For a constant hydraulic stress on an object, fractional change in object’s volume (Delta

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9-1.Fluid Mechanics

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For a constant hydraulic stress on an object, the fractional change in the object’s volume $(\Delta V/V)$ and its bulk modulus $(B)$ are related as

A

$\frac{{\Delta V}}{V} \propto B$

B

$\frac{{\Delta V}}{V} \propto \frac{1}{B}$

C

$\frac{{\Delta V}}{V} \propto B^2$

D

$\frac{{\Delta V}}{V} \propto B^{-2}$

Solution

$\mathrm{B}=\frac{\text { Stress }}{\text { Volume strain }}=\frac{\text { Stress }}{\Delta \mathrm{V} / \mathrm{V}}$

$\frac{\Delta \mathrm{V}}{\mathrm{V}}=\frac{\text { Stress }}{\mathrm{B}}$

As stress is constant. So, $\frac{\Delta \mathrm{V}}{\mathrm{V}} \propto \frac{1}{\mathrm{B}}$

Standard 11

Physics

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