Page 424 - Introduction to Continuum Mechanics

408 irrotational, Barotropic Flows of Inviscid Compressible Fluid

This equation will be satisfied for all time if

and

In addition, we require the normal velocity be continuous at all time on x\ = 0, so that
ftoi]
—r~ , is also continuous. Thus, by using Eq. (6.27.4),
dt
\ ! Xl = o

Substituting for the pressure, we obtain

Combining Eqs. (vi) (vii) and (ix) we obtain

Note that for the special casep^i = p-f^

This productpc is referred to as the "fluid impedance". This result shows that if the impedances
match, there is no reflection.

6.28 Irrotational, Barotropic Flows of Inviscid Compressible Fluid

Consider an irrotational flow field given by