Question

The pressure on an object of bulk modulus B undergoing hydraulic compression due to a stress exerted by surrounding fluid having volume strain $\left(\frac{\Delta V }{ V }\right)^{2}$ is

• A. $B ^{2}\left(\frac{\Delta V }{ V }\right)$
• B. $B \left(\frac{\Delta V }{ V }\right)^{2}$
• C. $\frac{1}{B}\left(\frac{\Delta V}{V}\right)$
• D. $B \left(\frac{\Delta V }{ V }\right)$

Answer 1

Answer: (D)

$B =\frac{\text { Normal stress }}{\text { Volume strain }}=\left|\frac{ p }{-\left(\frac{\Delta V }{ V }\right)}\right|=\mid-\frac{ pV }{\Delta V }$
$p = B \frac{\Delta V }{ V }= B \left(\frac{\Delta V }{ V }\right)$