Find the increase in pressure required to decrease the volume of a water sample by 0.01%. Bulk modulus of water = 2.1 x 10^9 N/m^2.
Find the increase in pressure required to decrease the volume of a water sample by 0.01%. Bulk modulus of water = 2.1 x 109 N/m2.
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Let the original volume =V when the pressure = 0. At a certain pressure P, the volume is V'.
Change in volume = -(V-V'),
Bulk strain = -(V-V')/V
Bulk modulus = B =2.1x10⁹ N/m²
Henve P = -B(V-V')/V = -B(1-V'/V) ......... (i)
→dP = B.dV'/V But given dV'/V' = 0.01/100
Increase in Bulk stress = pressure increase
=dP = B.(dV'/V')*(V'/V)
=2.1x10⁹(0.01/100)*1 N/m² =2.1x10⁵ N/m² (Taking V'/V ≈ 1)
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