Answer:
The pressure that the container will start to leak is 154.87 psi
Explanation:
Force on end plates F = p(πR²) ⇒ pπR²
There is an equal reaction from four bolts ∴ F = pπR² / 4 .............. (1)
due to force on bolt, each bolt stretch by [tex]\sigma_b[/tex]
Therefore; [tex]\sigma_b = \frac{F_bL}{A_bE_b}[/tex] .........................(2)
Leaking will start when tightening is outstretched by half turn per 16 turns per inch.
Cylinder experience a radial expansion as p increases. it is accompanied by poisson contraction [tex]\sigma_c[/tex] in axial direction. That is, the bolt do not have to experience a long stretch before the pressure breaks off the plate.
[tex]\sigma_b + \sigma_c = \frac{1}{2} *\frac{1}{16} = \frac{1}{32}[/tex] ...................... (3)
Axial deformation [tex]\sigma_c[/tex] of cylinder = L times axial ∈₀
see continuation in attached picture in writing to get the value of Pressure: since we have the value of P
R=8", L=16", t=0.125"
Area of bolts [tex]A_b = \frac{\pi}{4}(\frac{7}{16})^2 = 0.150 inch^2[/tex]
[tex]E_c = E_{cylinder} = 125[/tex]
[tex]E_b = E_{bolt} = 200[/tex]
V for brass = 0.3
[tex]P = \frac{1}{8*8*16} [\frac{0.150*12.5*200*0.125*10^9}{\pi*8*125*0.125+4*0.3*0.150*200}][/tex]
p = 1.67797.183 P ⇒ 154.87 psi
