fluid. The value of fluid bulk modulus shows how easily the volume of the fluid can be reduced
when the pressure acting on it is increased.
The bulk modulus of compressibility is formally defined as(10.29)
Equation (10.29) expressed mathematically is
(10.30)
where
EVmodulus of compressibility (N/m
2
)dPchange in pressure (increase in pressure) (N/m
2
)dVchange in volume (decrease in volume, negative value) ( m
3
)Voriginal volume ( m
3
)drchange in density (increase in density) (kg /m
3
)roriginal density (kg /m
3
)When the pressure is increased (a positive change in value), the volume of the fluid is
decreased (a negative change in value), and thus the need for a minus sign in front of the
dVterm to makeEVa positive value. In Equation (10.30), also note that when the pres-
sure is increased (a positive change in value), the density of the fluid is also increased (a pos-
itive change in value), and thus there is no need for a minus sign in front of thedrterm
to makeEVa positive value. The compressibility values for some common fluids are given
in Table 10.7.EV
dP
dV
V
dP
dr
r
EV
increase in pressure
decrease in volume
original volume
increase in pressure
increase in density
original density
10.6 Modulus of Elasticity, Modulus of Rigidity, and Bulk Modulus of Compressibility 289
TABLE 10.7 The Values of Compressibility Modulus
for Some Common FluidsCompressibility Compressibility
Fluid Modulus (N/m2
) Modulus (lbf/in
2
)
Ethyl alcohol 1.06 10
9
1.54 10
5
Gasoline 1.3 10
9
1.9 10
5
Glycerin 4.52 10
9
6.56 10
5
Mercury 2.85 10
10
4.14 10
6
SAE 30 oil 1.5 10
9
2.2 10
5
Water 2.24 10
9
3.25 10
5
62080_10_ch10_p251-302.qxd 5/22/10 12:32 AM Page 289
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