# Question 2.SP.3: At a depth of 8 km in the ocean the pressure is 81.8 MPa. As......

At a depth of $8 \mathrm{~km}$ in the ocean the pressure is 81.8 MPa. Assume that the specific weight of seawater at the surface is $10.05 \mathrm{kN} / \mathrm{m}^{3}$ and that the average volume modulus is $2.34 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$ for that pressure range. (a) What will be the change in specific volume between that at the (c) What will be the specific weight at that depth?

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(a) Eq. (2.2): $\quad v_{1}=1 / p_{1}=g / \gamma_{1}=9.81 / 10050=0.000976 \mathrm{~m}^{3} / \mathrm{kg}$

Eq. (2.3 a):$\quad \Delta v=-0.000976\left(81.8 \times 10^{6}-0\right) /\left(2.34 \times 10^{9}\right)$

$=-34.1 \times 10^{-6} \mathrm{~m}^{3} / \mathrm{kg} \quad$

(b) Eq. (2.3b): $\quad v_{2}=v_{1}+\Delta v=0.000942 \mathrm{~m}^{3} / \mathrm{kg} \quad$

(c) $\gamma_{2}=g / v_{2}=9.81 / 0.000942=10410 \mathrm{~N} / \mathrm{m}^{3} \quad$

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