Page 420 - Introduction to Continuum Mechanics

404 Acoustic Wave

where y = c p/c v, the ratio of specific heat under constant pressure and constant volume.
Solution, (a) Since the flow is steady, therefore, dp/dt = 0. Since the fluid is inviscid and
non-heat conducting, therefore Ty '= 0 and<?/ = 0. Thus, the energy equation (6.26.2) reduces
to

In other words, h 0 is a constant for each particle. But since the flow originates from a
homogeneous state, therefore

in the whole flow field.
(b) For an ideal gasp = pR®, u = c vQ, and R - c p-c v, therefore

where

and

6.27 Acoustic Wave

The propagation of sound can be approximated by considering the propagation of in-
finitesimal disturbances in a compressible inviscid fluid. For an inviscid fluid, neglecting body
forces, the equations of motion are

Let us suppose that the fluid is initially at rest with