## Thin Wall Cylinder

Consider an air cylinderâ€™s pressure gauge reads 2,000 kPa. If the cylinder is made of a 5 mm steel rolled plate, with an internal diameter of 600 mm, what is the tangential stress inside the tank?

##
__
__**Hint**

**Hint**

The cylinder can be considered thin-walled if:

$$$t< \frac{d_o}{20}$$$

where
$$t$$
is the wall thickness, and
$$d_o$$
is the outer diameter.

##
__
__**Hint 2**

**Hint 2**

$$$\sigma_t=\frac{P_ir}{t}$$$

where
$$\sigma_t$$
is the tangential (hoop) stress,
$$P_i$$
is the internal pressure,
$$r$$
is the mean radius, and
$$t$$
is the wall thickness.

The cylinder can be considered thin-walled if
$$t< \frac{d_o}{20}$$
where
$$t$$
is the wall thickness, and
$$d_o$$
is the outer diameter.

$$$t< \frac{(600mm+(2)5mm)}{20}=\frac{610mm}{20}=30.5mm$$$

Since
$$5mm< 30.5mm$$
, the cylinder is thin-walled. Thus, the hoop stress formula is:

$$$\sigma_t=\frac{P_ir}{t}$$$

where
$$\sigma_t$$
is the tangential (hoop) stress,
$$P_i$$
is the internal pressure,
$$r$$
is the mean radius, and
$$t$$
is the wall thickness.

$$$r=\frac{r_{inner}+r_{outer}}{2}=\frac{(600mm/2)+[(600mm/2)+5mm]}{2}$$$

$$$=\frac{300mm+305mm}{2}=302.5mm$$$

Thus, the tangential stress is:

$$$\sigma_t=\frac{(2MPa)(302.5mm)}{5mm}=121\:MPa$$$

121 MPa