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Compressibility of a Fluid Equations and Calculator

Fluids Flow Design and Engineering
Heat Transfer Engineering
Thermodynamics

Compressibility of a Fluid Equations and Calculator

Compressibility (also known as the coefficient of compressibility), β, is the fractional change in the volume of a fluid per unit change in pressure in a constant temperature process. Typical units are in²/lbf, ft²/lbf, 1=atm, and 1/kPa. (See Table 1.) It is the reciprocal of the bulk modulus, a quantity that is more commonly tabulated than compressibility. Equation 1 is written with a negative sign to show that volume decreases as pressure increases.

Compressibility changes only slightly with temperature. The small compressibility of liquids is typically considered to be insignificant, giving rise to the common understanding that liquids are incompressible.

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Eq. 1
β = ( -ΔV / V_o ) / Δp

Eq. 2
β = 1 / E

Eq. 3
ΔV = V_f - V_o

Eq. 4
Δp = p_f - p_o

Where:

E = bulk modulus, lbf/ft², (Pa)
β = compressibility, ft²/lbf, (Pa^-1)
ΔV = Change of volume, ft³, (m³)
V_f = Volume final, ft³, (m³)
V_o = Volume compressed, ft³, (m³)
Δp = Change of pressure, lbf/ft², (Pa)
p_o = Pressure initial, lbf/ft², (Pa)
p_f = Pressure compressed, lbf/ft², (Pa)

Approximate Compressibilities of Common Liquids at 1 atm

Liquid	Temperature	β (in2/lbf)	β (1/atm)
mercury	32 °F	0.028 x 10-5	0.39 x 10-5
glycerin	60°F	0.160 x 10-5	0.16 x 10-5
water	60°F	0.330 x 10-5	0.33 x 10-5
ethyl alcohol	32 °F	0.680 x 10-5	0.68 x 10-5
chloroform	32 °F	0.680 x 10-5	0.68 x 10-5
gasoline	60°F	1.0 x 10-5	1.0 x 10-5
hydrogen	20K	11 x 10-5	11 x 10-5
helium	2.1K	48 x 10-5	48 x 10-5

(Multiply 1/psi by 14.696 to obtain 1/atm.)
(Multiply in²/lbf by 0.145 to obtain 1/kPa.)

Reference:

• Victor L. Streeter, Handbook of Fluid Dynamics, Ó 1961, by McGraw-Hill Book Company.
• Civil Engineering Reference Manual, Fifteenth Edition, Michael R. Lindeburg, PE

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