Question

The UTS for the small diameter pipe​

Answer 1

well, if we look at the ring, the outer circle has a diameter of 3, that means its radius is half that or 1.5 or namely 3/2.

the radius of the inner circle will be that of the outer minus 1/8, namely 3/2 - 1/8 is the inner radius, or that is 11/8.

$\textit{area of a circular ring}\\\\ A=\pi (R^2-r^2)~~ \begin{cases} R=\stackrel{larger}{radius}\\ r=\stackrel{smaller}{radius}\\[-0.5em] \hrulefill\\ R=\frac{3}{2}\\[1em] r=\frac{11}{8} \end{cases}\implies A=\pi \left[ \left( \cfrac{3}{2} \right)^2~~ - ~~\left( \cfrac{11}{8} \right)^2 \right]$

$A=\pi \left(\cfrac{9}{4}-\cfrac{121}{64} \right)\implies A=\pi \left( \cfrac{23}{64} \right) \implies A=\cfrac{23\pi }{64}~in^2 \\\\[-0.35em] ~\dotfill\\\\ UTS=\cfrac{17364}{~~ \frac{23\pi }{64}~~}\implies UTS=\cfrac{1111296}{23\pi }\implies UTS\approx 15380$