Question

what is the value of bulk modulus for an incompressible liquid???

Answer 1

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Bulk Modulus = -dP / (dV/V) =

- VdP / dV

For incompressible fluid,

dV = 0

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Answer 2

The Bulk Modulus Elasticity can be calculated as

K = - dp / (dV / V0) 

   = - (p1 - p0) / ((V1 - V0) / V0)                      

where

K = Bulk Modulus of Elasticity (Pa, N/m^2)

dp = differential change in pressure on the object (Pa, N/m^2)

dV = differential change in volume of the object (m^3)

V0 = initial volume of the object  (m^3)

p0 = initial pressure (Pa, N/m^2)

p1 = final pressure (Pa, N/m^2)

V1 = final volume (m^3)

The Bulk Modulus Elasticity can alternatively be expressed or bulk modulus of incompressible liquid as

K = dp / (dρ / ρ0) 

   = (p1 - p0) / ((ρ1 - ρ0) / ρ0)                             

where

dρ = differential change in density of the object   (kg/m^3)

ρ0 = initial density of the object  (kg/m^3)

ρ1 = final density of the object (kg/m^3)

An increase in the pressure will decrease the volume . A decrease in the volume will increase the density.

A large Bulk Modulus indicates a relative incompressible fluid.