Question

Determine the pressure required to reduce the given volume of water by 2%. Bulk modulus of water is 2.2 × 10⁹ N m⁻².

Answer 1

Given, % change in volume = 2 %

we know, % change in volume = change in volume /original volume × 100
= ∆v/v × 100

so, ∆v/v × 100 = 2

or, ∆v/v = 2/100 = 0.02

Bulk modulus of water, $\beta$ = 2.2 × 10^9 N/m²

Now, bulk modulus, $\beta=\frac{P}{\frac{\Delta v}{v}}$

or, 2.2 × 10^9 = P/0.02

P = 2.2 × 10^9 × 0.02 = 4.4 × 10^7 N/m²

Hence, pressure required = 4.4 × 10^7 N/m²

Answer 2

Explanation:

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