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Mechanical Properties Of Fluids

Question

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How much should the pressure on a litre of water be changed to compress it by 0.10%?

Solution

Volume of water, V = 1 L
It is given that water is to be compressed by 0.10%.
Therefore,
Fractional change, ∆V / V = 0.1 / (100 × 1) = 10^-3
Bulk modulus, B = ρ / (∆V/V)
$rightwards double arrow$ ρ = B × (∆V/V)
Bulk modulus of water, B = 2.2 × 10⁹ Nm^-2
ρ = 2.2 × 10⁹ × 10^-3 = 2.2 × 10⁶ Nm^-2
Therefore, the pressure on water should be 2.2 ×10⁶ Nm^–2.

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