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

Q16  How much should the pressure on a litre of water be changed to compress it by 0.10%?

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Change in volume is \Delta V=0.10 \%

\\Volumetric\ Strain =\frac{0.1}{100}\\ \frac{\Delta V}{V}=0.001

Bulk modulus of water is B_{w}=2.2\times 10^{9}\ Nm^{-2}

\\B_{w}=\frac{P}{\frac{\Delta V}{V}}\\ P=\frac{\Delta V}{V}\times B_{w}\\ P=0.001\times 2.2\times 10^{9}\\ P=2.2\times 10^{6}Pa

A pressure of 2.2\times 10^{6}Pa is to be applied so that a litre of water compresses by 0.1%.

Note: The answer is independent of the volume of water taken into consideration. It only depends upon the percentage change.

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