Question

the average depth of indian ocean is about 3000m.if the fractional compression of the water at the bottom of the ocean is 1.5%,find the comprssibility of water.

Answer 1

We know one thing
P = P₀ + ρgh
Where P₀ is the atmospheric pressure , g is acceleration due to gravity, h is the height from the Earth surface and ρ is density of water
Here, P₀ = 10⁵ N/m² , g = 10m/s² , h = 3000m and ρ = 10³ Kg/m³
Now, P = 10⁵ + 10³ × 10 × 3000 = 3.01 × 10⁷ N/m²

Again, we have to use formula,
B = P/{-∆V/V}
Here, B is bulk modulus and { -∆V/V} is the fractional compression
So, -∆V/V = P/B
Put , P = 3.01 × 10⁷ N/m² and B= 2.2 × 10⁹ N/m²
∴ fractional compression = 3.01 × 10⁷/2.2 × 10⁹ = 1.368 × 10⁻²

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