 2 McqOptions

51.	A thin cylindrical shell of diameter d and thickness t is subjected to an internal pressure P. The Poisson’s ratio is v. The ratio of longitudinal strain to volumetric strain is
A.	$\frac{{1 - v}}{{2 - v}}$
B.	$\frac{{2 - v}}{{1 - v}}$
C.	$\frac{{1 - 2v}}{{3 - 4v}}$
D.	$\frac{{1 - 2v}}{{5 - 4v}}$
Answer» E.

Discussion

52.	A thin cylinder of internal diameter 1 m and thickness 0.02 m contains a gas. The tensile stress in the material is not to exceed 100 MPa then determine the internal pressure of the gas
A.	10 N/mm2
B.	6 N/mm2
C.	8 N/mm2
D.	4 N/mm2
Answer» E.

Discussion

53.	Maximum shear stress at any point in a thin cylinder of diameter (d) and thickness (t) subjected to an internal fluid pressure (p) is given by-
A.	pd / 2t
B.	pd / 4t
C.	pd / 8t
D.	pd / 6t
Answer» D. pd / 6t

Discussion

54.	A closed thin walled tube has thickness, t, mean enclosed area within the boundary of the centerline of tube’s thickness, Am, and shear stress t. Torsional moment of resistance, T of the section would be
A.	2τAmt
B.	τAmtok
C.	0.5τAmt
D.	4τAmt
Answer» B. τAmtok

Discussion

55.	A thin cylinder contains fluid at a pressure of 30 kg/cm2. The inside diameter of the shell is 60 cm and the tensile stress in the material is to be limited to 900 kg/cm2. The shell must have minimum wall thickness of
A.	1 mm
B.	2.7 mm
C.	10 mm
D.	9 mm
Answer» D. 9 mm

Discussion

56.	If a thin-walled cylinder with closed hemispherical ends with thickness 12 mm and inside diameter of 1250 mm is to withstand a pressure of 1.5 MPa, then the maximum shear stress induced is
A.	19.5 MPa
B.	39.05 MPa
C.	78.12 MPa
D.	90.5 MPa
Answer» B. 39.05 MPa

Discussion

57.	A spherical vessel with an inside diameter of 2 m is made of a material having allowable stress in the tension of 500 kg/cm2. The thickness of a shell to withstand a pressure of 50 kg/cm2 should be
A.	5 cm
B.	2.5 cm
C.	10 cm
D.	1.25 cm
Answer» B. 2.5 cm

Discussion

58.	If ‘p’ is the pressure on the cylinder, ‘d’ and ‘t’ are the diameter and wall thickness, E is the Young’s Modulus and μ is the Poisson’s Ratio, the volumetric strain (εv ) in thin wall cylinder can be given by
A.	$\frac{{pd}}{{2tE}} \times \left( {5 - 4\mu} \right)$
B.	$\frac{{pd}}{{4tE}} \times \left( {5 - 4\mu} \right)$
C.	$\frac{{pd}}{{6tE}} \times \left( {5+ 4\mu} \right)$
D.	$\frac{{pd}}{{8tE}} \times \left( {5 - 4\mu} \right)$
Answer» C. $\frac{{pd}}{{6tE}} \times \left( {5+ 4\mu} \right)$

Discussion

59.	Internal and external radii of a thick cylinder are a and b. It is subjected to an internal pressure of pi. The radial stress at a radius r in the cylinder is
A.	$\frac{{{a^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{a^2}}}{{{r^2}}}} \right)$
B.	$\frac{{{a^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{b^2}}}{{{r^2}}}} \right)$
C.	$\frac{{{b^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{a^2}}}{{{r^2}}}} \right)$
D.	$\frac{{{b^2}{p_i}}}{{{b^2} - {a^2}}}\left( {1 - \frac{{{b^2}}}{{{r^2}}}} \right)$
Answer» C. $\frac{{{b^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{a^2}}}{{{r^2}}}} \right)$

Discussion

60.	In thick cylinders, the circumferential stress:
A.	is zero
B.	varies along the thickness
C.	does not vary along the thickness
D.	is maximum at the centre
E.	is related to none of the other options
Answer» C. does not vary along the thickness

Discussion

61.	A cast-iron pipe of 750 mm diameter is used to carry water under pressure of 0.5886 MPa. What should be the thickness of the pipe if the permissible stress is 20 MPa?
A.	1.104 mm
B.	11.04 mm
C.	1104 mm
D.	110.4 mm
Answer» C. 1104 mm

Discussion

62.	A cylindrical tank of internal diameter 10 m is fabricated from 10 mm thick steel plate. What is the maximum tangential stress due to internal pressure of 4 kPa?
A.	1 MPa
B.	4 MPa
C.	2 MPa
D.	0.5 MPa
Answer» D. 0.5 MPa

Discussion

63.	THE_PISTON_ROD_OF_A_HYDRAULIC_CYLINDER_EXERTS_AN_OPERATING_FORCE_OF_10KN._THE_ALLOWABLE_STRESS_IN_THE_CYLINDER_IS_45N/MM¬¨¬®‚ÄÖ√¢¬ß._CALCULATE_THE_THICKNESS_OF_THE_CYLINDER_USING_LAME‚ÄÖ√Ñ√∂‚ÀÖ√Ë‚ÀÖ¬•S_EQUATION._DIAMETER_OF_THE_CYLINDER_IS_40MM_AND_PRESSURE_IN_CYLINDER_IS_10MPA.?$#
A.	2.05mm
B.	4.2mm
C.	5.07mm
D.	None of the listed
Answer» D. None of the listed

Discussion

64.	The_piston_rod_of_a_hydraulic_cylinder_exerts_an_operating_force_of_10kN._The_allowable_stress_in_the_cylinder_is_70N/mm¬¨¬®‚Äö√¢¬ß._Calculate_the_thickness_of_the_cylinder_using_Clavarinoe‚Äö√Ñ√∂‚àö√ë‚àö¬•s_equation._Diameter_of_the_cylinder_is_240mm.‚âà√≠¬¨‚à´=0.3_and_pressure_in_cylinder_is_15MPa.$#
A.	35mm
B.	30mm
C.	27mm
D.	None of the listed
Answer» D. None of the listed

Discussion

65.	Lame‚Äö√Ñ√∂‚àö√ë‚àö¬•s equation is generally used for ductile materials?#
A.	True
B.	False
Answer» C.

Discussion

66.	Lame‚Äö√Ñ√∂‚àö√ë‚àö¬•s equation used to find the thickness of the cylinder is based on maximum strain failure.$
A.	True
B.	False
Answer» C.

Discussion

67.	Cylinder having inner diameter to wall thickness ratio less than 15 are
A.	Thin cylinders
B.	Thick Cylinders
C.	Moderate cylinders
D.	None of the listed
Answer» C. Moderate cylinders

Discussion

68.	A seamless cylinder of storage capacity of 0.03m¬¨‚àë¬¨¬µ‚àö‚Ä¢is subjected to an internal pressure of 21MPa. The ultimate strength of material of cylinder is 350N/mm¬¨¬®‚Äö√¢¬ß.Determine the length of the cylinder if it is twice the diameter of the cylinder.$
A.	540mm
B.	270mm
C.	400mm
D.	350mm
Answer» B. 270mm

Discussion

69.	Tangential stress in a cylinder is given by [symbols have their usual meanings].
A.	PD/2t
B.	2PD/t
C.	PD/4t
D.	4PD/t
Answer» B. 2PD/t

Discussion

70.	A cylinder is considered thin when the ratio of inner diameter to wall thickness is more than 5.
A.	True
B.	False
Answer» C.

Discussion

51.	A thin cylindrical shell of diameter d and thickness t is subjected to an internal pressure P. The Poisson’s ratio is v. The ratio of longitudinal strain to volumetric strain is
A.	\(\frac{{1 - v}}{{2 - v}}\)
B.	\(\frac{{2 - v}}{{1 - v}}\)
C.	\(\frac{{1 - 2v}}{{3 - 4v}}\)
D.	\(\frac{{1 - 2v}}{{5 - 4v}}\)
Answer» E.

58.	If ‘p’ is the pressure on the cylinder, ‘d’ and ‘t’ are the diameter and wall thickness, E is the Young’s Modulus and μ is the Poisson’s Ratio, the volumetric strain (εv ) in thin wall cylinder can be given by
A.	\(\frac{{pd}}{{2tE}} \times \left( {5 - 4\mu} \right)\)
B.	\(\frac{{pd}}{{4tE}} \times \left( {5 - 4\mu} \right)\)
C.	\(\frac{{pd}}{{6tE}} \times \left( {5+ 4\mu} \right)\)
D.	\(\frac{{pd}}{{8tE}} \times \left( {5 - 4\mu} \right)\)
Answer» C. \(\frac{{pd}}{{6tE}} \times \left( {5+ 4\mu} \right)\)

59.	Internal and external radii of a thick cylinder are a and b. It is subjected to an internal pressure of pi. The radial stress at a radius r in the cylinder is
A.	\(\frac{{{a^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{a^2}}}{{{r^2}}}} \right)\)
B.	\(\frac{{{a^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{b^2}}}{{{r^2}}}} \right)\)
C.	\(\frac{{{b^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{a^2}}}{{{r^2}}}} \right)\)
D.	\(\frac{{{b^2}{p_i}}}{{{b^2} - {a^2}}}\left( {1 - \frac{{{b^2}}}{{{r^2}}}} \right)\)
Answer» C. \(\frac{{{b^2}{p_i}}}{{\left( {{b^2} - {a^2}} \right)}}\left( {1 - \frac{{{a^2}}}{{{r^2}}}} \right)\)

Explore topic-wise MCQs in Machine Design.

A thin cylindrical shell of diameter d and thickness t is subjected to an internal pressure P. The Poisson’s ratio is v. The ratio of longitudinal strain to volumetric strain is

A thin cylinder of internal diameter 1 m and thickness 0.02 m contains a gas. The tensile stress in the material is not to exceed 100 MPa then determine the internal pressure of the gas

Maximum shear stress at any point in a thin cylinder of diameter (d) and thickness (t) subjected to an internal fluid pressure (p) is given by-

A closed thin walled tube has thickness, t, mean enclosed area within the boundary of the centerline of tube’s thickness, Am, and shear stress t. Torsional moment of resistance, T of the section would be

A thin cylinder contains fluid at a pressure of 30 kg/cm2. The inside diameter of the shell is 60 cm and the tensile stress in the material is to be limited to 900 kg/cm2. The shell must have minimum wall thickness of

If a thin-walled cylinder with closed hemispherical ends with thickness 12 mm and inside diameter of 1250 mm is to withstand a pressure of 1.5 MPa, then the maximum shear stress induced is

A spherical vessel with an inside diameter of 2 m is made of a material having allowable stress in the tension of 500 kg/cm2. The thickness of a shell to withstand a pressure of 50 kg/cm2 should be

If ‘p’ is the pressure on the cylinder, ‘d’ and ‘t’ are the diameter and wall thickness, E is the Young’s Modulus and μ is the Poisson’s Ratio, the volumetric strain (εv ) in thin wall cylinder can be given by

Internal and external radii of a thick cylinder are a and b. It is subjected to an internal pressure of pi. The radial stress at a radius r in the cylinder is

In thick cylinders, the circumferential stress:

A cast-iron pipe of 750 mm diameter is used to carry water under pressure of 0.5886 MPa. What should be the thickness of the pipe if the permissible stress is 20 MPa?

A cylindrical tank of internal diameter 10 m is fabricated from 10 mm thick steel plate. What is the maximum tangential stress due to internal pressure of 4 kPa?

Lame‚Äö√Ñ√∂‚àö√ë‚àö¬•s equation is generally used for ductile materials?#

Lame‚Äö√Ñ√∂‚àö√ë‚àö¬•s equation used to find the thickness of the cylinder is based on maximum strain failure.$

Cylinder having inner diameter to wall thickness ratio less than 15 are

A seamless cylinder of storage capacity of 0.03m¬¨‚àë¬¨¬µ‚àö‚Ä¢is subjected to an internal pressure of 21MPa. The ultimate strength of material of cylinder is 350N/mm¬¨¬®‚Äö√¢¬ß.Determine the length of the cylinder if it is twice the diameter of the cylinder.$

Tangential stress in a cylinder is given by [symbols have their usual meanings].

A cylinder is considered thin when the ratio of inner diameter to wall thickness is more than 5.