Internal Pressure
Consider a cylinder is made out of a 5 inch stainless steel rolled plate, with an internal diameter of 30 inches. If the tangential (hoop) stress is 1,000 psi, what is the cylinder’s internal pressure (psi)? Assume a thick walled cylinder.
Expand Hint
For internal pressure only, the stresses at the inside wall are:
$$$\sigma_t=P_i\frac{r_o^{2}+r_i^{2}}{r_o^{2}-r_i^{2}}$$$
where
$$P_i$$
is the internal pressure,
$$r_o$$
is the outside radius, and
$$r_i$$
is the inside radius.
Hint 2
Because this is a thick walled vessel, the stresses caused by the internal pressure on the inside wall is:
$$$\sigma_t=P_i\frac{r_o^{2}+r_i^{2}}{r_o^{2}-r_i^{2}}$$$
where
$$P_i$$
is the internal pressure,
$$r_o$$
is the outside radius, and
$$r_i$$
is the inside radius.
The radii are:
$$$r_o=\frac{30}{2}+5=20\:inches$$$
$$$r_i=\frac{30}{2}=15\:inches$$$
Solving for tangential stress:
$$$1,000\frac{lb}{in^2}=P_i\times \frac{20^{2}+15^{2}}{20^{2}-15^{2}}$$$
$$$1,000\frac{lb}{in^2}=P_i\times \frac{400+225}{400-225}=P_i\times \frac{625}{175}$$$
$$$P_i=1,000\frac{lb}{in^2}\times \frac{175}{625}=280\:psi$$$
280 psi
Time Analysis
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