Question 23.2: Design a thin cylindrical vessel to store pressure at 20 MPa......
Design a thin cylindrical vessel to store pressure at 20 MPa with a storage capacity of 0.05 m³ Take ultimate stress of vessel material as 400 MPa and factor of safety as 2.5. The length of the vessel may be limited to three times the diameter.
Given p_i=20 \mathrm{MPa}, V=0.05 \mathrm{~m}^3, l=3 D, \sigma_{u l t}=400 \mathrm{MPa}, N=2.5, \sigma_{\text {all }}=\text { allowable }
\text { stress }=\frac{400}{2.5}=160 \mathrm{~mm} .
Volume, V=\left(\frac{\pi}{4} D^2\right) l=\left(\frac{\pi}{4} D^2\right) \times 3 D
=\frac{3\pi}{4}D^3 (23.9)
D=\left(\frac{4}{3 \pi} V\right)^{1 / 3}=\left(\frac{4 \times .05}{3 \pi}\right)^{1 / 3}
=0.2768 \mathrm{~m}
=276.8 \mathrm{~mm}
Take D=280 \mathrm{~mm}
From Hoop’s stress criterion,
\sigma_{\theta \theta}=\frac{p_i D}{2 \sigma_t}=\frac{p_i D}{2\left(\sigma_{\mathrm{all}}\right)}
=\frac{20 \times 280}{2 \times 160}
=17.5 \mathrm{~N} / \mathrm{mm}^2
which is less than the allowable stress. Hence, the design is safe
D=280 \mathrm{~mm} \quad l=280 \times 3=840 \mathrm{~mm}