Answer to Question #81113 in Mechanics | Relativity for AGUONYE KELVIN

Question

A bulk modulus of water is 2.1Gpa.compute the volume contraction of 100ml of water subjected to a pressure of 1.5MPa

Answer 1

Let’s recall the definition of the bulk modulus. The bulk modulus, K, is a material property characterizing the compressibility of the fluid. The bulk modulus can be calculated as follows:
K=-dp/(dV⁄V_0 ),
here, K=2.1 GPa is the bulk modulus of water, dp=1.5 MPa is the pressure change that is required in order to change the volume of water by dV, V_0=100 mL is the initial volume of water.
From this formula we can find the volume contraction dV:
dV=-V_0 dp/K=-100 mL∙(1.5∙〖10〗^6 Pa)/(2.1∙〖10〗^9 Pa)=-0.071 mL.
The sign minus indicates that an increase in pressure is accompanied by a decrease in volume.