Changes in Dimensions of a Thin Cylinder

Q.

What is the difference between a thin cylinder and a thick cylinder?

Q. A thin cylindrical shell of internal diameter $D$ and thickness ${}^{\prime }{t}^{\prime }$ is subjected to internal pressure ${}^{\prime }{p}^{\prime }$. The change in diameter is given by

1. $\frac{p{D}^2}{4tE}(2-\mu )$
2. $\frac{p{D}^2}{4tE}(1-2\mu )$
3. $\frac{p{D}^2}{2tE}(1-2\mu )$
4. $\frac{p{D}^2}{2tE}(2-\mu )$

Q. A long thin walled cylindrical shell, closed at both the ends, is subjected to an internal pressure. The ratio of the hoop stress (circumferential stress) to longitudinal stress developed in the shell is

1. 1 : 2
2. 1 : 1
3. 2 : 1
4. 4 : 1

Q. A thin cylinder of 100 mm internal diameter and 5 mm thickness is subjected to an internal pressure of 10 MPa and a torque of 2000 Nm. Calculate the magnitudes of the principal stresses (in MPa)

1. 109.8, 45.2
2. 109.8, 40.2
3. 109.8, 31
4. 109.8, 50

Q. A thin cylindrical pressure vessel with closed- ends is subjected to internal pressure. The ratio of circumferential (hoop) stress to the longitudinal stress is

1. 0.25
2. 0.50
3. 1.0
4. 2.0

Q. A thin cylinder of thickness ${}^{\prime }{t}^{\prime }$, width ${}^{\prime }{b}^{\prime }$ and internal radius ${}^{\prime }{r}^{\prime }$ is subjected to a pressure ${}^{\prime }{p}^{\prime }$ on the entire internal surface. What is the change in radius of the cylinder? ($\mu$ is the Poisson's ratio and $E$ is the modulus of elasticity) ?

1. $\frac{p^{2}r(2-\mu )}{Et}$
2. $\frac{p{r}^2(2-\mu )}{Et}$
3. $\frac{p{r}^2(2-\mu )}{2Et}$
4. $\frac{p(1-\mu )}{Et{r}^2}$

Q. A cylindrical tank with closed ends is filled with compressed air at a pressure of 500 kPa. The inner radius of the tank is 2 m, and it has wall thickness of 10 mm. The magnitude of maximum in - plane shear stress (in MPa) is________

1. 25

Q. A thin gas cylinder with an internal radius of 100 mm is subject to an internal pressure of 10 MPa. The maximum permissible working stress is restricted to 100 MPa. The minimum cylinder wall thickness (in mm) for safe design must be ____

1. 10

Q.
A cylindrical container of radius $R=1m$, wall thickness $1mm$ is filled with water up to a depth of $2m$ and suspended along its upper rim. The density of water is $1000kg/m^3$ and acceleration due to gravity is $10m/s^2$. The self-weight of the cylinder is negligible. The formula for hoop stress in a thin-walled cylinder can be used at all points along the height of the cylindrical container.



If the Young's modulus and Poisson's ratio of the container material are 100 Gpa and 0.3 respectively, the axial strain in the cylinder wall at mid - depth is

1. $2\times {10}^{-5}$
2. $6\times {10}^{-5}$
3. $7\times {10}^{-5}$
4. $1.2\times {10}^{-4}$