Question #218935
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
1
Expert's answer
2021-07-20T21:27:01-0400

d=758mmd = 758 mm


t=18mmt = 18 mm


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


E=2.1×105NmmE = 2.1 \times 10^ 5 \frac{N}{mm}


μ=0.25\mu = 0.25


Change in diameter (δd)(\delta d) :


δd=pd24tE[11m]\delta d = \frac{pd^2}{4tE}[1-\frac{1}{m}]


δd=7×75824×18×2.1×105[10.25]=0.1995mm\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)


ev=3×δdde_v = 3\times \frac{\delta d}{d}


V=π6×d3=π6×7582=300841mm3V = \frac{\pi}{6}\times d^3 = \frac{\pi}{6}\times 758^2 =300841mm^3


δvv=3×δdd\frac{\delta v}{v} = 3\times \frac{\delta d}{d}


δd=3×300814×0.1995758=237.51mm3\delta d =3 \times 300814 \times \frac{0.1995}{758} =237.51 mm^3




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