Page 427 - Introduction to Continuum Mechanics

Newtonian Viscous Fluid 411

Since

therefore, from (iii)

Thus,

For small Mach number M, (i.e., v/c< < 1), we can use the binomial expansion to obtain from
the above equation

Noting that

we have, from (vi)

For small Mach number M, the above equation is approximately

which is the same as that for an incompressible fluid. In other words, for steady isentropic
flow, the fluid may be considered as incompressible if the Mach number is small (say < 0.3.)