Answer to Question #226480 in Mechanical Engineering for Aboody

Question

1.    Eight kilometers below the surface of the ocean the pressure is 82Mpa. Determine the density of the seawater at this depth if the density at the surface is 1025kg/m³ and the average bulk modulus of elasticity is 2.3GPa.

Answer 1

Pressure 8km below the surface:

P₂=$h\rho g$

=8000*9.81*1025=80.44*10⁶N/m²

$\beta=\frac{∆pV}{∆V}$

$\frac{∆p}{\beta}=\frac{∆V}{V}=1-\frac{\rho}{\rho'}$

$\rho'=\frac{\rho}{1-\frac{∆p}{\beta}}$

∆p=82*10⁶-80.44*10⁶=1.56*10⁶

$\rho'=\frac{1025}{1-\frac{1.56*10^{6}}{2.3*10^{9}}}$

$=\frac{1025}{1-6.7826*10^{-4}}$

$=\frac{1025}{0.9993}$

$=1025.72kg/m^{3}$