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Question
Compute the fractional change in volume of a glass slab, when subjected to a hydraulic pressure of 10 atm.
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Solution 1
Hydraulic pressure exerted on the glass slab, p = 10 atm = 10 × 1.013 × 105 Pa
Bulk modulus of glass, B = 37 × 109 Nm–2
Bulk modulus, `B = p/(triangle V/V)`
Where `triangle V/V = p/B`
`=(10xx1.013xx10^5)/(37xx10^9)`
`=2.73 xx 10^(-5)`
Hence, the fractional change in the volume of the glass slab is 2.73 × 10–5.
Solution 2
P = 10 atm = 10 x 1.013 xx 105 Pa; `k = 37 xx 10^9 Nm^(-2)`
Volumetric strain = `(triangleV)/V = P/K = (10xx1.013xx10^5)/(37xx10^9) = 2.74 xx 10^(-5)`
:.Fractional change in volume = `(triangleV)/V = 2.74 xx 10^(-5)`
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