The

*volume velocity* of a gas flow is defined as particle
velocity

times the

cross-sectional area of the flow, or

where

denotes position along the flow, and

denotes time in
seconds. Volume velocity is thus in physical units of volume per
second (m

/s).
When a flow is confined within an enclosed channel, as it is in an
acoustic tube,

*volume velocity is conserved* when the tube
changes cross-sectional area, assuming the density

remains
constant. This follows directly from conservation of

mass in a flow:
The total mass passing a given point

along the flow is given by
the mass density

times the integral of the volume volume
velocity at that point, or

As a simple example, consider a constant flow through two cylindrical
acoustic tube sections having cross-sectional areas

and

,
respectively. If the particle velocity in cylinder 1 is

, then
the particle velocity in cylinder 2 may be found by solving

for

.
It is common in the field of acoustics to denote volume velocity by an
upper-case

. Thus, for the two-cylinder acoustic tube example above,
we would define

and

, so that

would express the conservation of volume velocity from one tube
segment to the next.

**Next Section:** Pressure is Confined Kinetic Energy**Previous Section:** Particle Velocity of a Gas