Estimate the change in the density of water in ocean at a depth of 400 m below the surface. The density of water at the surface = 1030 kg/m^3
Estimate the change in the density of water in ocean at a depth of 400 m below the surface. The density of water at the surface = 1030 kg/m3 and the bulk modulus of water = 2x109 N/m2.
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At a depth x m below the surface the pressure P =ρgx
Bulk strain = P/B =ρgx/B
→ΔV/V =ρgx/B
→ΔV = ρgxV/B
Density at x m below the surface, ρ'= ρV/V'
{V' is the compressed volume V, V' =V-ΔV}
=ρV/(V-ρgxV/B) =ρB/(B-ρgx)
=1030*2x10⁹/(2x10⁹ - 1030*10*400) =2.06x10¹²/1.9958x10⁹
=1032 kg/m³ {Putting x=400 m}
The change in density, dρ =ρ'-ρ =1032-1030 = 2 kg/m³
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