Example 1.6 At a great depth in the ocean, the pressure is 80 MPa. Assume that specific weight at the surface is 10 KN/m and the average bulk modulus of elasticity is 2.34 GPa .
Find change in specific volume at that depth.

Explanation:

The bulk modulus K is given by

K = -V (dP/dV)

Substituting dP = 82.26 MPa (and assuming this is the water pressure only)

and K = 2344 MPa, we have

(a) dV/V = - 82.26/2344 = -3.5%

(b) If the specific weight at the surface is 10.10 kN/m^3,

and if g = 9.81 m/s^2, then the density at the surface is

10100 N/m^3 divided by 9.81 m/s^2 = 1029.6 kg/m^3,

so the specific volume at the surface would be 1/1029.6 = 0.0009713 m^3/kg

or 0.9713 cm^3/g

So the specific volume at 8 km depth would be

0.9713 cm^3/g diminished by 3.5%, which comes out to 0.9373 cm^3/g.

This ignores the likely effects of the water at 8 km being much colder.

(c) The specific weight at 8 km will be 3.5% greater than at the surface,

again ignoring thermal effects. So the specific weight at 8 km would be 10.45 kN/m^3

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