Question

Compute the fractional change in volume of a glass slab, when subjected to a hydraulic pressure of 10 atm.

Answer 1

Given

• Hydraulic pressure applied: \( P = 10 \,\text{atm} \)
• Bulk modulus of glass: \( B = 37 \times 10^{9} \,\text{N m}^{-2} \)
• \( 1 \,\text{atm} = 1.013 \times 10^{5} \,\text{Pa} \)

1. Convert pressure to SI units

\( P = 10 \times 1.013 \times 10^{5} = 1.013 \times 10^{6} \,\text{Pa} \)

2. Use bulk modulus relation

Bulk modulus is defined as

\( B = -\,\dfrac{P}{\Delta V / V} \Rightarrow \dfrac{\Delta V}{V} = -\,\dfrac{P}{B} \)

3. Compute fractional change in volume

\( \dfrac{\Delta V}{V} = -\,\dfrac{1.013 \times 10^{6}}{37 \times 10^{9}} \approx -2.74 \times 10^{-5} \)

Fractional change in volume: \( \dfrac{\Delta V}{V} \approx -2.7 \times 10^{-5} \). (Negative sign indicates a decrease in volume.)