Answer to Question #218935 in Mechanical Engineering for Jeff

Question

A vessel in the shape of a spherical shell 758 mm in diameter, 18 mm shell thickness is completely filled with a
Fluid at atmospheric pressure. Additional fluid is then pumped in till the pressure increases by 7 N/mm. Find the volume of this additional fluid given that 1/m=0.25 and
E=2.1X 10

Answer 1

$d = 758 mm$

$t = 18 mm$

$p = 7 \frac{N}{mm}$

$E = 2.1 \times 10^ 5 \frac{N}{mm}$

$\mu = 0.25$

Change in diameter $(\delta d)$ :

$\delta d = \frac{pd^2}{4tE}[1-\frac{1}{m}]$

$\delta d = \frac{7\times 758^2}{4\times 18\times 2.1\times 10^5}[1-0.25]=0.1995 mm$

Change in volume (δv)

$e_v = 3\times \frac{\delta d}{d}$

$V = \frac{\pi}{6}\times d^3 = \frac{\pi}{6}\times 758^2 =300841mm^3$

$\frac{\delta v}{v} = 3\times \frac{\delta d}{d}$

$\delta d =3 \times 300814 \times \frac{0.1995}{758} =237.51 mm^3$