The pressure on an object of bulk modulus B undergoing hydraulic compression due to a stress exerted by surrounding fluid having volume strain ((Δ V / V ))2 is

Question

The pressure on an object of bulk modulus B undergoing hydraulic compression due to a stress exerted by surrounding fluid having volume strain ((Δ V / V ))2 is (A) B 2((Δ V / V )) (B) B ((Δ V / V ))2 (C) (1/B)((Δ V/V)) (D) B ((Δ V / V ))

Tardigrade Admin · Accepted Answer

B =( text Normal stress / text Volume strain )=|( p /-((Δ V ) V ))|= mid-( pV /Δ V ) p = B (Δ V / V )= B ((Δ V / V ))

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

$B^{2} (\frac{Δ V}{V})$

$B (\frac{Δ V}{V})^{2}$

$\frac{1}{B} (\frac{Δ V}{V})$

$B (\frac{Δ V}{V})$

$B = \frac{Normal stress}{Volume strain} = ∣ ∣ \frac{p}{- ( \frac{Δ V}{V} )} ∣ ∣ =∣ - \frac{p V}{Δ V}$
$p = B \frac{Δ V}{V} = B (\frac{Δ V}{V})$

Q. The pressure on an object of bulk modulus B undergoing hydraulic compression due to a stress exerted by surrounding fluid having volume strain (VΔV​)2 is

B2(VΔV​)

B(VΔV​)2

B1​(VΔV​)

B(VΔV​)