First slide

Pressure in a fluid-mechanical properties of fluids

Question

Find the elastic potential energy per unit volume of water (in x10³ Jm^-3) at a depth of 1 km. Given, compressibility of water = 5x10^-10 SI units and density of water = 1000 kg m^-3.

Moderate

Solution

$Energy per unit volume = \frac{1}{2} (stress)(strain)$
$\begin{array}{l} u = \frac{U}{V} = \frac{1}{2} (stress) (\frac{stress}{Bulk modulus}) \\ = \frac{1}{2} (ρ g h)^{2} (Compressibility) \\ = \frac{1}{2} (1000 \times 9.8 \times 1000)^{2} (5 \times 10^{- 10}) \\ = 2.4 \times 10^{4} {Jm}^{- 3} = 24 \times 10^{3} {Jm}^{- 3} \end{array}$

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