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A reservoir of capacity 0.01 m3 is completely filled with a fluid of coefficient of compressibility 0.75 × 10-9 m2/N. The amount of fluid that will spill over (in m3), if pressure in the reservoir is reduced by 2 × 107 N/m2 is
1. 1 × 10-4
2. 1.5 × 10-4
3. 0.15 × 10-4
4. None of the above

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Correct Answer - Option 2 : 1.5 × 10-4

Concept:

In thermodynamics and Fluid Engineering, compressibility is a measure of the relative volume change of a fluid as a response to pressure (or mean stress) change.

Compressibility in Fluid Engineering is expressed as follows:

\(β=\frac{1}{K} = \frac{{ - 1}}{{\frac{{VdP}}{{dV}}}} = -\frac{{dV}}{{VdP}}\)

where, ∂p = change of pressure, ∂v = change in the volume

K = bulk modulus

(-ve) sign indicates, there is a decrease in volume due to an increase in pressure.

Calculation:

Given:

β = 0.75× 10-9 m2/N, V = 0.01 m3, dP = 2× 107 Pa

Compressibility (β) = \(\frac{1}{k} = \frac{{ - 1}}{{\frac{{VdP}}{{dV}}}} = \frac{{ - dV}}{{VdP}}\)

\(\left( β \right) = \frac{{ - dV}}{{VdP}}\)

\(0.75 × {10^{ - 9}} = - \frac{{ - dV}}{{0.01 × \left( { - 2 × {{10}^7}} \right)}}\)

dV = 1.5 × 10-4

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