In this example we will look at the volume deformation of water. The bulk modulu

Question

In this example we will look at the volume deformation of water. The bulk modulus of water is 2.2×109Pa (=2.2×109N/m2). By how much does a cubic meter of water decrease in volume when it is taken from the surface of the ocean down to a depth of 1.0 km, where the pressure is 9.8×106Pa greater than at the surface?

SET UP AND SOLVE The bulk modulus is

B=pV/V0

We solve this equation for V:

V==pV0B=(9.8×106Pa)(1.0m3)(2.2×109N/m2)4.5×103m3=4500cm3

REFLECT The negative sign indicates that the volume has decreased while the pressure has increased. Although the pressure at a 1 km depth is roughly 100 times that at the surface, the fractional change in volume is only about 0.5%.

A fluid with an initial volume of 0.26 m3 is subjected to a pressure decrease of 4.3×103Pa. The volume is then found to have increased by 0.21 cm3 . What is the bulk modulus of the fluid?

Explanation / Answer

B = - dP*dV/V0

V0 = 0.26 m^3

dP= -(4.3*10^-3) Pa

dV = 0.21 cm^3 = +2.1*10^-7 m^3

B = -(-4.3*10^-3)*2.1*10^-7/0.26

B = 3.47*10^-9 N/m^2

Bulk modulus of fluid = 3.47*10^-9 N/m^2

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