Question

he pressure of water at a depth of 10 km in the ocean is measured to be 100 MN/m2. The specific weight of the sea water at the surface is 10.2 kN/m3 while the average bulk modulus is 2.4 x 106 kN/m2. Calculate a) Change in specific volume (dV) between the volume at surface and at the 10 km depth. [4] b) The specific volume [3] c) Specific weight of the sea water at 10 km

Answer 1

solution: (a) change in specific volume can be well calculated using formula of bulk modulus which is given by:

B = P V / V

Where B is bulk modulus, v is specific volume, P is pressure and show the change in particulars.

pressure at the surface of sea water is always atmospheric pressure which is = 101.325 KN/m²

therefor P = 100000 - 101.325 = 99898.6 KN/m²

V = volume/ mass = density^-1 = 1/10.2 = 0.098 m³

now, V = P V / B = 99898.6 0.98 / 2.4 10⁶ = 0.0408 m³

(b) specific volume = volume / mass = density^-1 = 0.098 m³

(c) specific weight at 10 km depth is given by pressure formula, which is:

P = gh where g = specific weight

g = P/h = 100000 / 10000 = 10 KN/m²