Compressibility of Fluids

Key Concepts: Fluids fall into two general categories – liquids and gases. In generally liquids

(i.e. water) are treated as incompressible fluids whereas gases (i.e. air) are compressible fluids.

In a Nut Shell: A property used to characterize compressibility of a fluid is bulk modulus, E_V . For gases a change in pressure results in a change in volume giving rise to the definition of bulk modulus.

E_V = - dp / (dV/V)

Or in terms of density

E_V = dp / (dρ/ρ)

The table below list dimensions and common units.

Quantity Dimensions Common Units

EV Bulk Modulus	F/L^2	lb/in^2, lb/ft^2, N/m^2
dp Change in Pressure	F/L^2	lb/in^2, lb/ft^2, N/m^2
V Volume or dV Change in volume	L^3	in^3, ft^3, mm^3, m^3
ρ density or dρ Change in density	M / L^3	Slugs/ ft^3 , kg / m^3

The “ideal” gas law is: P = ρ R T (relates pressure to density and temperature)

P = absolute pressure, ρ = density, R = gas constant (a property depending on gas)

T = absolute temperature Note: R = 1716 ft lb/slug ^oR for air

For a isothermal process P / ρ = constant. For an isentropic process P / ρ^K = constant

where K is the ratio of specific heats of the gas K = C_P / C_V

Click here for examples.

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Copyright © 2019 Richard C. Coddington
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